{"title":"Mathematical logic","description":"Books on the subject of Mathematical logic","products":[{"product_id":"burden-of-proof-presumption-and-argumentation-hardback-9781107046627","title":"Burden of Proof, Presumption and Argumentation (Hardback) 9781107046627","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eBurden of Proof, Presumption and Argumentation\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book explains how burden of proof and presumption work as powerful devices in argumentation, based on studying many clearly explained legal and non-legal examples.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDouglas Walton (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107046627, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 June 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e318 pages, 52 b\/w illus.\u003cbr\u003e23.5 x 15.6 x 2.1 cm, 0.56 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'Walton's intellectual tour de force brings together argumentation theory, AI and law to provide a framework within which this most difficult but also highly important issue of argumentation can be addressed.' Burkhard Schafer, University of Edinburgh\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe notion of burden of proof and its companion notion of presumption are central to argumentation studies. This book argues that we can learn a lot from how the courts have developed procedures over the years for allocating and reasoning with presumptions and burdens of proof, and from how artificial intelligence has built precise formal and computational systems to represent this kind of reasoning. The book provides a model of reasoning with burden of proof and presumption, based on analyses of many clearly explained legal and non-legal examples. The model is shown to fit cases of everyday conversational argumentation as well as argumentation in legal cases. Burden of proof determines (1) under what conditions an arguer is obliged to support a claim with an argument that backs it up and (2) how strong that argument needs to be to prove the claim in question.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Introduction to basic concepts\u003cbr\u003e 2. Burdens of proof in legal reasoning\u003cbr\u003e 3. Presumption in legal reasoning\u003cbr\u003e 4. Shifting of the burden of proof in witness testimony\u003cbr\u003e 5. Burden of proof in dialogue systems\u003cbr\u003e 6. Solving the problems of burden of proof\u003cbr\u003e 7. Burdens of proof in different types of dialogue\u003cbr\u003e 8. Burdens of proof in everyday conversational arguments.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Jurisprudence \u0026amp; philosophy of law [\u003ca title=\"See our other books on Jurisprudence \u0026amp; philosophy of law\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Jurisprudence%20\u0026amp;%20philosophy%20of%20law%20%5BLAB%5D%22\"\u003eLAB\u003c\/a\u003e], Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\u003c\/a\u003e], Analytical philosophy \u0026amp; Logical Positivism [\u003ca title=\"See our other books on Analytical philosophy \u0026amp; Logical Positivism\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Analytical%20philosophy%20\u0026amp;%20Logical%20Positivism%20%5BHPCF5%5D%22\"\u003eHPCF5\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006031712536,"sku":"9781107046627","price":56.39,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107046627i_9e27a3bf-ab3b-4a3d-9d7c-e418bd377b2e.jpg?v=1691361601"},{"product_id":"logic-colloquium-2006-hardback-9780521110815","title":"Logic Colloquium 2006 (Hardback) 9780521110815","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLogic Colloquium 2006\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThe 2006 proceedings from the Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eS. Barry Cooper (Edited by), Herman Geuvers (Edited by), Anand Pillay (Edited by), Jouko Väänänen (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521110815, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 7 September 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e384 pages\u003cbr\u003e23.5 x 15.8 x 2.5 cm, 0.63 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. The most topical areas of current research are covered: valued fields, Hrushovski constructions (from model theory), algorithmic randomness, relative computability (from computability theory), strong forcing axioms and cardinal arithmetic, large cardinals and determinacy (from set theory), as well as foundational topics such as algebraic set theory, reverse mathematics, and unprovability. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Definability and elementary equivalence in the Ershov difference hierarchy Marat M. Arslanov\u003cbr\u003e 2. A unified approach to algebraic set theory Benno van den Berg and Leke Moerdijk\u003cbr\u003e 3. Brief introduction to unprovability Andrey Bovykin\u003cbr\u003e 4. Higher-order abstract syntax in type theory Venanzio Capretta and Amy P. Felty\u003cbr\u003e 5. An introduction to b-minimality Raf Cluckers\u003cbr\u003e 6. The sixth lecture on algorithmic randomness Rod Downey\u003cbr\u003e 7. The inevitability of logical strength: strict reverse mathematics Harvey M. Friedman\u003cbr\u003e 8. Applications of logic in algebra: examples from clone theory\u003cbr\u003e 9. On infinite imaginaries Ehud Hrushovski\u003cbr\u003e 10. Strong minimal covers and a question of Yates: the story so far Andrew E. M. Lewis\u003cbr\u003e 11. Embeddings into the Turing degrees Antonio Montalban\u003cbr\u003e 12. Randomness - beyond Lebesgue measure Jan Reimann\u003cbr\u003e 13. The derived model theorem J. R. Steel\u003cbr\u003e 14. Forcing axioms and cardinal arithmetic Boban Velivckovic\u003cbr\u003e 15. Hrushovski's amalgamation construction Frank O. Wagner.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46006480863512,"sku":"9780521110815","price":98.39,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521110815i_170a1c0a-b723-40b0-b60e-6547f894821d.jpg?v=1691371185"},{"product_id":"elements-of-set-theory-hardback-9780122384400","title":"Elements of Set Theory (Hardback) 9780122384400","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eElements of Set Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eHerbert B. Enderton (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780122384400, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 23 May 1977\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e296 pages\u003cbr\u003e22.9 x 15.1 x 2.3 cm, 0.53 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eContents\u003cbr\u003ePreface \u003cbr\u003eList of Symbols \u003cbr\u003eChapter 1 Introduction \u003cbr\u003e     Baby Set Theory \u003cbr\u003e     Sets—An Informal View\u003cbr\u003e     Classes\u003cbr\u003e     Axiomatic Method \u003cbr\u003e     Notation \u003cbr\u003e     Historical Notes \u003cbr\u003eChapter 2 Axioms and Operations\u003cbr\u003e     Axioms \u003cbr\u003e     Arbitrary Unions and Intersections \u003cbr\u003e     Algebra of Sets \u003cbr\u003e     Epilogue \u003cbr\u003e     Review Exercises \u003cbr\u003eChapter 3 Relations and Functions\u003cbr\u003e     Ordered Pairs\u003cbr\u003e     Relations \u003cbr\u003e     n-Ary Relations \u003cbr\u003e     Functions \u003cbr\u003e     Infinite Cartesian Products\u003cbr\u003e     Equivalence Relations \u003cbr\u003e     Ordering Relations \u003cbr\u003e     Review Exercises \u003cbr\u003eChapter 4 Natural Numbers \u003cbr\u003e     Inductive Sets \u003cbr\u003e     Peano's Postulates \u003cbr\u003e     Recursion on ? \u003cbr\u003e     Arithmetic \u003cbr\u003e     Ordering on ?\u003cbr\u003e     Review Exercises \u003cbr\u003eChapter 5 Construction of the Real Numbers\u003cbr\u003e     Integers \u003cbr\u003e     Rational Numbers \u003cbr\u003e     Real Numbers \u003cbr\u003e     Summaries \u003cbr\u003e     Two \u003cbr\u003eChapter 6 Cardinal Numbers and the Axiom of Choice\u003cbr\u003e     Equinumerosity \u003cbr\u003e     Finite Sets \u003cbr\u003e     Cardinal Arithmetic \u003cbr\u003e     Ordering Cardinal Numbers \u003cbr\u003e     Axiom of Choice \u003cbr\u003e     Countable Sets \u003cbr\u003e     Arithmetic of Infinite Cardinals \u003cbr\u003e     Continuum Hypothesis \u003cbr\u003eChapter 7 Orderings and Ordinals\u003cbr\u003e     Partial Orderings \u003cbr\u003e     Well Orderings \u003cbr\u003e     Replacement Axioms \u003cbr\u003e     Epsilon-Images \u003cbr\u003e     Isomorphisms \u003cbr\u003e     Ordinal Numbers \u003cbr\u003e     Debts Paid \u003cbr\u003e     Rank \u003cbr\u003eChapter 8 Ordinals and Order Types\u003cbr\u003e     Transfinite Recursion Again \u003cbr\u003e     Alephs \u003cbr\u003e     Ordinal Operations \u003cbr\u003e     Isomorphism Types \u003cbr\u003e     Arithmetic of Order Types \u003cbr\u003e     Ordinal Arithmetic \u003cbr\u003eChapter 9 Special Topics\u003cbr\u003e     Well-Founded Relations\u003cbr\u003e     Natural Models \u003cbr\u003e     Cofinality \u003cbr\u003eAppendix Notation, Logic, and Proofs \u003cbr\u003eSelected References for Further Study\u003cbr\u003eList of Axioms\u003cbr\u003eIndex\u003cbr\u003e\u003cbr\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46648082825496,"sku":"9780122384400","price":46.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780122384400_f4afb8fe-e455-42ca-ade4-851acce2bbda.jpg?v=1695006725"},{"product_id":"numbers-and-proofs-paperback-9780340676530","title":"Numbers and Proofs (Paperback \/ softback) 9780340676530","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eNumbers and Proofs\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eReg Allenby (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780340676530, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 26 September 1997\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e288 pages, Illustrated\u003cbr\u003e24.4 x 17.1 x 1.9 cm, 0.54 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow.\u003cbr\u003e Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up \"truths\" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eThe need for proof * Statements and connectives * True or false? * Sets, negations, notations and functions * Proofs....for all * There exists....proofs * The principle of mathematical induction * The integers and rational numbers * The rational numbers and the real numbers * Real numbers and complex numbers * Guessing, analogy and transformation * Generalisation and specialisation * Fallacies and paradoxes * A mixed bag * Solutions appendix * Answers to exercises * References.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Butterworth-Heinemann","offers":[{"title":"Default Title","offer_id":46648110285080,"sku":"9780340676530","price":37.68,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780340676530_5afb79dc-0992-4982-af74-b1fc8fdc0e0a.jpg?v=1694976419"},{"product_id":"computability-complexity-and-languages-fundamentals-of-theoretical-computer-science-hardback-9780122063824","title":"Computability, Complexity, and Languages; Fundamentals of Theoretical Computer Science (Hardback) 9780122063824","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eComputability, Complexity, and Languages\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eFundamentals of Theoretical Computer Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eMartin Davis (Author), Ron Sigal (Author), Elaine J. Weyuker (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780122063824, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 18 March 1994\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e609 pages\u003cbr\u003e22.9 x 15.1 x 3.4 cm, 0.97 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"If there is a single book on the theory of computing that should be in every college library collection, this is it. Although written as a text for an advanced undergraduate course in theoretical computer science, the book may serve as an introductory resource, or the foundation for independent study, in many areas of theoretical computing: grammars, automata theory, computability, complexity theory, and unsolvability. The beauty of this book is that the breadth of coverage is complemented with extraordinary depth.\"\u003cb\u003e --CHOICE\u003cbr\u003e\u003c\/b\u003e\u003cbr\u003e\"Theoretical computer science is often viewed as a collection of disparate topics, including computability theory, formal language theory, complexity theory, logic, and so on. This well-written book attempts to unify the subject by introducing each of these topics in turn, then showing how they relate to each other... This is an excellent book that succeeds in tying together a number of areas in theoretical computer science.\" \u003cb\u003e--COMPUTING REVIEWS\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eComputability, Complexity, and Languages\u003c\/i\u003e is an introductory text that covers the key areas of computer science, including recursive function theory, formal languages, and automata. It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreliminaries. \u003cb\u003eComputability:\u003c\/b\u003e Programs and Computable Functions. Primitive Recursive Functions. A Universal Program. Calculations on Strings. Turing Machines. Processes and Grammars. Classifying Unsolvable Problems. \u003cb\u003eGrammars and Automata:\u003c\/b\u003e Regular Languages. Context-Free Languages. Context-Sensitive Languages. \u003cb\u003eLogic:\u003c\/b\u003e Propositional Calculus. Quantification Theory. \u003cb\u003eComplexity:\u003c\/b\u003e Abstract Complexity. Polynomial?Time Computability. \u003cb\u003eSemantics:\u003c\/b\u003e Approximation Orderings. Denotational Semantics of Recursion Equations. Operational Semantics of Recursion Equations. Suggestions for Further Reading. Subject Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Algorithms \u0026amp; data structures [\u003ca title=\"See our other books on Algorithms \u0026amp; data structures\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algorithms%20\u0026amp;%20data%20structures%20%5BUMB%5D%22\"\u003eUMB\u003c\/a\u003e], Applied mathematics [\u003ca title=\"See our other books on Applied mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Applied%20mathematics%20%5BPBW%5D%22\"\u003ePBW\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Morgan Kaufmann","offers":[{"title":"Default Title","offer_id":46648130208024,"sku":"9780122063824","price":46.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780122063824_2ec9f293-a7cf-4a3d-8d8a-e308c1425004.jpg?v=1695006719"},{"product_id":"a-course-in-mathematical-logic-hardback-9780720428445","title":"A Course in Mathematical Logic (Hardback) 9780720428445","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Course in Mathematical Logic\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eJ.L. Bell (Author), M. Machover (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780720428445, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 January 1977\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e620 pages\u003cbr\u003e23.4 x 15.6 x 3.4 cm, 1.12 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The book is valuable for anyone interested in mathematical logic and may serve as a reference source for graduate students and specialists.\" \u003cb\u003e--Zentralblatt für Mathematik\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eA comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.\u003cbr\u003e\u003cbr\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cb\u003e1.\u003c\/b\u003e Beginning Mathematical Logic. \u003cb\u003e2.\u003c\/b\u003e First-Order Logic. \u003cb\u003e3.\u003c\/b\u003e First-Order Logic (continued). \u003cb\u003e4.\u003c\/b\u003e Boolean Algebras. \u003cb\u003e5.\u003c\/b\u003e Model Theory. \u003cb\u003e6.\u003c\/b\u003e Recursion Theory. \u003cb\u003e7.\u003c\/b\u003e Logic - Limitative Results. \u003cb\u003e8.\u003c\/b\u003e Recursion Theory (continued). \u003cb\u003e9.\u003c\/b\u003e Intuitionistic First-Order Logic. \u003cb\u003e10. \u003c\/b\u003eAxiomatic Set Theory. \u003cb\u003e11.\u003c\/b\u003e Nonstandard Analysis. Bibliography.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648313348376,"sku":"9780720428445","price":46.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780720428445.jpg?v=1694090552"},{"product_id":"genetic-programming-an-introduction-hardback-9781558605107","title":"Genetic Programming; An Introduction (Hardback) 9781558605107","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eGenetic Programming\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eWolfgang Banzhaf (Author), Peter Nordin (Author), Robert E. Keller (Author), Frank D. Francone (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781558605107, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 February 1998\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e496 pages\u003cbr\u003e24.4 x 17.5 x 3 cm, 0.99 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"[The authors] have performed a remarkable double service with this excellent book on genetic programming. First, they give an up-to-date view of the rapidly growing field of automatic creation of computer programs by means of evolution and, second, they bring together their own innovative and formidable work on evolution of assembly language machine code and linear genomes.\" \u003cb\u003e--John R. Koza\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eSince the early 1990s, genetic programming (GP)—a discipline whose goal is to enable the automatic generation of computer programs—has emerged as one of the most promising paradigms for fast, productive software development.   