{"product_id":"the-foundations-of-mathematics-hardback-9780470085011","title":"The Foundations of Mathematics (Hardback) 9780470085011","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eThe Foundations of 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\"\u003eThomas Q. Sibley (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780470085011, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 21 April 2008\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e408 pages\u003cbr\u003e23.6 x 15.5 x 2.8 cm, 0.68 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\u003ci\u003eThe Foundations of Mathematics\u003c\/i\u003e provides a careful introduction to proofs in mathematics, along with basic concepts of logic, set theory and other broadly used areas of mathematics.  The concepts are introduced in a pedagogically effective manner without compromising mathematical accuracy and completeness.  Thus, in Part I students explore concepts before they use them in proofs.  The exercises range from reading comprehension questions and many standard exercises to proving more challenging statements, formulating conjectures and critiquing a variety of false and questionable proofs.  The discussion of metamathematics, including Gödel’s Theorems, and philosophy of mathematics provides an unusual and valuable addition compared to other similar texts\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePART I  \u003cp\u003eChapter 1: LANGUAGE, LOGIC, AND SETS\u003cbr\u003e 1.1 Logic and Language\u003cbr\u003e 1.2 Implication\u003cbr\u003e 1.3 Quantifiers and Definitions\u003cbr\u003e 1.4 Introduction to Sets\u003cbr\u003e 1.5 Introduction to Number Theory\u003cbr\u003e 1.6 Additional Set Theory\u003cbr\u003e Definitions from Chapter 1\u003cbr\u003e