GP combines biological metaphors gleaned from Darwin's theory of evolution with computer-science approaches drawn from the field of machine learning to create programs that are capable of adapting or recreating themselves for open-ended tasks.This unique introduction to GP provides a detailed overview of the subject and its antecedents, with extensive references to the published and online literature.  In addition to explaining the fundamental theory and important algorithms, the text includes practical discussions covering a wealth of potential applications and real-world implementation techniques.  Software professionals needing to understand and apply GP concepts will find this book an invaluable practical and theoretical guide.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1  Genetic Programming as Machine Learning\u003cbr\u003e2  Genetic Programming and Biology\u003cbr\u003e3  Computer Science and Mathematical Basics\u003cbr\u003e4  Genetic Programming as Evolutionary Computation\u003cbr\u003e5  Basic Concepts—The Foundation\u003cbr\u003e6  Crossover—The Center of the Storm\u003cbr\u003e7  Genetic Programming and Emergent Order\u003cbr\u003e8  Analysis—Improving Genetic Programming with Statistics\u003cbr\u003e9  Different Varieties of Genetic Programming\u003cbr\u003e10  Advanced Genetic Programming\u003cbr\u003e11  Implementation—Making Genetic Programming Work\u003cbr\u003e12  Applications of Genetic Programming\u003cbr\u003e13  Summary and Perspectives\u003cbr\u003eA  Printed and Recorded Resources\u003cbr\u003eB  Information Available on the Internet\u003cbr\u003eC  GP Software \u003cbr\u003eD  Events\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Machine learning [\u003ca title=\"See our other books on Machine learning\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Machine%20learning%20%5BUYQM%5D%22\"\u003eUYQM\u003c\/a\u003e], Computer programming \/ software development [\u003ca title=\"See our other books on Computer programming \/ software development\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20programming%20\/%20software%20development%20%5BUM%5D%22\"\u003eUM\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Morgan Kaufmann","offers":[{"title":"Default Title","offer_id":46648483381528,"sku":"9781558605107","price":74.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781558605107.jpg?v=1694588812"},{"product_id":"constructivism-in-mathematics-vol-2-hardback-9780444703583","title":"Constructivism in Mathematics, Vol 2 (Hardback) 9780444703583","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eConstructivism in Mathematics, Vol 2\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eA.S. Troelstra (Author), D. van Dalen (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444703583, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 November 1988\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e140 pages\u003cbr\u003e23.3 x 15.6 x 1.7 cm, 1.14 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eStudies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II\u003c\/i\u003e focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras.\u003c\/p\u003e  \u003cp\u003eThe publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences.\u003c\/p\u003e  \u003cp\u003eThe book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras.\u003c\/p\u003e  \u003cp\u003eThe publication is a valuable reference for mathematicians and researchers interested in mathematics and logic. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eConstructivism in Mathematics: Contents Preliminaries\u003cbr\u003e7. The Topology of Metric Spaces\u003cbr\u003e     1. Basic Definitions\u003cbr\u003e     2. Complete, Separable Metric Spaces\u003cbr\u003e     3. Located Sets\u003cbr\u003e     4. Complete, Totally Bounded Spaces\u003cbr\u003e     5. Locally Compact Spaces\u003cbr\u003e     6. Notes\u003cbr\u003e     Exercises\u003cbr\u003e8. Algebra\u003cbr\u003e     1. Identity, Apartness and Order\u003cbr\u003e     2. Groups\u003cbr\u003e     3. Rings and Modules\u003cbr\u003e     4. Linear Algebra\u003cbr\u003e     5. Polynomial Rings\u003cbr\u003e     6. Fields and Local Rings\u003cbr\u003e     7. The Fundamental Theorem of Algebra\u003cbr\u003e     8. Notes\u003cbr\u003e     Exercises\u003cbr\u003e9. Finite-Type Arithmetic and Theories of Operators\u003cbr\u003e     1. Intuitionistic Finite-Type Arithmetic\u003cbr\u003e     2. Normalization, and a Term Model For HA?\u003cbr\u003e     3. The Theory APP\u003cbr\u003e     4. Models for APP\u003cbr\u003e     5. Abstract Realizability in APP\u003cbr\u003e     6. Extensionality and Choice in APP and HA?\u003cbr\u003e     7. Some Metamathematical Applications\u003cbr\u003e     8. Theories of Operators and Classes\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e10. Proof Theory of Intuitionistic Logic\u003cbr\u003e     1. Preliminaries\u003cbr\u003e     2. Normalization\u003cbr\u003e     3. The Structure of Normal Derivations of N-IQCE\u003cbr\u003e     4. The Decidability of IPC\u003cbr\u003e     5. Other Applications of Normalization\u003cbr\u003e     6. Conservative Addition of Predicative Classes\u003cbr\u003e     7. Sequent Calculi\u003cbr\u003e     8. N-IQC as a Calculus of Terms\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e11. The Theory of Types and Constructive Set Theory\u003cbr\u003e     1. Towards a Theory of Types\u003cbr\u003e     2. The Theory MLi0\u003cbr\u003e     3. Some Alternative Formulations of MLi0\u003cbr\u003e     4. The Types Nk and Reformulation of the E-Rules\u003cbr\u003e     5. The Theory ML0\u003cbr\u003e     6. Embeddings into APP\u003cbr\u003e     7. Extensions of MLi0 and ML0\u003cbr\u003e     8. Constructive Set Theory\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e12. Choice Sequences\u003cbr\u003e     1. Introduction\u003cbr\u003e     2. Lawless Sequences\u003cbr\u003e     3. The Elimination Translation for the Theory LS\u003cbr\u003e     4. Other Notions of Choice Sequence\u003cbr\u003e     5. Notes\u003cbr\u003e     Exercises\u003cbr\u003e13. Semantical Completeness\u003cbr\u003e     1. Beth Models\u003cbr\u003e     2. Completeness for Intuitionistic Validity\u003cbr\u003e     3. Incompleteness Results\u003cbr\u003e     4. Lattices, Heyting Algebras and Complete Heyting Algebras\u003cbr\u003e     5. Algebraic Semantics for IPC\u003cbr\u003e     6. O-Sets and Structures\u003cbr\u003e     7. Validity as Forcing\u003cbr\u003e     8. Postscript on Realizability\u003cbr\u003e     9. Notes\u003cbr\u003e     Exercises\u003cbr\u003e14. Sheaves, Sites and Higher-Order Logic\u003cbr\u003e     1. Presheaves, Sheaves and Sheaf-Completion\u003cbr\u003e     2. O-Presheaf and O-Sheaf Structures\u003cbr\u003e     3. Some Notions from Category Theory\u003cbr\u003e     4. Forcing Over Sites\u003cbr\u003e     5. Sheaf Models for Higher-Order Logic\u003cbr\u003e     6. Notes\u003cbr\u003e     Exercises\u003cbr\u003e15. Applications of Sheaf Models\u003cbr\u003e     1. Interpretation of N, Q, Z, R,N in Sh(O(T))\u003cbr\u003e     2. The Axiom of Countable Choice\u003cbr\u003e     3. Topologies in Sheaves Over a cHa\u003cbr\u003e     4. A Derived Rule of Local Continuity\u003cbr\u003e     5. The Monoid Model for CS\u003cbr\u003e     6. A Site Model for LS\u003cbr\u003e     7. Notes\u003cbr\u003e     Exercises\u003cbr\u003e16. Epilogue\u003cbr\u003e     1. The Role of Language and \"Informal Rigour\"\u003cbr\u003e     2. Intuitionistic Logic, Formalisms, and Equality\u003cbr\u003e     3. Brouwer's Theory of the Creative Subject\u003cbr\u003e     4. Dummett's Anti-Realist Argument\u003cbr\u003eBibliography\u003cbr\u003eIndex\u003cbr\u003eIndex of Names\u003cbr\u003eList of Symbols\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46648500814104,"sku":"9780444703583","price":46.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444703583_a8318b46-c9b9-4dd8-b0d6-11396ff6abcb.jpg?v=1694987417"},{"product_id":"pure-mathematics-hardback-9780444880598","title":"Pure Mathematics (Hardback) 9780444880598","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePure Mathematics\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eJ.L. Britton (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444880598, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 January 1992\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e260 pages\u003cbr\u003e24.4 x 17.5 x 2.2 cm, 0.78 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"This work... should be not only in the regular science libraries but also in special computer science reference collections. I hope Turing's works will be available to all students, as Turing's vision is perpetually relevant.\" \u003cb\u003e--Computing Reviews\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThe collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cb\u003ePublished Papers.\u003c\/b\u003e Equivalence of Left and Right Almost Periodicity.\u003cbr\u003eFinite Approximations to Lie Groups. The Extensions of a Group. A Method\u003cbr\u003efor the Calculation of the Zeta-Function. Rounding-Off Errors in Matrix\u003cbr\u003eProcesses. The Word Problem in Semi-Groups with Cancellation. Some\u003cbr\u003eCalculations of the Riemann Zeta-Function. Solvable and Unsolvable\u003cbr\u003eProblems. \u003cb\u003eUnpublished Papers.\u003c\/b\u003e A Note on Normal Numbers. The Word\u003cbr\u003eProblem in Compact Groups. On Permutation Groups. The Difference\u003cbr\u003e\u003ci\u003e\u0026amp;PSgr;(x)-x\u003c\/i\u003e. On a Theorem of Littlewood (with S. Skewes).\u003cbr\u003e\u003cb\u003eRelated Papers.\u003c\/b\u003e An Analysis of Turing's \u003cq\u003eThe Word Problem in Semi-Groups with Cancellation\u003c\/q\u003e (W.W. Boone). On the Difference\u003cbr\u003e\u0026amp;pgr;\u003ci\u003e(x)\u003c\/i\u003e-li \u003ci\u003ex\u003c\/i\u003e (A.M. Cohen, M.J.E. Mayhew). \u003cb\u003eTuring's\u003cbr\u003eStatistical Work.\u003c\/b\u003e Studies in the History of Probability and Statistics\u003cbr\u003eXXXVII. A.M. Turing's Statistical Work in World War II (Biometrika 66).\u003cbr\u003eIntroductory Remarks for the Article in Biometrika 66 (Specially written\u003cbr\u003efor this Volume by I.J. Good). Notes and Summaries. Bibliography. Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Algorithms \u0026amp; data structures [\u003ca title=\"See our other books on Algorithms \u0026amp; data structures\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algorithms%20\u0026amp;%20data%20structures%20%5BUMB%5D%22\"\u003eUMB\u003c\/a\u003e], History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], Complex analysis, complex variables [\u003ca title=\"See our other books on Complex analysis, complex variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Complex%20analysis,%20complex%20variables%20%5BPBKD%5D%22\"\u003ePBKD\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e], Groups \u0026amp; group theory [\u003ca title=\"See our other books on Groups \u0026amp; group theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Groups%20\u0026amp;%20group%20theory%20%5BPBG%5D%22\"\u003ePBG\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648517034264,"sku":"9780444880598","price":45.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444880598_122617e2-4a12-4e01-b31a-e6de6d4017e5.jpg?v=1694987454"},{"product_id":"calculus-for-engineering-students-fundamentals-real-problems-and-computers-paperback-9780128172100","title":"Calculus for Engineering Students; Fundamentals, Real Problems, and Computers (Paperback) 9780128172100","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eCalculus for Engineering Students\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eFundamentals, Real Problems, and Computers\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e\u003cp\u003eAccentuates the uses of calculus in engineering through applications and Computer Algebra Systems (CAS)\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eJesus Martin Vaquero (Edited by), Michael Carr (Edited by), Araceli Quieruga-Dios (Edited by), Daniela Richtarikova (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128172100, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 13 August 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e370 pages\u003cbr\u003e22.9 x 15.1 x 2.4 cm, 0.59 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eCalculus for Engineering Students: Fundamentals, Real Problems, and Computers\u003c\/i\u003e insists that mathematics cannot be separated from chemistry, mechanics, electricity, electronics, automation, and other disciplines. It emphasizes interdisciplinary problems as a way to show the importance of calculus in engineering tasks and problems. While concentrating on actual problems instead of theory, the book uses Computer Algebra Systems (CAS) to help students incorporate lessons into their own studies. Assuming a working familiarity with calculus concepts, the book provides a hands-on opportunity for students to increase their calculus and mathematics skills while also learning about engineering applications.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Real functions and limits (one and multiple variables)\u003cbr\u003e2. Differentiation (one and multiple variables)\u003cbr\u003e3. Complex numbers and functions\u003cbr\u003e4. Real and complex sequences and series\u003cbr\u003e5. Function series (including Taylor and Fourier series)\u003cbr\u003e6. Applications of integrals (one variable)\u003cbr\u003e7. Double and multiple integrals\u003cbr\u003e8. Nonlinear equations (and systems of nonlinear equations)\u003cbr\u003e9. Linear optimization and the simplex method\u003cbr\u003e10. Nonlinear optimization\u003cbr\u003e11. First-order and systems of first-order differential equations\u003cbr\u003e12. Higher-order and systems of higher-order ordinary differential equations\u003cbr\u003e13. Partial differential equations\u003cbr\u003e14. Laplace and z transforms\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Applied mathematics [\u003ca title=\"See our other books on Applied mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Applied%20mathematics%20%5BPBW%5D%22\"\u003ePBW\u003c\/a\u003e], Integral calculus \u0026amp; equations [\u003ca title=\"See our other books on Integral calculus \u0026amp; equations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Integral%20calculus%20\u0026amp;%20equations%20%5BPBKL%5D%22\"\u003ePBKL\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46648517689624,"sku":"9780128172100","price":66.26,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128172100.jpg?v=1694092026"},{"product_id":"categorical-logic-and-type-theory-paperback-9780444508539","title":"Categorical Logic and Type Theory (Paperback \/ softback) 9780444508539","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eCategorical Logic and Type Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eB. Jacobs (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444508539\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 10 May 2001\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e778 pages\u003cbr\u003e23.3 x 15.6 x 4.7 cm, 1.2 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The author's achievement in collecting and organizing a very large body of material in coherent form,... this is first and foremost an encyclopaedic work, into which specialists will delve with much pleasure and profit... One very welcome feature of the book is a comprehensive bibliography of nearly 350 items...\" \u003cb\u003e--Zentralblatt für Mathematik, vol.905R.A.G. Seely\u003c\/b\u003e\"This book will be the standard reference in its field for some time to come.\" \u003cb\u003e--The Bulletin of Symbolic Logic, Vol. 6\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eChapter Headings only.\u003c\/i\u003e Preface. Contents. Preliminaries. Prospectus. Introduction to fibred category theory. Simple type theory. Equational logic. First order predicate logic. Higher order predicate logic. The effective topos. Internal category theory. Polymorphic type theory. Advanced fibred category theory. First order dependent type theory. Higher order dependent type theory. References. Notation index. Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Computer science [\u003ca title=\"See our other books on Computer science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20science%20%5BUY%5D%22\"\u003eUY\u003c\/a\u003e], Philosophy of science [\u003ca title=\"See our other books on Philosophy of science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy%20of%20science%20%5BPDA%5D%22\"\u003ePDA\u003c\/a\u003e], Algebraic topology [\u003ca title=\"See our other books on Algebraic topology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebraic%20topology%20%5BPBPD%5D%22\"\u003ePBPD\u003c\/a\u003e], Algebraic geometry [\u003ca title=\"See our other books on Algebraic geometry\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebraic%20geometry%20%5BPBMW%5D%22\"\u003ePBMW\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46648518246680,"sku":"9780444508539","price":84.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444508539.jpg?v=1694979907"},{"product_id":"constructivism-in-mathematics-vol-1-hardback-9780444702661","title":"Constructivism in Mathematics, Vol 1 (Hardback) 9780444702661","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eConstructivism in Mathematics, Vol 1\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eA.S. Troelstra (Author), D. van Dalen (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444702661, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 July 1988\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e355 pages\u003cbr\u003e23.3 x 15.6 x 2.5 cm, 0.66 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThese two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Algorithms \u0026amp; data structures [\u003ca title=\"See our other books on Algorithms \u0026amp; data structures\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algorithms%20\u0026amp;%20data%20structures%20%5BUMB%5D%22\"\u003eUMB\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e], Cybernetics \u0026amp; systems theory [\u003ca title=\"See our other books on Cybernetics \u0026amp; systems theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Cybernetics%20\u0026amp;%20systems%20theory%20%5BGPFC%5D%22\"\u003eGPFC\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46648528306456,"sku":"9780444702661","price":43.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444702661_066a518f-e104-4fc4-bab3-9f0932f56555.jpg?v=1694987413"},{"product_id":"symbolic-logic-and-mechanical-theorem-proving-hardback-9780121703509","title":"Symbolic Logic and Mechanical Theorem Proving (Hardback) 9780121703509","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSymbolic Logic and Mechanical Theorem Proving\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eChin-Liang Chang (Author), Richard Char-Tung Lee (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780121703509, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 15 June 1973\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e331 pages\u003cbr\u003e22.9 x 15.2 x 2.4 cm, 0.64 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e?Preface\u003cbr\u003eAcknowledgments\u003cbr\u003e1. Introduction\u003cbr\u003e     1.1 Artificial Intelligence, Symbolic Logic, and Theorem Proving\u003cbr\u003e     1.2 Mathematical Background\u003cbr\u003e     References\u003cbr\u003e2. The Propositional Logic\u003cbr\u003e     2.1 Introduction\u003cbr\u003e     2.2 Interpretations of Formulas in the Propositional Logic\u003cbr\u003e     2.3 Validity and Inconsistency in the Propositional Logic\u003cbr\u003e     2.4 Normal Forms in the Propositional Logic\u003cbr\u003e     2.5 Logical Consequences\u003cbr\u003e     2.6 Applications of the Propositional Logic\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e3. The First-Order Logic\u003cbr\u003e     3.1 Introduction\u003cbr\u003e     3.2 Interpretations of Formulas in the First-Order Logic\u003cbr\u003e     3.3 Prenex Normal Forms in the First-Order Logic\u003cbr\u003e     3.4 Applications of the First-Order Logic\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e4. Herbrand's Theorem\u003cbr\u003e     4.1 Introduction\u003cbr\u003e     4.2 Skolem Standard Forms\u003cbr\u003e     4.3 The Herbrand Universe of a Set of Clauses\u003cbr\u003e     4.4 Semantic Trees\u003cbr\u003e     4.5 Herbrand's Theorem\u003cbr\u003e     4.6 Implementation of Herbrand's Theorem\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e5. The Resolution Principle\u003cbr\u003e     5.1 Introduction\u003cbr\u003e     5.2 The Resolution Principle for the Propositional Logic\u003cbr\u003e     5.3 Substitution and Unification\u003cbr\u003e     5.4 Unification Algorithm\u003cbr\u003e     5.5 The Resolution Principle for the First-Order Logic\u003cbr\u003e     5.6 Completeness of the Resolution Principle\u003cbr\u003e     5.7 Examples Using the Resolution Principle\u003cbr\u003e     5.8 Deletion Strategy\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e6. Semantic Resolution and Lock Resolution\u003cbr\u003e     6.1 Introduction\u003cbr\u003e     6.2 An Informal Introduction to Semantic Resolution\u003cbr\u003e     6.3 Formal Definitions and Examples of Semantic Resolution\u003cbr\u003e     6.4 Completeness of Semantic Resolution\u003cbr\u003e     6.5 Hyperresolution and the Set-of-Support Strategy: Special Cases of Semantic Resolution\u003cbr\u003e     6.6 Semantic Resolution Using Ordered Clauses\u003cbr\u003e     6.7 Implementation of Semantic Resolution\u003cbr\u003e     6.8 Lock Resolution\u003cbr\u003e     6.9 Completeness of Lock Resolution\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e7. Linear Resolution\u003cbr\u003e     7.1 Introduction\u003cbr\u003e     7.2 Linear Resolution\u003cbr\u003e     7.3 Input Resolution and Unit Resolution\u003cbr\u003e     7.4 Linear Resolution Using Ordered Clauses and the Information of Resolved Literals\u003cbr\u003e     7.5 Completeness of Linear Resolution\u003cbr\u003e     7.6 Linear Deduction and Tree Searching\u003cbr\u003e     7.7 Heuristics in Tree Searching\u003cbr\u003e     7.8 Estimations of Evaluation Functions\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e8. The Equality Relation\u003cbr\u003e     8.1 Introduction\u003cbr\u003e     8.2 Unsatisfiability under Special Classes of Models\u003cbr\u003e     8.3 Paramodulation—An Inference Rule for Equality\u003cbr\u003e     8.4 Hyperparamodulation\u003cbr\u003e     8.5 Input and Unit Paramodulations\u003cbr\u003e     8.6 Linear Paramodulation\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e9. Some Proof Procedures Based on Herbrand's Theorem\u003cbr\u003e     9.1 Introduction\u003cbr\u003e     9.2 The Prawitz Procedure\u003cbr\u003e     9.3 The V-Resolution Procedure\u003cbr\u003e     9.4 Pseudosemantic Trees\u003cbr\u003e     9.5 A Procedure for Generating Closed Pseudosemantic Trees\u003cbr\u003e     9.6 A Generalization of the Splitting Rule of Davis and Putnam\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e10. Program Analysis\u003cbr\u003e     10.1 Introduction\u003cbr\u003e     10.2 An Informal Discussion\u003cbr\u003e     10.3 Formal Definitions of Programs\u003cbr\u003e     10.4 Logical Formulas Describing the Execution of a Program\u003cbr\u003e     10.5 Program Analysis by Resolution\u003cbr\u003e     10.6 The Termination and Response of Programs\u003cbr\u003e     10.7 The Set-of-Support Strategy and the Deduction of the Halting Clause\u003cbr\u003e     10.8 The Correctness and Equivalence of Programs\u003cbr\u003e     10.9 The Specialization of Programs\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e11. Deductive Question Answering, Problem Solving, and Program Synthesis\u003cbr\u003e     11.1 Introduction\u003cbr\u003e     11.2 Class A Questions\u003cbr\u003e     11.3 Class B Questions\u003cbr\u003e     11.4 Class C Questions\u003cbr\u003e     11.5 Class D Questions\u003cbr\u003e     11.6 Completeness of Resolution for Deriving Answers\u003cbr\u003e     11.7 The Principles of Program Synthesis\u003cbr\u003e     11.8 Primitive Resolution and Algorithm A (A Program-Synthesizing Algorithm)\u003cbr\u003e     11.9 The Correctness of Algorithm A\u003cbr\u003e     11.10 The Application of Induction Axioms to Program Synthesis\u003cbr\u003e     11.11 Algorithm A (An Improved Program-Synthesizing Algorithm)\u003cbr\u003e     References\u003cbr\u003e     Exercises\u003cbr\u003e12. Concluding Remarks\u003cbr\u003e     References\u003cbr\u003eAppendix A\u003cbr\u003e     A.1 A Computer Program Using Unit Binary Resolution\u003cbr\u003e     A.2 Brief Comments on the Program\u003cbr\u003e     A.3 A Listing of the Program\u003cbr\u003e     A.4 Illustrations\u003cbr\u003e     References\u003cbr\u003eAppendix B\u003cbr\u003eBibliography\u003cbr\u003eIndex\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Expert systems \/ knowledge-based systems [\u003ca title=\"See our other books on Expert systems \/ knowledge-based systems\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Expert%20systems%20\/%20knowledge-based%20systems%20%5BUYQE%5D%22\"\u003eUYQE\u003c\/a\u003e], Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Algorithms \u0026amp; data structures [\u003ca title=\"See our other books on Algorithms \u0026amp; data structures\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algorithms%20\u0026amp;%20data%20structures%20%5BUMB%5D%22\"\u003eUMB\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46648535154968,"sku":"9780121703509","price":40.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780121703509_101daf1f-0a03-4f50-8ec8-65bf2eaff93e.jpg?v=1695006676"},{"product_id":"morphogenesis-hardback-9780444884862","title":"Morphogenesis (Hardback) 9780444884862","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMorphogenesis\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eP.T. Saunders (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444884862, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 26 November 1992\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e168 pages\u003cbr\u003e25.4 x 17.8 x 1.8 cm, 0.54 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThe collected works of Turing, including a substantial amount of unpublished material, will comprise four volumes: Mechanical Intelligence, Pure Mathematics, Morphogenesis and Mathematical Logic. Alan Mathison Turing (1912-1954) was a brilliant man who made major contributions in several areas of science. Today his name is mentioned frequently in philosophical discussions about the nature of Artificial Intelligence. Actually, he was a pioneer researcher in computer architecture and software engineering; his work in pure mathematics and mathematical logic extended considerably further and his last work, on morphogenesis in plants, is also acknowledged as being of the greatest originality and of permanent importance. He was one of the leading figures in Twentieth-century science, a fact which would have been known to the general public sooner but for the British Official Secrets Act, which prevented discussion of his wartime work. What is maybe surprising about these papers is that although they were written decades ago, they address major issues which concern researchers today.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eThe Chemical Basis of Morphogenesis (Phil. Trans. R. Soc. London B 237). A Diffusion Reaction Theory of Morphogenesis in Plants (with C.W. Wardlaw). Morphogen Theory of Phyllotaxis: I. Geometrical and Descriptive Phyllotaxis. II. Chemical Theory of Morphogenesis. III. A Solution of the Morphogenetic Equations for the Case of Spherical Symmetry (with B. Richards). Outline of the Development of the Daisy. Bibliography. Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Algorithms \u0026amp; data structures [\u003ca title=\"See our other books on Algorithms \u0026amp; data structures\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algorithms%20\u0026amp;%20data%20structures%20%5BUMB%5D%22\"\u003eUMB\u003c\/a\u003e], History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], Complex analysis, complex variables [\u003ca title=\"See our other books on Complex analysis, complex variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Complex%20analysis,%20complex%20variables%20%5BPBKD%5D%22\"\u003ePBKD\u003c\/a\u003e], Groups \u0026amp; group theory [\u003ca title=\"See our other books on Groups \u0026amp; group theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Groups%20\u0026amp;%20group%20theory%20%5BPBG%5D%22\"\u003ePBG\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648544559384,"sku":"9780444884862","price":49.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444884862_53285ce7-8117-45bc-9c35-6dee40206ccf.jpg?v=1694987457"},{"product_id":"continued-fractions-with-applications-hardback-9780444892652","title":"Continued Fractions with Applications (Hardback) 9780444892652","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eContinued Fractions with Applications\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eL. Lorentzen (Author), H. Waadeland (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444892652, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 April 1992\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e616 pages\u003cbr\u003e23.4 x 15.6 x 3.4 cm, 1.04 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eA. Bultheel\u003cbr\u003e\"...ample material to make the reader fall in love with continued fractions... If you are interested in learning about continued fractions, this book should be on the top of your reading list.\" \u003cb\u003e--Newsletter on Computational and Applied Mathematics\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis book is aimed at two kinds of readers: firstly, people working in or near mathematics, who are curious about continued fractions; and secondly, senior or graduate students who would like an extensive introduction to the analytic theory of continued fractions. The book contains several recent results and new angles of approach and thus should be of interest to researchers throughout the field. The first five chapters contain an introduction to the basic theory, while the last seven chapters present a variety of applications. Finally, an appendix presents a large number of special continued fraction expansions. This very readable book also contains many valuable examples and problems.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eI. Introductory Examples. II. More Basics. III. Convergence Criteria. IV. Continued Fractions and Three-Term Recurrence Relations. V. Correspondence of Continued Fractions. VI. Hypergeometric Functions. VII. Moments and Orthogonality. VIII. Pad\u0026amp;eacute\u003cbr\u003e Approximants. IX. Some Applications in Number Theory. X. Zero-free Regions. XI. Digital Filters and Continued Fractions. XII. Applications to Some Differential Equations. Appendix: Some Continued Fraction Expansions. References. Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e], Optimization [\u003ca title=\"See our other books on Optimization\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Optimization%20%5BPBU%5D%22\"\u003ePBU\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e], Number theory [\u003ca title=\"See our other books on Number theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Number%20theory%20%5BPBH%5D%22\"\u003ePBH\u003c\/a\u003e], Algebra [\u003ca title=\"See our other books on Algebra\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algebra%20%5BPBF%5D%22\"\u003ePBF\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648551342360,"sku":"9780444892652","price":46.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444892652_e98b1abe-234f-4575-819a-82ae0ccf07c7.jpg?v=1694987453"},{"product_id":"logic-a-history-of-its-central-concepts-hardback-9780444529374","title":"Logic: A History of its Central Concepts (Hardback) 9780444529374","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLogic: A History of its Central Concepts\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eAddressing the central topics in the history of logic, showing how logicians, philosophers, mathematicians and others have understood these topics over the years and guided their development to the present century\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Edited by), Francis Jeffry Pelletier (Edited by), John Woods (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444529374, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 11 October 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e708 pages\u003cbr\u003e24.6 x 18.7 x 3.7 cm, 1.65 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"This last volume of the Handbook of the history of logic is devoted to the history of its central concepts...These highly readable histories stretch from antiquity to the present day and are provided with very generous bibliographies.\" --\u003cb\u003eZentralblatt MATH\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eThe Handbook of the History of Logic is a multi-volume research instrument that brings to the development of logic the best in modern techniques of historical and interpretative scholarship. It is the first work in English in which the history of logic is presented so extensively. The volumes are numerous and large. Authors have been given considerable latitude to produce chapters of a length, and a level of detail, that would lay fair claim on the ambitions of the project to be a definitive research work. Authors have been carefully selected with this aim in mind. They and the Editors join in the conviction that a knowledge of the history of logic is nothing but beneficial to the subject's present-day research programmes. One of the attractions of the Handbook's several volumes is the emphasis they give to the enduring relevance of developments in logic throughout the ages, including some of the earliest manifestations of the subject. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. History of the Consequence Relation, \u003ci\u003eby Greg Restall and Conrad Asmus \u003c\/i\u003e2. A History of the Quantification, \u003ci\u003eby Daniel Bonevac \u003c\/i\u003e3. A Brief History of Negation, \u003ci\u003eby J. L. Speranza and Laurence R. Horn \u003c\/i\u003e4. A History of the Connectives, \u003ci\u003eby Daniel Bonevac and Josh Dever \u003c\/i\u003e5. History of Truth-Values, \u003ci\u003eby Jean-Yves Béziau \u003c\/i\u003e6. Traditions of  Modalities, \u003ci\u003eby Simo Knuuttila \u003c\/i\u003e7. Natural Deduction, \u003ci\u003eby Jeff Pelletier and Allen Hazen \u003c\/i\u003e8. History of Connexivity, \u003ci\u003eby Storrs McCall \u003c\/i\u003e9. History of Types, \u003ci\u003eby Fairouz Kamareddine, Twan Laan and Rob Nederpelt \u003c\/i\u003e10. History of the Fallacies, \u003ci\u003eby John Woods \u003c\/i\u003e11. History of Logic-Diagrams, \u003ci\u003eby Amirouche Moktefi and Sun-Joo Shin\u003c\/i\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648690114840,"sku":"9780444529374","price":186.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444529374_538e68c9-8e9d-471c-bb0f-d50459083ce8.jpg?v=1694987170"},{"product_id":"computational-logic-hardback-9780444516244","title":"Computational Logic (Hardback) 9780444516244","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eComputational Logic\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cp\u003ePresenting the growing richness and diversity of computational logic and its applications\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Edited by), Jörg H. Siekmann (Edited by), John Woods (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444516244, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 28 November 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e736 pages\u003cbr\u003e23.4 x 19 x 3.8 cm, 1.19 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eHandbook of the History of Logic\u003c\/i\u003e brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated.\u003c\/p\u003e  \u003cp\u003eLogical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: “Calculemus?. The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eINTRODUCTION 1. Computational Logic, \u003ci\u003eJörg Siekmann \u003c\/i\u003e2. Logic and the Development of the Computer, \u003ci\u003eMartin Davis \u003c\/i\u003eGENERAL 3. What is a Logical System? An Evolutionary View: 1964-2014, \u003ci\u003eDov Gabbay \u003c\/i\u003eAUTOMATED REASONING 4. Interactive Theorem Proving, \u003ci\u003eJohn R. Harrison, Josef Urban, Frederik Wiedijk \u003c\/i\u003e5. Automation of Higher Order Logic, \u003ci\u003eChristoph Benzmüller, Dale Miller \u003c\/i\u003e6. Equational Logics and Rewriting, \u003ci\u003eClaude Kirchner, Helene Kirchner \u003c\/i\u003e7. Possibilistic Logic  An Overview, \u003ci\u003eDidier Dubois, Henri Prade \u003c\/i\u003e8.\u003ci\u003e \u003c\/i\u003eComputerizing Mathematical Text, \u003ci\u003eFairouz\u003c\/i\u003e \u003ci\u003eKamareddine, Joe Wells, Christoph Zengler and Henk Barendregt  \u003c\/i\u003eSPECIFICATION and VERIFICATION 9. Concurrency Theory: A Historical Perspective on Coinduction and Process Calculi, \u003ci\u003eJos\u003c\/i\u003e \u003ci\u003eBaeten, Davide Sangiorgi \u003c\/i\u003e10. Logical Synthesis of Reactive Systems - from Church's Problem to Modern Applications, \u003ci\u003eBernd Finkbeiner \u003c\/i\u003eCOMPUTER SCIENCE 11. Degrees of Unsolvability, \u003ci\u003eKlaus Ambos-Spies, Peter A. Fejer \u003c\/i\u003e12. Computational Complexity, \u003ci\u003eLance Fortnow, Steven Homer \u003c\/i\u003e13. Logic Programming, \u003ci\u003eBob Kowalski \u003c\/i\u003e14. Logic and Databases, \u003ci\u003eJack Minker, Dietmar Seipel, Carlo Zaniolo \u003c\/i\u003e15. Logics for Intelligent Agents and Multi Agent Systems, \u003ci\u003eJohn-Jules\u003c\/i\u003e \u003ci\u003eMeyer\u003c\/i\u003e 16. Description Logics, \u003ci\u003eMatthias Knorr, Pascal Hitzler \u003c\/i\u003e17. Logics for the Semantic Web, \u003ci\u003ePascal Hitzler, Jens Lehmann, Axel Polleres\u003c\/i\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648826364184,"sku":"9780444516244","price":170.36,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444516244.jpg?v=1694979939"},{"product_id":"the-nuts-and-bolts-of-proofs-an-introduction-to-mathematical-proofs-paperback-9780323990202","title":"The Nuts and Bolts of Proofs; An Introduction to Mathematical Proofs (Paperback \/ softback) 9780323990202","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Nuts and Bolts of Proofs\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction to Mathematical Proofs\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eDemonstrates the construction of proofs to help students develop the skills they need to transition to higher-level, more abstract math courses\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAntonella Cupillari (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780323990202\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 21 March 2023\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e416 pages\u003cbr\u003e23.5 x 19 x 2.6 cm, 0.86 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eThe Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs, Fifth Edition\u003c\/i\u003e provides basic logic of mathematical proofs and how they work. The book offers techniques for both reading and writing proofs, discusses techniques in proving if\/then statements by contrapositive and proofing by contradiction, includes the negation statement, and\/or, examines various theorems, such as the if and only-if, equivalence theorems, existence theorems, and the uniqueness theorems. In addition, the use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are also covered. The book also provides mathematical topics for practicing proof techniques.\u003c\/p\u003e  \u003cp\u003eIncluded here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book accessible as well as invaluable.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. Getting Started\u003cbr\u003e2. Basic Techniques to Prove If\/Then Statements\u003cbr\u003e3. Special Kinds of Theorems\u003cbr\u003e4. Some Mathematical Topics on Which to Practice Proof Techniques\u003cbr\u003e5. Review Exercises\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46648827150616,"sku":"9780323990202","price":45.68,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780323990202_6aa68d9a-fd66-483c-9823-dcf11e1cde1b.jpg?v=1694976318"},{"product_id":"handbook-of-automated-reasoning-hardback-9780444508126","title":"Handbook of Automated Reasoning (Hardback) 9780444508126","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHandbook of Automated Reasoning\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eAlan J.A. Robinson (Edited by), Andrei Voronkov (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444508126, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 June 2001\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1188 pages\u003cbr\u003e24 x 16.5 x 5.4 cm, 2.43 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePart V. Higher-order logic and logical frameworks. \u003cbr\u003e\u003cbr\u003eChapter 15. Classical Type Theory (Peter B. Andrews). \u003cbr\u003e\u003cbr\u003e1. Introduction to type theory.  \u003cbr\u003e2. Metatheoretical foundations.  \u003cbr\u003e3. Proof search.  \u003cbr\u003e4. Conclusion.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 16. Higher-Order Unification and Matching (Gilles Dowek). \u003cbr\u003e\u003cbr\u003e1. Type Theory and Other Set Theories.  \u003cbr\u003e2. Simply Typed \u0026amp;lgr;-calculus.  \u003cbr\u003e3. Undecidability.  \u003cbr\u003e4. Huet's Algorithm.  \u003cbr\u003e5. Scopes Management.  \u003cbr\u003e6. Decidable Subcases.  \u003cbr\u003e7. Unification in \u0026amp;lgr;-calculus with Dependent Types.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 17. Logical Frameworks (Frank Pfenning). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Abstract syntax.  \u003cbr\u003e3. Judgments and deductions.  \u003cbr\u003e4. Meta-programming and proof search.  \u003cbr\u003e5. Representing meta-theory.  \u003cbr\u003e6. Appendix: the simply-typed \u0026amp;lgr;-calculus.  \u003cbr\u003e7. Appendix: the dependently typed \u0026amp;lgr;-calculus.  \u003cbr\u003e8. Conclusion.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 18. Proof-Assistants Using Dependent Type Systems (Henk Barendregt, Herman Geuvers). \u003cbr\u003e\u003cbr\u003e1. Proof checking.  \u003cbr\u003e2. Type-theoretic notions for proof checking.  \u003cbr\u003e3. Type systems for proof checking.  \u003cbr\u003e4. Proof-development in type systems.  \u003cbr\u003e5. Proof assistants.  \u003cbr\u003eBibliography. Index. Name index.  \u003cbr\u003e\u003cbr\u003ePart VI. Nonclassical logics. \u003cbr\u003e\u003cbr\u003eChapter 19. Nonmonotonic Reasoning: Towards Efficient Calculi\u003cbr\u003eand Implementations (Jurgen Dix, Ulrich Furbach, Ilkka Niemela). \u003cbr\u003e\u003cbr\u003e1. General Nonmonotonic Logics.  \u003cbr\u003e2. Automating General Nonmonotonic Logics. \u003cbr\u003e3. From Automated Reasoning to Disjunctive Logic Programming.  \u003cbr\u003e4. Nonmonotonic Semantics of Logic Programs.  \u003cbr\u003e5. Implementing Nonmonotonic Semantics.  \u003cbr\u003e6. Benchmarks.  \u003cbr\u003e7. Conclusion.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 20. Automated Deduction for Many-Valued Logics \u003cbr\u003e(Matthias Baaz, Christian G. Fermuller, Gernot Salzer). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. What is a many-valued logic?  \u003cbr\u003e3. Classification of proof systems for many-valued logics.  \u003cbr\u003e4. Signed logic: reasoning classically about finitely-valued logics.  \u003cbr\u003e5. Signed resolution.  \u003cbr\u003e6. An example.  \u003cbr\u003e7. Optimization of transformation rules.  \u003cbr\u003e8. Remarks on infinitely-valued logics.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 21. Encoding Two-Valued Nonclassical Logics in Classical Logic (Hans Jurgen Ohlbach, Andreas Nonnengart, Maarten de Rijke, Dov M. Gabbay). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Background.  \u003cbr\u003e3. Encoding consequence relations.  \u003cbr\u003e4. The standard relational translation.  \u003cbr\u003e5. The functional translation.  \u003cbr\u003e6. The semi-functional translation.  \u003cbr\u003e7. Variations and alternatives.  \u003cbr\u003e8. Conclusion.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 22. Connections in Nonclassical Logics (Arild Waaler). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Prelude: Connections in classical first-order logic.  \u003cbr\u003e3. Labelled systems.  \u003cbr\u003e4. Propositional intuitionistic logic.  \u003cbr\u003e5. First--order intuitionistic logic.  \u003cbr\u003e6. Normal modal logics up to S4.  \u003cbr\u003e7. The S5 family.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003ePart VII. Decidable classes and model building. \u003cbr\u003e\u003cbr\u003eChapter 23. Reasoning in Expressive Description Logics (Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini, Daniele Nardi). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Description Logics.  \u003cbr\u003e3. Description Logics and Propositional Dynamic Logics.  \u003cbr\u003e4. Unrestricted Model Reasoning.  \u003cbr\u003e5. Finite Model Reasoning.  \u003cbr\u003e6. Beyond Basic Description Logics.  \u003cbr\u003e7. Conclusions.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 24. Model Checking (Edmund M. Clarke, Bernd-Holger Schlingloff). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Logical Languages, Expressiveness.  \u003cbr\u003e3. Second Order Languages.  \u003cbr\u003e4. Model Transformations and Properties.  \u003cbr\u003e5. Equivalence reductions.  \u003cbr\u003e6. Completeness.  \u003cbr\u003e7. Decision Procedures.  \u003cbr\u003e8. Basic Model Checking Algorithms.  \u003cbr\u003e9. Modelling of Reactive Systems.  \u003cbr\u003e10. Symbolic Model Checking. \u003cbr\u003e11. Partial Order Techniques.  \u003cbr\u003e12. Bounded Model Checking.  \u003cbr\u003e13. Abstractions.  \u003cbr\u003e14. Compositionality and Modular Verification.  \u003cbr\u003e15. Further Topics.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 25. Resolution Decision Procedures (Christian G. Fermuller, Alexander Leitsch, Ullrich Hustadt, Tanel Tammet). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Notation and definitions.  \u003cbr\u003e3. Decision procedures based on ordering refinements.  \u003cbr\u003e4. Hyperresolution as decision procedure.  \u003cbr\u003e5. Resolution decision procedures for description logics.  \u003cbr\u003e6. Related work. \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003ePart VIII. Implementation. \u003cbr\u003eChapter 26. Term Indexing  (R. Sekar, I.V. Ramakrishnan, Andrei Voronkov). \u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Background.  \u003cbr\u003e3. Data structures for representing terms and indexes.  \u003cbr\u003e4. A common framework for indexing.  \u003cbr\u003e5. Path indexing.  \u003cbr\u003e6. Discrimination trees.  \u003cbr\u003e7. Adaptive automata.  \u003cbr\u003e8. Automata-driven indexing.  \u003cbr\u003e9. Code trees.  \u003cbr\u003e10. Substitution trees.  \u003cbr\u003e11. Context trees.  \u003cbr\u003e12. Unification factoring.  \u003cbr\u003e13. Multiterm indexing.  \u003cbr\u003e14. Issues in perfect filtering.  \u003cbr\u003e15. Indexing modulo AC-theories.  \u003cbr\u003e16. Elements of term indexing.  \u003cbr\u003e17. Indexing in practice.  \u003cbr\u003e18. Conclusion.  \u003cbr\u003eBibliography. Index.  \u003cbr\u003e\u003cbr\u003eChapter 27. Combining Superposition, Sorts and Splitting (Christoph Weidenbach). \u003cbr\u003e\u003cbr\u003e1. What This Chapter is (not) About.  \u003cbr\u003e2. Foundations.  \u003cbr\u003e3. A First Simple Prover.  \u003cbr\u003e4. Inference and Reduction Rules.  \u003cbr\u003e5. Global Design Decisions.  \u003cbr\u003eBibliography. A Links to Saturation Based Provers. Index.  \u003cbr\u003e\u003cbr\u003eChapter 28. Model Elimination and Connection Tableau Procedures  \u003cbr\u003e(Reinhold Letz, Gernot Stenz).\u003cbr\u003e\u003cbr\u003e1. Introduction.  \u003cbr\u003e2. Clausal Tableaux and Connectedness.  \u003cbr\u003e3. Further Structural Refinements of Clausal Tableaux.  \u003cbr\u003e4. Global Pruning Methods in Model Elimination.  \u003cbr\u003e5. Shortening of Proofs.  \u003cbr\u003e6. Completeness of Connection Tableaux.  \u003cbr\u003e7. Architectures of Model Elimination Implementations.  \u003cbr\u003e8. Implementation of Refinements by Constraints.  \u003cbr\u003e9. Experimental Results.  \u003cbr\u003e10. Outlook.  \u003cbr\u003eBibliography. Index. Concept index.  \u003cbr\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Expert systems \/ knowledge-based systems [\u003ca title=\"See our other books on Expert systems \/ knowledge-based systems\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Expert%20systems%20\/%20knowledge-based%20systems%20%5BUYQE%5D%22\"\u003eUYQE\u003c\/a\u003e], Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Computer architecture \u0026amp; logic design [\u003ca title=\"See our other books on Computer architecture \u0026amp; logic design\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20architecture%20\u0026amp;%20logic%20design%20%5BUYF%5D%22\"\u003eUYF\u003c\/a\u003e], Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46648836817176,"sku":"9780444508126","price":131.89,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444508126.jpg?v=1694979942"},{"product_id":"the-nuts-and-bolts-of-proofs-an-introduction-to-mathematical-proofs-paperback-9780123822178","title":"The Nuts and Bolts of Proofs; An Introduction to Mathematical Proofs (Paperback \/ softback) 9780123822178","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Nuts and Bolts of Proofs\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction to Mathematical Proofs\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e\u003cp\u003eThis valuable resource demonstrates the construction of proofs to help students develop the skills they need to transition to higher-level, more abstract math courses\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAntonella Cupillari (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780123822178, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 14 February 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e296 pages\u003cbr\u003e23.4 x 19 x 1.9 cm, 0.62 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"It is written with great accuracy and a level of enthusiasm necessary for the Herculean task of launching mathematical handle-turners into the world of mathematical thinking…for those required to teach ‘transition courses’, I recommend perusal of this book as a possible course text.\" --\u003cb\u003eMAA online, December 3, 2013\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003ci\u003eThe Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs\u003c\/i\u003e provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if\/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and\/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book invaluable.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. Getting Started2. Basic Techniques to Prove If\/Then Statements3. Special kinds of Theorems4. Some mathematical topics on which to practice proof techniques5. Review Exercises\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46648885444888,"sku":"9780123822178","price":30.39,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780123822178.jpg?v=1695014049"},{"product_id":"lectures-on-the-curry-howard-isomorphism-hardback-9780444520777","title":"Lectures on the Curry-Howard Isomorphism (Hardback) 9780444520777","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLectures on the Curry-Howard Isomorphism\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eMorten Heine Sørensen (Author), Pawel Urzyczyn (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444520777, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 July 2006\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e456 pages\u003cbr\u003e22.9 x 15.1 x 2.8 cm, 0.83 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThe Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction  to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.\u003cp\u003eKey features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning\u003c\/p\u003e\n\u003cp\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePrefaceAcknowledgements1. Typefree lambda-calculus2. Intuitionistic logic3. Simply typed lambdacalculus4. The Curry-Howard isomorphism5. Proofs as combinators6. Classical logic and control operators7. Sequent calculus8. First-order logic9. First-order arithmetic10. Gödel's system T11. Second-order logic and polymorphism12. Second-order arithmetic13. Dependent types14. Pure type systems and the lambda-cubeA Mathematical BackgroundB Solutions and hints to selected exercisesBibliographyIndex\u003cp\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46648951439640,"sku":"9780444520777","price":115.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444520777.jpg?v=1694095661"},{"product_id":"electrical-load-forecasting-modeling-and-model-construction-paperback-9780128102213","title":"Electrical Load Forecasting; Modeling and Model Construction (Paperback) 9780128102213","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eElectrical Load Forecasting\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eModeling and Model Construction\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eAchieve a high level forecasting accuracy and save valuable time and money\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eS.A. Soliman (Author), Ahmad Mohammad Al-Kandari (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128102213\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 19 August 2016\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e440 pages\u003cbr\u003e22.9 x 15.1 x 2.8 cm, 0.7 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eApprox.420 pages\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. State of the Art2. Static State Estimation3. Short Term Load Forecasting Models4. Fuzzy Systems and Fuzzy linear Regression5. Dynamic State Estimation6. Load Forecasting Computational Results: Static State Estimation7. Load Forecasting Computational Results Fuzzy Linear Regression8. Dynamic Electric Load Forecasting\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Energy industries \u0026amp; utilities [\u003ca title=\"See our other books on Energy industries \u0026amp; utilities\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Energy%20industries%20\u0026amp;%20utilities%20%5BKNB%5D%22\"\u003eKNB\u003c\/a\u003e], Economic forecasting [\u003ca title=\"See our other books on Economic forecasting\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Economic%20forecasting%20%5BKCJ%5D%22\"\u003eKCJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46649012683032,"sku":"9780128102213","price":93.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128102213.jpg?v=1694096027"},{"product_id":"sets-and-extensions-in-the-twentieth-century-hardback-9780444516213","title":"Sets and Extensions in the Twentieth Century (Hardback) 9780444516213","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eSets and Extensions in the Twentieth Century\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eCovers the rich history of scientific turning points in set theory, providing fresh insights and points of view\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Volume editor), Akihiro Kanamori (Volume editor), John Woods (Volume editor)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444516213, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 24 January 2012\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e880 pages\u003cbr\u003e25.7 x 18.2 x 4.3 cm, 1.97 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eSet theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eSet Theory from Cantor to Cohen, by Akihiro Kanamori History of the Continuum in the 20th Century, by Juris Stepr¯ans Infinite Combinatorics, by Jean A. Larson Large Cardinals with Forcing, by Akihiro Kanamori Inner Models for Large Cardinals, by William J. Mitchell A Brief History of Determinacy, by Paul B. Larson Singular Cardinals: From Hausdorff’s Gaps to Shelah’s pcf Theory, by Menachem Kojman Alternative Set Theories, by M. Randall Holmes, Thomas Forster, and Thierry Libert Types, Sets, and Categories, by John L. Bell The History of Categorical Logic: 1963–1977, by Jean-Pierre Marquis and Gonzalo E. Reyes Russell’s Orders in Kripke’s Theory of Truth and Computational Type Theory, by Fairouz Kamareddine, Twan Laan, and Robert Constable\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e], Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\u003c\/a\u003e], Computational linguistics [\u003ca title=\"See our other books on Computational linguistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computational%20linguistics%20%5BCFX%5D%22\"\u003eCFX\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46649075597592,"sku":"9780444516213","price":173.25,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444516213.jpg?v=1694979961"},{"product_id":"computability-theory-an-introduction-to-recursion-theory-hardback-9780123849588","title":"Computability Theory; An Introduction to Recursion Theory (Hardback) 9780123849588","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eComputability Theory\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction to Recursion Theory\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e\u003cp\u003eAccessible undergraduate textbook for a one-term course on computability theory (i.e., recursion theory)\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eHerbert B. Enderton (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780123849588, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 30 December 2010\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e192 pages\u003cbr\u003e22.9 x 15.1 x 1.9 cm, 0.46 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"...would benefit its target audience, especially now that a lot of mathematics courses eschew proofs...As with Enderton's well-known text in mathematical logic,...this is a thoughtfully written account of the basic facts, and I for one will likely use it in the future.\" --\u003cb\u003eMathematical Reviews, Computability Theory\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"This textbook on basic computability theory is at the upper-undergraduate level.\" --\u003cb\u003eZentralblatt \u003cb\u003eMATH, 2012\u003c\/b\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"Enderton (U. of California, Los Angeles) has written a clear, focused, and surprisingly literate textbook — it is a rare mathematician who is this adept with words — describing the history and theory of recursion theory that will be ideal for one-semester advanced courses in mathematics and computer science. After the concepts and theories are introduced, the equivalence of computable partial function and recursive partial function are demonstrated, in part through proofs of the unsolvability of the halting problem and of the enumeration theorem. Other chapters describe the properties of recursively enumerable sets, the link between computability theory and Gödel's incompleteness theorem, relative computability and degrees of unsolvability, and polynomial time computability. Appendices are included on Mathspeak, countability, and decadic notation.\" --\u003cb\u003eSciTechBookNews\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\"Computability is concerned with the question of what computers can do in principle. Since Enderton directly contributed to the very areas that this book covers (computability and computational complexity), he is able to provide a concise and comprehensive firsthand view on the subject. As a scholar in the field, as well as in the history of logic, he frequently includes historical passages when presenting new concepts in the book…. This is a beautifully written and beautifully printed book.... The book fits perfectly as a textbook, covering standard material for one- or two-semester courses in computability or recursion theory. It is also an excellent study guide and reference for students and researchers in related areas. It is a lovely, short book that contains great ideas.\" --\u003cb\u003eComputing Reviews\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eComputability Theory: An Introduction to Recursion Theory \u003c\/i\u003eprovides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level.  The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. \u003ci\u003eComputability Theory\u003c\/i\u003e is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. The Computability Concept;2. General Recursive Functions;3. Programs and Machines;4. Recursive Enumerability;5. Connections to Logic;6. Degrees of Unsolvability;7. Polynomial-Time Computability;Appendix: Mathspeak;Appendix: Countability;Appendix: Decadic Notation;\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Computer science [\u003ca title=\"See our other books on Computer science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20science%20%5BUY%5D%22\"\u003eUY\u003c\/a\u003e], Business applications [\u003ca title=\"See our other books on Business applications\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Business%20applications%20%5BUF%5D%22\"\u003eUF\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46649082708248,"sku":"9780123849588","price":58.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780123849588.jpg?v=1695014045"},{"product_id":"fuzzy-sets-and-systems-theory-and-applications-hardback-9780122227509","title":"Fuzzy Sets and Systems; Theory and Applications (Hardback) 9780122227509","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFuzzy Sets and Systems\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eTheory and Applications\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDidier J. Dubois (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780122227509, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 December 1980\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e393 pages\u003cbr\u003e22.9 x 15.1 x 2.6 cm, 0.81 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Maths for engineers [\u003ca title=\"See our other books on Maths for engineers\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Maths%20for%20engineers%20%5BTBJ%5D%22\"\u003eTBJ\u003c\/a\u003e], Chaos theory [\u003ca title=\"See our other books on Chaos theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Chaos%20theory%20%5BPBWS%5D%22\"\u003ePBWS\u003c\/a\u003e], Mathematical modelling [\u003ca title=\"See our other books on Mathematical modelling\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20modelling%20%5BPBWH%5D%22\"\u003ePBWH\u003c\/a\u003e], Applied mathematics [\u003ca title=\"See our other books on Applied mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Applied%20mathematics%20%5BPBW%5D%22\"\u003ePBW\u003c\/a\u003e], Linear programming [\u003ca title=\"See our other books on Linear programming\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Linear%20programming%20%5BPBUH%5D%22\"\u003ePBUH\u003c\/a\u003e], Real analysis, real variables [\u003ca title=\"See our other books on Real analysis, real variables\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Real%20analysis,%20real%20variables%20%5BPBKB%5D%22\"\u003ePBKB\u003c\/a\u003e], Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Sport \u0026amp; leisure industries [\u003ca title=\"See our other books on Sport \u0026amp; leisure industries\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Sport%20\u0026amp;%20leisure%20industries%20%5BKNSP%5D%22\"\u003eKNSP\u003c\/a\u003e], Personnel \u0026amp; human resources management [\u003ca title=\"See our other books on Personnel \u0026amp; human resources management\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Personnel%20\u0026amp;%20human%20resources%20management%20%5BKJMV2%5D%22\"\u003eKJMV2\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46649197822232,"sku":"9780122227509","price":46.19,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780122227509_8b89e5c5-47e7-4381-a899-05e239575bf3.jpg?v=1695006699"},{"product_id":"a-transition-to-abstract-mathematics-learning-mathematical-thinking-and-writing-hardback-9780123744807","title":"A Transition to Abstract Mathematics; Learning Mathematical Thinking and Writing (Hardback) 9780123744807","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eA Transition to Abstract Mathematics\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eLearning Mathematical Thinking and Writing\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eThis second edition assists engineering and physical science students on fundamental proof techniques and learning to think and write mathematics\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eRandall Maddox (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780123744807\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 13 October 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e384 pages\u003cbr\u003e23.4 x 19 x 2.6 cm, 0.96 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eConstructing concise and correct proofs is one of the most challenging aspects of learning to work with advanced mathematics. Meeting this challenge is a defining moment for those considering a career in mathematics or related fields. \u003ci\u003eA Transition to Abstract Mathematics\u003c\/i\u003e teaches readers to construct proofs and communicate with the precision necessary for working with abstraction. It is based on two premises: composing clear and accurate mathematical arguments is critical in abstract mathematics, and that this skill requires development and support. Abstraction is the destination, not the starting point.Maddox methodically builds toward a thorough understanding of the proof process, demonstrating and encouraging mathematical thinking along the way. Skillful use of analogy clarifies abstract ideas. Clearly presented methods of mathematical precision provide an understanding of the nature of mathematics and its defining structure. After mastering the art of the proof process, the reader may pursue two independent paths. The latter parts are purposefully designed to rest on the foundation of the first, and climb quickly into analysis or algebra. Maddox addresses fundamental principles in these two areas, so that readers can apply their mathematical thinking and writing skills to these new concepts. From this exposure, readers experience the beauty of the mathematical landscape and further develop their ability to work with abstract ideas.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eNotation and AssumptionsSection I: Foundations of Logic and Proof Writing Ch 1. LogicCh 1. Language and MathematicsCh 2. Properties of Real Numbers Ch 3. Sets and Their Properties Ch 4. FunctionsSection II: Basic Principles of AnalysisCh 5. The Real NumbersCh 6. Sequences of Real Numbers Ch 7. Functions of a Real VariableSection III: Basic Principles of AlgebraCh 6. GroupsCh 7. RingsIndex\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Reference works [\u003ca title=\"See our other books on Reference works\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Reference%20works%20%5BChildren's%20\/%20Teenage%5D%20%5BYRG%5D%22\"\u003eChildren's \/ Teenage YRG\u003c\/a\u003e], Educational: Sciences, general science [\u003ca title=\"See our other books on Educational: Sciences, general science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Educational:%20Sciences,%20general%20science%20%5BYQS%5D%22\"\u003eYQS\u003c\/a\u003e], Educational: Mathematics \u0026amp; numeracy [\u003ca title=\"See our other books on Educational: Mathematics \u0026amp; numeracy\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Educational:%20Mathematics%20\u0026amp;%20numeracy%20%5BYQM%5D%22\"\u003eYQM\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46649291505944,"sku":"9780123744807","price":61.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780123744807.jpg?v=1694099544"},{"product_id":"infinite-words-automata-semigroups-logic-and-games-hardback-9780125321112","title":"Infinite Words; Automata, Semigroups, Logic and Games (Hardback) 9780125321112","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInfinite Words\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAutomata, Semigroups, Logic and Games\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eBeing the very first comprehensive treatment of the theory of Infinite Words, this book is \u003ci\u003ethe\u003c\/i\u003e reference for researchers and graduates in this field.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDominique Perrin (Author), Jean-Éric Pin (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780125321112\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 12 February 2004\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e550 pages\u003cbr\u003e22.9 x 15.1 x 3.2 cm, 1 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The most impressive aspect of the book \"Infinite Words\" by Dominique Perrin and Jean-Eric Pin is the extent of its coverage. It is a virtually complete compendium of everything to do with infinite words: infinite-time automata; connections to semigroups, topology and logic; infinite games; bi-infinite words; infinite trees.\" \u003cb\u003e--Robert McNaughton, Emeritus Professor Ph.D., Harvard University, USA\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eApprox.550 pages\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Computer science [\u003ca title=\"See our other books on Computer science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20science%20%5BUY%5D%22\"\u003eUY\u003c\/a\u003e], Applied mathematics [\u003ca title=\"See our other books on Applied mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Applied%20mathematics%20%5BPBW%5D%22\"\u003ePBW\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46649425985816,"sku":"9780125321112","price":144.29,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780125321112.jpg?v=1694100917"},{"product_id":"fuzzy-neural-networks-for-real-time-control-applications-concepts-modeling-and-algorithms-for-fast-learning-paperback-9780128026878","title":"Fuzzy Neural Networks for Real Time Control Applications; Concepts, Modeling and Algorithms for Fast Learning (Paperback) 9780128026878","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFuzzy Neural Networks for Real Time Control Applications\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eConcepts, Modeling and Algorithms for Fast Learning\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e\u003cp\u003eThis book presents the basics of fuzzy neural networks, in particular type-2 fuzzy neural networks, for the identification and learning control of real time systems. In addition to conventional parameter tuning methods, e.g. GD, SMC theory-based learning algorithms, which are simple and have closed forms, and their stability analysis have also been introduced. This book has been prepared in a way that can be easily understood by those who are experienced and inexperienced in this field. Readers can benefit from the computer source codes for both identification and control purposes which are given at the end of the book.\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eErdal Kayacan (Author), Mojtaba Ahmadieh Khanesar (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128026878\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 17 September 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e264 pages\u003cbr\u003e22.9 x 15.1 x 1.8 cm, 0.43 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eApprox.242 pages\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eDedication\u003c\/p\u003e \u003cp\u003ePreface\u003c\/p\u003e \u003cp\u003eAcknowledgements\u003c\/p\u003e \u003cp\u003eList of Acronyms\/Abbreviations\/Index terms\u003c\/p\u003e \u003cp\u003e1- Mathematical Preliminaries\u003c\/p\u003e \u003cp\u003e2- Fundamentals of Type-1 Fuzzy Logic Theory\u003c\/p\u003e \u003cp\u003e3- Fundamentals of Type-2 Fuzzy Logic Theory\u003c\/p\u003e \u003cp\u003e4- Type-2 Fuzzy Neural Networks\u003c\/p\u003e \u003cp\u003e5- Gradient Descent Methods for Type-2 Fuzzy Neural Networks\u003c\/p\u003e \u003cp\u003e6- Extended Kalman Filter Algorithm for the tuning of Type-2 Fuzzy Neural Networks\u003c\/p\u003e \u003cp\u003e7- Sliding Mode Control Theory-Based Parameter Adaptation Rules for Fuzzy Neural Networks\u003c\/p\u003e \u003cp\u003e8- Hybrid Training Method for Type-2 Fuzzy Neural Networks Using Particle Swarm Optimization\u003c\/p\u003e \u003cp\u003e9- Noise Reduction Property of Type-2 Fuzzy Neural Networks\u003c\/p\u003e \u003cp\u003e10- Case Studies: Identification Examples\u003c\/p\u003e \u003cp\u003e11- Case Studies: Control Examples\u003c\/p\u003e \u003cp\u003eAppendix\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46649591267608,"sku":"9780128026878","price":58.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128026878.jpg?v=1694102059"},{"product_id":"pattern-recognition-and-signal-analysis-in-medical-imaging-paperback-9780128101162","title":"Pattern Recognition and Signal Analysis in Medical Imaging (Paperback) 9780128101162","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003ePattern Recognition and Signal Analysis in Medical Imaging\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eEssential tool for students and professionals that compiles, organizes and thoroughly explains proven and new cutting-edge methods in pattern recognition for medical imaging\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAnke Meyer-Baese (Author), Volker J. Schmid (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128101162, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 19 August 2016\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e466 pages, 50 illustrations\u003cbr\u003e23.4 x 19 x 2.9 cm, 0.97 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\"The second edition of this book brings sharp focus to the development of integrated systems for use in the clinical sector, enabling both imaging and the automatic assessment of the resultant data…This book is an essential tool for students and professionals, compiling and explaining proven and cutting-edge methods in pattern recognition for medical imaging.\" --\u003cb\u003eZentralblatt MATH 1284-1\u003c\/b\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eMedical imaging is one of the heaviest funded biomedical engineering research areas. The second edition of \u003ci\u003ePattern Recognition and Signal Analysis in Medical Imaging\u003c\/i\u003e brings sharp focus to the development of integrated systems for use in the clinical sector, enabling both imaging and the automatic assessment of the resultant data. \u003c\/p\u003e  \u003cp\u003eSince the first edition, there has been tremendous development of new, powerful technologies for detecting, storing, transmitting, analyzing, and displaying medical images. Computer-aided analytical techniques, coupled with a continuing need to derive more information from medical images, has led to a growing application of digital processing techniques in cancer detection as well as elsewhere in medicine. \u003c\/p\u003e  \u003cp\u003eThis book is an essential tool for students and professionals, compiling and explaining proven and cutting-edge methods in pattern recognition for medical imaging. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eFoundations of Medical Imaging; Feature Selection and Extraction; Theory of Subband Decomposition and Wavelets; The Wavelet Transform in Medical Imaging; Genetic Algorithms; Statistical Pattern Recognition; Syntactic Pattern Recognition; Neural Networks; Theory; Neural Networks: Applications; Fuzzy Logic: Theory and Clustering Algorithms; Computer Aided Diagnosis Systems\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Signal processing [\u003ca title=\"See our other books on Signal processing\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Signal%20processing%20%5BUYS%5D%22\"\u003eUYS\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Biomedical engineering [\u003ca title=\"See our other books on Biomedical engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Biomedical%20engineering%20%5BMQW%5D%22\"\u003eMQW\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46649755074840,"sku":"9780128101162","price":77.79,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128101162.jpg?v=1694103329"},{"product_id":"intelligent-data-analysis-for-biomedical-applications-challenges-and-solutions-paperback-9780128155530","title":"Intelligent Data Analysis for Biomedical Applications; Challenges and Solutions (Paperback) 9780128155530","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eIntelligent Data Analysis for Biomedical Applications\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eChallenges and Solutions\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e\u003cp\u003eBuilds a bridge between computing techniques and biomedical applications by integrating intelligent data analysis techniques in biomedical systems\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eD. Jude Hemanth (Edited by), Deepak Gupta (Edited by), Valentina Emilia Balas (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128155530, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 19 March 2019\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e294 pages\u003cbr\u003e22.9 x 15.1 x 1.9 cm, 0.5 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eIntelligent Data Analysis for Biomedical Applications: Challenges and Solutions\u003c\/i\u003e presents specialized statistical, pattern recognition, machine learning, data abstraction and visualization tools for the analysis of data and discovery of mechanisms that create data. It provides computational methods and tools for intelligent data analysis, with an emphasis on problem-solving relating to automated data collection, such as computer-based patient records, data warehousing tools, intelligent alarming, effective and efficient monitoring, and more. This book provides useful references for educational institutions, industry professionals, researchers, scientists, engineers and practitioners interested in intelligent data analysis, knowledge discovery, and decision support in databases.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1. A Review on Intelligent Data Analysis System for an IoT-Based Capsule Endoscopy System\u003cbr\u003e2. Ant Colony optimization-based image texture segmentation in medical images\u003cbr\u003e3. A Feature Fusion Based Discriminant Learning Model for Diagnosis of Neuromuscular Disorders Using Single Channel Needle EMG Signal\u003cbr\u003e4. Evolution of Consciousness Systems with bacteria\u003cbr\u003e5. Analysis of transform-based compression techniques for MRI and CT images\u003cbr\u003e6. Liveness Assured Multimodal Biometrics using Electrocardiogram for Smart Health Applications\u003cbr\u003e7. Medical Image Retrieval System in PACS Environment for Clinical Decision Making\u003cbr\u003e8. A Neuro Fuzzy Inference Model for Diabetic Retinopathy Classification\u003cbr\u003e9. Predictive Analysis of breast cancer using machine learning techniques\u003cbr\u003e10. Right Ventricle Image Segmentation from MRI using optimization techniques\u003cbr\u003e11. Computational Automated System for Red Blood Cell Detection and Segmentation\u003cbr\u003e12. Fuzzy logic based approaches for gene regulatory network inference\u003cbr\u003e13. Evolutionary Algorithm with Memetic Search for Optic Disc Localization in Retinal Fundus Images\u003cbr\u003e14. A novel approach of targeting prognostics of Bruxism disorder using C4-P4 channel of EEG signal\u003cbr\u003e15. Physiotherapy and Rehabilitation Assessment System Using Bio-inspired Visual Cortex Computational Model\u003cbr\u003e16. Classification of Myocardial Ischemia in Contrast Enhancement Using Machine Learning\u003cbr\u003e17. Simple link sensor network based remote monitoring of multiple patients\u003cbr\u003e18. Prognosticating the risk of fibrosis progression in non-alcoholic fatty liver diseases\u003cbr\u003e19. Alzheimer Disease Detection from Structural MR Images using Fuzzy C-Means based Deep Belief Neural Network\u003cbr\u003e20. Optimal Control of Fractional Order HIV-Immune System Using Neural Network Approach\u003cbr\u003e21. Diagnosis of Ocular Disease using Optical Coherence Tomography Image\u003cbr\u003e22. Hybrid Approach for Classification of EEG Signals using T-F Images with Wavelets and Texture Features\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Signal processing [\u003ca title=\"See our other books on Signal processing\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Signal%20processing%20%5BUYS%5D%22\"\u003eUYS\u003c\/a\u003e], Computer science [\u003ca title=\"See our other books on Computer science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Computer%20science%20%5BUY%5D%22\"\u003eUY\u003c\/a\u003e], Mathematical \u0026amp; statistical software [\u003ca title=\"See our other books on Mathematical \u0026amp; statistical software\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20\u0026amp;%20statistical%20software%20%5BUFM%5D%22\"\u003eUFM\u003c\/a\u003e], Mechanical engineering [\u003ca title=\"See our other books on Mechanical engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20%5BTGB%5D%22\"\u003eTGB\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46649965379864,"sku":"9780128155530","price":84.66,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128155530.jpg?v=1694104805"},{"product_id":"optimization-theory-based-on-neutrosophic-and-plithogenic-sets-paperback-9780128196700","title":"Optimization Theory Based on Neutrosophic and Plithogenic Sets (Paperback) 9780128196700","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eOptimization Theory Based on Neutrosophic and Plithogenic Sets\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cp\u003ePresents foundational literature about systems that can handle high levels of uncertainty in complex real-world problems\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eFlorentin Smarandache (Edited by), Mohamed Abdel-Basset (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128196700\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 17 January 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e446 pages\u003cbr\u003e22.9 x 15.1 x 2.8 cm, 0.8 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eApprox.432 pages\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. Neutrosophic Set Theory and Application in Management Science 2. Logistics Engineering: Modelling, Optimization and Simulation 3. Operations Research and Operations Management 4. Production Planning and Control 5. Neutrosophic set-based Project Management 6. Neutrosophic set-based Linear Programming Problems 7. Neutrosophic set-based Integer Programming Problems 8. Neutrosophic set-based Goal Programming Problems 9. Neutrosophic set-based Game Theory 10. Neutrosophic set-based Nonlinear Programming problems and its applications 11. Neutrosophic based on Operations Research applications 12. Neutrosophic set-based Computational Modelling 13. Soft Computing, and logic for optimum results 14. Design of Nonlinear Optimal Controllers 15. Neutrosophic Geophysics 16. Neutrosophic Computational Systems Biology 17. Neutrosophic Molecular Modeling 18. Refined Neutrosophic Set and Logic 19. Neutrosophic Over-\/Under-\/Off-Set and -Logic 20. Neutrosophic Mathematical Programming 21. Neutrosophic Possibilistic Optimization 22. Neutrosophic Image Processing 23. Neutrosophic Civil Engineering 24. Neutrosophic Electric Engineering 25. Neutrosophic Regression Analysis 26. Neutrosophic Data Analysis 27. Fundamental theories for Operational Research under Uncertainty 28. Neutrosophic sets-based Multi-Criteria Group Decision Making 29. Neutrosophic set-based Economic Forecasting 30. Complex neutrosophic set-based Group Decision Making 31. Neutrosophic and Plithogenic Evolutionary Algorithms 32. Neutrosophic and Plithogenic Memetic Algorithms 33. Neutrosophic and Plithogenic Genetic Algorithms 34. Plithogenic Set and its Applications 35. Plithogenic Logic and its Applications 36. Plithogenic Probability and its Optimization Applications 37. Neutrosophic and Plithogenic Time Series Prediction\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Applied mathematics [\u003ca title=\"See our other books on Applied mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Applied%20mathematics%20%5BPBW%5D%22\"\u003ePBW\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46650151665944,"sku":"9780128196700","price":144.39,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128196700.jpg?v=1694106060"},{"product_id":"analysis-and-synthesis-of-singular-systems-paperback-9780128237397","title":"Analysis and Synthesis of Singular Systems (Paperback) 9780128237397","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAnalysis and Synthesis of Singular Systems\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eProvides comprehensive and systematic methods, including  advanced approaches that can be used to analyze or control singular systems\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eZhiguang Feng (Author), Jiangrong Li (Author), Peng Shi (Author), Haiping Du (Author), Zhengyi Jiang (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780128237397, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 6 November 2020\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e262 pages\u003cbr\u003e22.9 x 15.1 x 1.7 cm, 0.43 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"Singular systems are called descriptor systems or generalized state-space systems. They frequently appear in vehicle suspension systems, flexible robots, large-scale electric networks, chemical engineering systems, and complex ecosystems. Singular systems are a more natural description of dynamic systems than the standard state-space systems. This is due to the fact that singular systems can preserve the structure of physical systems more than accurately by including non-dynamic constraints and impulsive elements. In other words, singular systems are described by differential equations coupled with functional equa tions. Consequently, the stability problem is much more complicated than that for standard state-space systems, because it requires considering not only stability, but also regularity and absence of impulses (for continuous-time singular systems) and causality (for discrete-time singular systems). These are some reasons that singular systems not only have practical significance, but also are of great theoretical inter est. The purpose of this book is to present a systematic theory about analysis and synthesis of singular systems by introducing recent theoretical findings. In very few words, this book includes the following eight chapters, namely: Chapter 1 is the introduction; in Chapter 2 dissipative control and filtering for discrete-time linear singular systems are considered; in Chapter 3 the H8-control with transients problem for nonzero initial conditions is solved; in Chapters 4 and 5, considering the time delay, the problems of delay-dependent H8-control and dissipative synthesis for singular delay systems are stated, respec tively; in Chapter 6, for singular Markovian systems, by applying equivalent sets technique, some new formulation of dissipativity conditions are obtained; Chapter 7 carries out sliding mode control (SMC) problem for singular stochastic Markov systems (SSMSs); in Chapter 8, for nonlinear singular systems, by using Takagi-Sugeno (T-S) fuzzy model to describe, the issues of admissibility analysis and controller design for T-S fuzzy singular systems are investigated. By its purpose, this book is a base for further theoretical research or guidance of engineering applications. It can serve as a reference for undergraduate and postgraduate students who are interested in singular systems and can be useful for all automatic control engineers and scientists which must treat and solve problems involving singular systems.\" \u003cb\u003e--zbMath, 2020, Mihail Voicu reviewer, expert opinion\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eAnalysis and Synthesis of Singular Systems\u003c\/i\u003e provides a base for further theoretical research and a design guide for engineering applications of singular systems. The book presents recent advances in analysis and synthesis problems, including state-feedback control, static output feedback control, filtering, dissipative control, H8 control, reliable control, sliding mode control and fuzzy control for linear singular systems and nonlinear singular systems. Less conservative and fresh novel techniques, combined with the linear matrix inequality (LMI) technique, the slack matrix method, and the reciprocally convex combination approach are applied to singular systems. \u003c\/p\u003e  \u003cp\u003eThis book will be of interest to academic researchers, postgraduate and undergraduate students working in control theory and singular systems. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e1. Introduction 2. Dissipative Control and Filtering of Singular Systems 3. H8 Control with Transients for Singular Systems 4. Delay-dependent Admissibility and H8 Control of Discrete Singular Delay Systems 5. Delay-dependent Dissipativity Analysis and Synthesis of Singular Delay Systems 6. State-feedback Control for Singular Markovian Systems 7. Sliding Mode Control of Singular Stochastic Markov Jump Systems 8. Admissibility and Admissibilization for Fuzzy Singular Systems\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mechanical engineering [\u003ca title=\"See our other books on Mechanical engineering\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mechanical%20engineering%20%5BTGB%5D%22\"\u003eTGB\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Academic Press","offers":[{"title":"Default Title","offer_id":46650307019032,"sku":"9780128237397","price":83.97,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780128237397.jpg?v=1694107385"},{"product_id":"classical-recursion-theory-volume-ii-hardback-9780444502056","title":"Classical Recursion Theory, Volume II (Hardback) 9780444502056","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eClassical Recursion Theory, Volume II\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eP. Odifreddi (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444502056, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 7 September 1999\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e0 pages\u003cbr\u003e24.1 x 15.9 x 1.3 cm, 1.52 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"The scope of the material is amazing. For instance, I can think of no other book with a treatment of w-REA sets inductive reference, and models of lambda calculus! This is especially gratifying in a world of continuing mathematical fragmentation.\" \u003cb\u003e--Mathematical Reviews\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eVolume II of \u003ci\u003eClassical Recursion Theory\u003c\/i\u003e describes the universe from a local (bottom-upor synthetical) point of view, and covers the whole spectrum, from therecursive to the arithmetical sets.The first half of the book provides a detailed picture of the computablesets from the perspective of Theoretical Computer Science. Besides giving adetailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexityclasses, ranging from small time and space bounds to the elementary functions,with a particular attention to polynomial time and space computability. It alsodeals with primitive recursive functions and larger classes, which are ofinterest to the proof theorist. The second half of the book starts with the classical theory of recursivelyenumerable sets and degrees, which constitutes the core of Recursion orComputability Theory. Unlike other texts, usually confined to the Turingdegrees, the book covers a variety of other strong reducibilities, studyingboth their individual structures and their mutual relationships. The lastchapters extend the theory to limit sets and arithmetical sets. The volumeends with the first textbook treatment of the enumeration degrees, whichadmit a number of applications from algebra to the Lambda Calculus.The book is a valuable source of information for anyone interested inComplexity and Computability Theory. The student will appreciate the detailedbut informal account of a wide variety of basic topics, while the specialistwill find a wealth of material sketched in exercises and asides. A massivebibliography of more than a thousand titles completes the treatment on thehistorical side.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface. Introduction. Theories of Recursive functions. Hierarchies of recursive functions. Recursively enumerable sets. Recursively enumerable degrees. Limit sets. Arithmetical sets. Arithmetical degrees. Enumeration degrees. Bibliography. Notation index. Subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Numerical analysis [\u003ca title=\"See our other books on Numerical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Numerical%20analysis%20%5BPBKS%5D%22\"\u003ePBKS\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46651418083608,"sku":"9780444502056","price":139.49,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444502056.jpg?v=1694112320"},{"product_id":"theory-of-relations-hardback-9780444505422","title":"Theory of Relations (Hardback) 9780444505422","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTheory of Relations\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eR. Fraisse (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444505422, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 15 December 2000\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e456 pages\u003cbr\u003e22.9 x 15.1 x 2.8 cm, 0.78 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eRelation theory originates with Hausdorff (Mengenlehre 1914) and Sierpinski (Nombres transfinis, 1928) with the study of order types, specially among chains = total orders = linear orders.  One of its first important problems was partially solved by Dushnik, Miller 1940 who, starting from the chain of reals, obtained an infinite strictly decreasing sequence of chains (of continuum power) with respect to embeddability.  In 1948 I conjectured that every strictly decreasing sequence of denumerable chains is finite.  This was affirmatively proved by Laver (1968), in the more general case of denumerable unions of scattered chains (ie: which do not embed the chain Q of rationals), by using the barrier and the better orderin gof Nash-Williams (1965 to 68). \u003cbr\u003eAnother important problem is the extension to posets of classical properties of chains.  For instance one easily sees that a chain A is scattered if the chain of inclusion of its initial intervals is itself scattered (6.1.4).  Let us again define a scattered poset A by the non-embedding of Q in A.  We say that A is finitely free if every antichain restriction of A is finite (antichain = set of mutually incomparable elements of the base). In 1969 Bonnet and Pouzet proved that a poset A is finitely free and scattered iff the ordering of inclusion of initial intervals of A is scattered.  In 1981 Pouzet proved the equivalence with the a priori stronger condition that A is topologically scattered: (see 6.7.4; a more general result is due to Mislove 1984); ie: every non-empty set of initial intervals contains an isolated elements for the simple convergence topology. \u003cbr\u003eIn chapter 9 we begin the general theory of relations, with the notions of local isomorphism, free interpretability and free operator (9.1 to 9.3), which is the relationist version of a free logical formula.  This is generalized by the back-and-forth notions in 10.10: the (k,p)-operator is the relationist version of the elementary formula (first order formula with equality). \u003cbr\u003eChapter 12 connects relation theory with permutations: theorem of the increasing number of orbits (Livingstone, Wagner in 12.4). Also in this chapter homogeneity is introduced, then more deeply studied in the Appendix written by Norbert Saucer. \u003cbr\u003eChapter 13 connects relation theory with finite permutation groups;  the main notions and results are due to Frasnay.  Also mention the extension to relations of adjacent elements, by Hodges, Lachlan, Shelah who by this mean give an exact calculus of the reduction threshold. \u003cbr\u003eThe book covers almost all present knowledge in Relation Theory, from origins (Hausdorff 1914, Sierpinski 1928) to classical results (Frasnay 1965, Laver 1968, Pouzet 1981) until recent important publications (Abraham, Bonnet 1999). \u003cbr\u003eAll results are exposed in axiomatic set theory.  This allows us, for each statement, to specify if it is proved only from ZF axioms of choice, the continuum hypothesis or only the ultrafilter axiom or the axiom of dependent choice, for instance.\u003cbr\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction. 1. Review of axiomatic set theory, relation. 2. Coherence lemma, cofinality, tree, ideal. 3. Ramsey theorem, partition, incidence matrix. 4. Good, bad sequence, well partial ordering. 5. Embeddability between relations and chains. 6. Scattered chain, scattered poset. 7. Well quasi-ordering of scattered chains. 8. Bivalent tableau, Szpilrajn chain. 9. Free operator, chainability, strong interval. 10. Age, \u0026amp;agr\u003cbr\u003e-morphism, back-and-forth. 11. Relative isomorphism, saturated relation. 12. Homogeneous relation, orbit. 13. Compatibility and chainability theorems. A. On countable homogeneous systems: Sauer\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Set theory [\u003ca title=\"See our other books on Set theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Set%20theory%20%5BPBCH%5D%22\"\u003ePBCH\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46651423621400,"sku":"9780444505422","price":129.65,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444505422.jpg?v=1694979892"},{"product_id":"mathematics-and-the-divine-a-historical-study-hardback-9780444503282","title":"Mathematics and the Divine; A Historical Study (Hardback) 9780444503282","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMathematics and the Divine\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eA Historical Study\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003e•\tMoments of brilliant synthesis between mathematical rigor and religious openness\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eTeun Koetsier (Edited by), Luc Bergmans (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444503282, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 9 December 2004\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e716 pages\u003cbr\u003e24 x 16.5 x 3.7 cm, 1.4 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"...Mathematics and the Divine makes a valuable contribution to opening up the history of this topic. It should provide welcome encouragement and assistance to others who would like to explore this arena further for themselves.\" \u003cb\u003e--in THE MATHEMATICAL ASSOCIATION OF AMERICA\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eMathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn’t the Divine that which is immeasurable ?The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man’s quest for the Absolute in the course of history.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e1.\tHo Peng-Yoke, Chinese Number Mysticism\u003cbr\u003e2.\tKim Plofker, Derivation and Revelation: the Legitimacy of Mathematical Models in Indian Cosmology\u003cbr\u003e3.\tReviel Netz, The Pythagoreans\u003cbr\u003e4.\tIan Mueller, Mathematics and the Divine in Plato\u003cbr\u003e5.\tJean-François Mattéi, Nicomachus of Gerasa and the Divine Arithmetical Ladder\u003cbr\u003e6.\tDominic J. O'Meara, Geometry and the Divine in Proclus\u003cbr\u003e7.\tMarie-Pierre Terrien, Religious Architecture and Mathematics during Late Antiquity\u003cbr\u003e8.\tDavid A. King, The Sacred Geography of Islam\u003cbr\u003e9.\tFaith Wallis, 'Number Mystique' in early medieval computus texts\u003cbr\u003e10.\tMaurice-Ruben Hayoun, Is the Divine Universe Divisible\u003cbr\u003e11.\tCharles Lohr, Mathematics and the Divine: Ramon Lull\u003cbr\u003e12.\tHugue Garcia, Christian Gnosis\u003cbr\u003e13.\tEdith Dudley Sylla, Swester Katrei and Gregory of Rimini: Angels, God and Mathematics in the Fourteenth Century\u003cbr\u003e14.\tJean-Michel Counet, Mathematics and the Divine in Nicholas of Cusa\u003cbr\u003e15.\tTeun Koetsier and Karin Reich, Michael Stifel and his Numerology\u003cbr\u003e16.\tIvo Schneider, Between Rosicrucians and Kabbala - the Mathematics of the Biblical Numbers of Johannes Faulhaber\u003cbr\u003e17.\tEberhard Knobloch, Mathematics and the Divine: Athanasius Kircher\u003cbr\u003e18.\tVolker R. Remmert, Galileo, God and Mathematics\u003cbr\u003e19.\tAndré Charrak, The Mathematical Model of Creation According to Kepler\u003cbr\u003e20.\tJean-Marie Nicolle, The Mathematical Analogy in the Proof of God's Existence by Descartes\u003cbr\u003e21.\tDonald Adamson, Pascal's Views on Mathematics and the Divine\u003cbr\u003e22.\tGer Harmsen, Spinoza and the Geometrical Method of Proof\u003cbr\u003e23.\tPhilip Beeley and Siegmund Probst, John Wallis (1616-1703): Mathematician and Divine\u003cbr\u003e24.\tKees de Pater, Newton and the Ocean of Truth\u003cbr\u003e25.\tHerbert Breger, Leibniz: Mathematics and the Divine\u003cbr\u003e26.\tWolfgang Breidert, Berkeley's Defence of the Infinite God in Contrast to the Infinite in Mathematics\u003cbr\u003e27.\tRuediger Thiele, Leonhard Euler and the Divine\u003cbr\u003e28.\tRuediger Thiele, Georg Cantor and the Divine\u003cbr\u003e29.\tLuc Bergmans, Gerrit Mannoury and his Fellow Significians on Mathematics and Mysticism\u003cbr\u003e30.\tTeun Koetsier, Arthur Schopenhauer and L. E. J. Brouwer: A Comparison\u003cbr\u003e31.\tSergei S. Demidov and Charles E. Ford, On the Road to a Unified View: Priest Pavel Florensky - Theologian, Philosopher and Scientist\u003cbr\u003e32.\tFrançois De Gandt, Husserl and Impossible Numbers: a Sceptical Experience\u003cbr\u003e33.\tBruno Pinchard, Symbol and Space According to René Guénon\u003cbr\u003e34.\tTeun Koetsier, Eddington: Science and the Unseen World\u003cbr\u003e35.\tAlbert van der Schoot, The Divined Proportion\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46651424309528,"sku":"9780444503282","price":197.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444503282.jpg?v=1694979913"},{"product_id":"logic-from-russell-to-church-hardback-9780444516206","title":"Logic from Russell to Church (Hardback) 9780444516206","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLogic from Russell to Church\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Edited by), John Woods (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444516206, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 26 May 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1068 pages\u003cbr\u003e28 x 19 x 5 cm, 1.656 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis volume is number five in the 11-volume \u003ci\u003eHandbook of the History of Logic.\u003c\/i\u003e It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003eList of Contributors\u003cbr\u003eRussell's Logic(Andrew D. Irvine)\u003cbr\u003eLogic for Meinongian Object Theory Semantics (Dale Jacquette)\u003cbr\u003eThe Logic of Brouwer and Heyting (Joan Rand Moschovakis)\u003cbr\u003eThoralf Albert Skolem (Jens Erik Fenstad and Hao Wang)\u003cbr\u003eThe Logic of the Tractatus (Michael Potter)\u003cbr\u003eLesniewski's Logic (Peter Simons)\u003cbr\u003eHibert's Proof Theory (Wilfried Sieg)\u003cbr\u003eHilbert's Epsilon Calculus and its Successors(Hartly Slater)\u003cbr\u003eGödel’s Logic (Mark van Atten and Juliette Kennedy)\u003cbr\u003eTarski’s Logic (Keith Simmons)\u003cbr\u003eEmil Post (Alasdair Urquhart)\u003cbr\u003eGentzen’s Logic (Jan von Plato)\u003cbr\u003eLambda-calculus and Combinators in the 20th Century (Felice Cardone and J. Roger Hindley)\u003cbr\u003eThe Logic of Church and Curry (Jonathan P. Seldin) \u003cbr\u003eParadoxes, Self-reference and Truth in the Twentieth Century (Andrea Cantini)\u003cbr\u003eIndex\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematics [\u003ca title=\"See our other books on Mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematics%20%5BPB%5D%22\"\u003ePB\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46651430306072,"sku":"9780444516206","price":178.69,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444516206.jpg?v=1694980017"},{"product_id":"the-rise-of-modern-logic-from-leibniz-to-frege-hardback-9780444516114","title":"The Rise of Modern Logic: from Leibniz to Frege (Hardback) 9780444516114","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Rise of Modern Logic: from Leibniz to Frege\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Edited by), John Woods (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444516114, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 8 March 2004\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e780 pages\u003cbr\u003e24 x 16.5 x 4 cm, 1.53 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eWith the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an \"uneasy\" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface (D.M. Gabbay, J. Woods).\u003cbr\u003eList of Contributors.\u003cbr\u003eLeibniz's Logic (W. Lenzen).\u003cbr\u003eKant: From General to Transcendental Logic (M. Tiles).\u003cbr\u003eHegel's Logic (J.W. Burbidge).\u003cbr\u003eBolzano as Logician (P. Rusnock, R. George).\u003cbr\u003eHusserl's Logic (R. Tieszen).\u003cbr\u003eAlgebraical Logic 1685-1900 (T. Hailperin).\u003cbr\u003eThe Algebra of Logic (V.S. Valencia).\u003cbr\u003eThe Mathematical Turn in Logic (I. Grattan-Guinness).\u003cbr\u003eSchröder's Logic (V. Peckhaus).\u003cbr\u003ePeirce's Logic (R. Hilpinen).\u003cbr\u003eFrege's Logic (P. Sullivan).\u003cbr\u003eIndex.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Philosophy: logic [\u003ca title=\"See our other books on Philosophy: logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Philosophy:%20logic%20%5BHPL%5D%22\"\u003eHPL\u003c\/a\u003e], History: specific events \u0026amp; topics [\u003ca title=\"See our other books on History: specific events \u0026amp; topics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History:%20specific%20events%20\u0026amp;%20topics%20%5BHBT%5D%22\"\u003eHBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"North Holland","offers":[{"title":"Default Title","offer_id":46651433648408,"sku":"9780444516114","price":182.55,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444516114.jpg?v=1694979938"},{"product_id":"quantification-in-nonclassical-logic-hardback-9780444520128","title":"Quantification in Nonclassical Logic (Hardback) 9780444520128","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eQuantification in Nonclassical Logic\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eThis book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Author), Dimitrij Skvortsov (Author), Valentin Shehtman (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444520128, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 9 June 2009\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e640 pages\u003cbr\u003e22.9 x 15.1 x 3.5 cm, 1.16 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eQuantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy andlanguage in ancient times; they were studied by traditional informalmethods until the 20th century. In the last century the tools becamehighly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e1.) Basic Propositional Logic 2.) Basic Predicate Logic3.) Kripke Semantics4.) Algebraic Semantics5.) Metaframe Semantics6.) Kripke completeness for varying domains7.) Kripke completeness for constant domains\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46651440169240,"sku":"9780444520128","price":121.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444520128.jpg?v=1694979994"},{"product_id":"inductive-logic-hardback-9780444529367","title":"Inductive Logic (Hardback) 9780444529367","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eInductive Logic\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003e\u003cp\u003e\u003ci\u003eInductive Logic\u003c\/i\u003e is number 10 in the 11-volume \u003ci\u003eHandbook of the History of Logic.\u003c\/i\u003e\u003c\/p\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDov M. Gabbay (Edited by), John Woods (Edited by), Stephan Hartmann (Volume editor)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444529367\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 5 May 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e800 pages\u003cbr\u003e25.7 x 18.2 x 4 cm, 1.79 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003e\u003ci\u003eInductive Logic\u003c\/i\u003e is number ten in the 11-volume \u003ci\u003eHandbook of the History of Logic\u003c\/i\u003e. While there are many examples were a science split from philosophy and became autonomous (such as physics with Newton and biology with Darwin), and while there are, perhaps, topics that are of exclusively philosophical interest, inductive logic — as this handbook attests — is a research field where philosophers and scientists fruitfully and constructively interact. This handbook covers the rich history of scientific turning points in Inductive Logic, including probability theory and decision theory. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eIntroduction (Dov Gabbay, Stephan Hartman and John Woods)\u003c\/p\u003e \u003cp\u003eInduction before Hume (J. R. Milton)\u003c\/p\u003e \u003cp\u003eHume and the Problem of Induction (Marc Lange)\u003c\/p\u003e \u003cp\u003eThe Debate between Whewell and Mill on the Nature of Scientific Induction (Malcolm Forster)\u003c\/p\u003e \u003cp\u003eAn Explorer upon Untrodden Ground: Peirce on Abduction (Stathis Psillos)\u003c\/p\u003e \u003cp\u003eThe Modern Epistemic Interpretations of Probability: Logicism and Subjectivism (Maria Carla Galavotti)\u003c\/p\u003e \u003cp\u003ePopper and Hypothetico-deductivism (Alan Musgrave)\u003c\/p\u003e \u003cp\u003eHempel and the Paradoxes of Confirmation (Jan Sprenger)\u003c\/p\u003e \u003cp\u003eCarnap and the Logic of Induction (Sandy Zabell)\u003c\/p\u003e \u003cp\u003eThe Development of the Hintikka Program (Ilkka Niiniluoto)\u003c\/p\u003e \u003cp\u003eHans Reichenbach’s Probability Logic (Frederick Eberhardt and Clark Glymour)\u003c\/p\u003e \u003cp\u003eGoodman and the Demise of Syntactic and Semantics Models (Robert Schwartz)\u003c\/p\u003e \u003cp\u003eDevelopment of Subjective Bayesianism (James Joyce)\u003c\/p\u003e \u003cp\u003eVarieties of Bayesianism (Jonathan Weisberg)\u003c\/p\u003e \u003cp\u003eInductive Logic and Empirical Psychology (Nick Chater, Mike Oaksford, Ulrike Hahn and Evan Heit)\u003c\/p\u003e \u003cp\u003eInductive Logic and Statistics (Jan-Willem Romeijn)\u003c\/p\u003e \u003cp\u003eStatistical Learning Theory (Ulrike von Luxburg and Bernhard Schoelkopf)\u003c\/p\u003e \u003cp\u003eFormal Learning Theory in Context (Daniel Osherson and Scott Weinstein)\u003c\/p\u003e \u003cp\u003eMechanizing Induction (Ronald Ortner and Hannes Leitgeb)\u003c\/p\u003e \u003cp\u003eIndex\u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: History of mathematics [\u003ca title=\"See our other books on History of mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20mathematics%20%5BPBX%5D%22\"\u003ePBX\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Freshly Printed Books","offers":[{"title":"Default Title","offer_id":46651491320088,"sku":"9780444529367","price":194.99,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444529367.jpg?v=1694113429"},{"product_id":"algorithms-and-complexity-hardback-9780444880710","title":"Algorithms and Complexity (Hardback) 9780444880710","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eAlgorithms and Complexity\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eBozzano G Luisa (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444880710, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 12 September 1990\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e260 pages\u003cbr\u003e24.4 x 17.5 x 2.2 cm, 1.97 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"...providing professionals and students with a comprehensive overview of the main results and developments in this evolving field.\" \u003cb\u003e--L'Enseignement Mathematique\u003cbr\u003e\u003c\/b\u003e\u003cbr\u003eW. Kern\u003cbr\u003e\"...one of the most useful and needed publications in the field.\"\u003cb\u003e --Optima\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis first part presents chapters on models of computation, complexity theory, data structures, and efficient computation in many recognized sub-disciplines of Theoretical Computer Science.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eMachine Models and Simulations (P. van Emde Boas). A Catalog of Complexity Classes (D.S. Johnson). Machine-Independent Complexity Theory (J.I. Seiferas). Kolmogorov Complexity and its Applications (M. Li, P.M.B. Vit\u0026amp;aacute\u003cbr\u003enyi). Algorithms for Finding Patterns in Strings (A.V. Aho). Data Structures (K. Mehlhorn, A. Tsakalidis). Computational Geometry (F.F. Yao). Algorithmic Motion Planning in Robotics (J.T. Schwartz, M. Sharir). Average-Case Analysis of Algorithms and Data Structures (J.S. Vitter, Ph. Flajolet). Graph Algorithms (J. van Leeuwen). Algebraic Complexity Theory (V. Strassen). Algorithms in Number Theory (A.K. Lenstra, H.W. Lenstra Jr.). Cryptography (R. Rivest). The Complexity of Finite Functions (R.B. Boppana, M. Sipser). Communication Networks (N. Pippenger). VLSI Theory (Th. Lengauer). Parallel Algorithms for Shared-Memory Machines (R.M. Karp, V. Ramachandran). General Purpose Parallel Architectures (L.G. Valiant). Subject Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical theory of computation [\u003ca title=\"See our other books on Mathematical theory of computation\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20theory%20of%20computation%20%5BUYA%5D%22\"\u003eUYA\u003c\/a\u003e], Combinatorics \u0026amp; graph theory [\u003ca title=\"See our other books on Combinatorics \u0026amp; graph theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Combinatorics%20\u0026amp;%20graph%20theory%20%5BPBV%5D%22\"\u003ePBV\u003c\/a\u003e], Optimization [\u003ca title=\"See our other books on Optimization\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Optimization%20%5BPBU%5D%22\"\u003ePBU\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e], Mathematical foundations [\u003ca title=\"See our other books on Mathematical foundations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20foundations%20%5BPBC%5D%22\"\u003ePBC\u003c\/a\u003e], Cybernetics \u0026amp; systems theory [\u003ca title=\"See our other books on Cybernetics \u0026amp; systems theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Cybernetics%20\u0026amp;%20systems%20theory%20%5BGPFC%5D%22\"\u003eGPFC\u003c\/a\u003e], Information theory [\u003ca title=\"See our other books on Information theory\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Information%20theory%20%5BGPF%5D%22\"\u003eGPF\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46651539882264,"sku":"9780444880710","price":48.57,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444880710_e0c94947-1696-4adc-80b4-113e7a0ebf80.jpg?v=1694987468"},{"product_id":"handbook-of-proof-theory-hardback-9780444898401","title":"Handbook of Proof Theory (Hardback) 9780444898401","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eHandbook of Proof Theory\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eS.R. Buss (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780444898401, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 9 July 1998\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e810 pages\u003cbr\u003e23.4 x 15.6 x 4.1 cm, 1.41 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eToshiyasu Arai\u003cbr\u003e\"The Handbook is most welcome in the logic community. I recommend the Handbook to researchers and graduate students in logic, mathematics, computer science, philosophy, linguistics, artificial intelligence, automated reasoning and cognitive sciences.\" \u003cb\u003e--Bulletin of Symbolic Logic\u003c\/b\u003e\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.\u003cp\u003eThe chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.\u003cbr\u003e\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface. List of Contributors. \u003cb\u003eChapter I.\u003c\/b\u003e An Introduction to Proof Theory (S.R. Buss). \u003cb\u003eChapter II.\u003c\/b\u003e First-Order Proof Theory of Arithmetic (S.R. Buss).\u003cb\u003e Chapter III.\u003c\/b\u003e Hierarchies of Provably Recursive Functions (M. Fairtlough, S.S. Wainer). \u003cb\u003eChapter IV.\u003c\/b\u003e Subsystems of Set Theory and Second Order Number Theory (W. Pohlers). \u003cb\u003eChapter V.\u003c\/b\u003e Gödel's Functional (\"Dialectica\") Interpretation (J. Avigad, S. Feferman). \u003cb\u003eChapter VI. \u003c\/b\u003e Realizability (A.S. Troelstra). \u003cb\u003eChapter VII.\u003c\/b\u003e The Logic of Provability (G. Japaridze, D. de Jongh). \u003cb\u003eChapter VIII.\u003c\/b\u003e The Lengths of Proofs (P. Pudl´k). \u003cb\u003eChapter IX.\u003c\/b\u003e A Proof-Theoretic Framework for Logic Programming (G. Jäger, R.F. Stärk). \u003cb\u003eChapter X.\u003c\/b\u003e Types in Logic, Mathematics and Programming (R.L. Constable). Name Index. Subject Index.\u003cbr\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Expert systems \/ knowledge-based systems [\u003ca title=\"See our other books on Expert systems \/ knowledge-based systems\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Expert%20systems%20\/%20knowledge-based%20systems%20%5BUYQE%5D%22\"\u003eUYQE\u003c\/a\u003e], Artificial intelligence [\u003ca title=\"See our other books on Artificial intelligence\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Artificial%20intelligence%20%5BUYQ%5D%22\"\u003eUYQ\u003c\/a\u003e], Algorithms \u0026amp; data structures [\u003ca title=\"See our other books on Algorithms \u0026amp; data structures\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Algorithms%20\u0026amp;%20data%20structures%20%5BUMB%5D%22\"\u003eUMB\u003c\/a\u003e], Discrete mathematics [\u003ca title=\"See our other books on Discrete mathematics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Discrete%20mathematics%20%5BPBD%5D%22\"\u003ePBD\u003c\/a\u003e], Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Elsevier Science","offers":[{"title":"Default Title","offer_id":46651548533016,"sku":"9780444898401","price":96.39,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780444898401_828ecd2e-daae-4d2f-88f4-a8d26341af12.jpg?v=1694987465"},{"product_id":"foundations-of-genetic-algorithms-1991-foga-1-hardback-9781558601703","title":"Foundations of Genetic Algorithms 1991 (FOGA 1) (Hardback) 9781558601703","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFoundations of Genetic Algorithms 1991 (FOGA 1)\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cfont size=\"4\"\u003eGregory J.E. Rawlins (Edited by)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781558601703, Elsevier Science\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 1 September 1991\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e348 pages\u003cbr\u003e24.1 x 15.9 x 2.5 cm, 0.64 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e\u003cp\u003eFoundations of Genetic Algorithms 1991 (FOGA 1) discusses the theoretical foundations of genetic algorithms (GA) and classifier systems.\u003c\/p\u003e  \u003cp\u003eThis book compiles research papers on selection and convergence, coding and representation, problem hardness, deception, classifier system design, variation and recombination, parallelization, and population divergence. Other topics include the non-uniform Walsh-schema transform; spurious correlations and premature convergence in genetic algorithms; and variable default hierarchy separation in a classifier system. The grammar-based genetic algorithm; conditions for implicit parallelism; and analysis of multi-point crossover are also elaborated. This text likewise covers the genetic algorithms for real parameter optimization and isomorphisms of genetic algorithms. This publication is a good reference for students and researchers interested in genetic algorithms. \u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cb\u003ePart 1: Genetic Algorithm Hardness\u003cbr\u003e\u003c\/b\u003e\u003cbr\u003eThe Nonuniform Walsh-Schema Transform\u003cbr\u003e\u003cbr\u003eEpistasis Variance: A Viewpoint on GA-Hardness\u003cbr\u003e\u003cbr\u003eDeceptiveness and Genetic Algorithm Dynamics\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePart 2: Selection and Convergence\u003cbr\u003e\u003c\/b\u003e\u003cbr\u003eAn Extension to the Theory of Convergence and a Proof of the Time Complexity of Genetic Algorithms\u003cbr\u003e\u003cbr\u003eA Comparative Analysis of Selection Schemes Used in Genetic Algorithms\u003cbr\u003e\u003cbr\u003eA Study of Reproduction in Generational and Steady State Genetic Algorithms\u003cbr\u003e\u003cbr\u003eSpurious Correlations and Premature Convergence in Genetic Algorithms\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePart 3: Classifier Systems\u003cbr\u003e\u003c\/b\u003e\u003cbr\u003eRepresenting Attribute-Based Concepts in a Classifier System\u003cbr\u003e\u003cbr\u003eQuasimorphisms or Queasymorphisms? Modeling Finite Automaton Environments\u003cbr\u003e\u003cbr\u003eVariable Default Hierarchy Separation in a Classifier System\u003cbr\u003e\u003cbr\u003e\u003cb\u003ePart 4: Coding and Representation\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eA Hierarchical Approach to Learning the Boolean Multiplexer Function\u003cbr\u003e\u003cbr\u003eA Grammar-Based Genetic Algorithm\u003cbr\u003e\u003cbr\u003eGenetic Algorithms for Real Parameter Optimization\u003cbr\u003e\u003cbr\u003ePart 5: Framework Issues\u003cbr\u003e\u003cbr\u003eFundamental Principles of Deception in Genetic Search\u003cbr\u003e\u003cbr\u003eIsomorphisms of Genetic Algorithms\u003cbr\u003e\u003cbr\u003eConditions for Implicit Parallelism\u003cbr\u003e\u003cbr\u003ePart 6: Variation and Recombination\u003cbr\u003e\u003cbr\u003eThe CHC Adaptive Search Algorithm: How to Have Safe Search When Engaging in Nontraditional Genetic Recombination\u003cbr\u003e\u003cbr\u003eGenetic Operators for Sequencing Problems\u003cbr\u003e\u003cbr\u003eAn Analysis of Multi-Point Crossover\u003cbr\u003e\u003cbr\u003eEvolution in Time and Space—The Parallel Genetic Algorithm\u003cbr\u003e\u003cbr\u003eAuthor Index\u003cbr\u003e\u003cbr\u003eKey Word Index\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Mathematical logic [\u003ca title=\"See our other books on Mathematical logic\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Mathematical%20logic%20%5BPBCD%5D%22\"\u003ePBCD\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Morgan Kaufmann","offers":[{"title":"Default Title","offer_id":46651664040216,"sku":"9781558601703","price":49.99,"currency_code":"GBP","in_stock":false}]}],"url":"https:\/\/freshlyprintedbooks.co.uk\/collections\/mathematical-logic.oembed?page=2","provider":"Freshly Printed Books","version":"1.0","type":"link"}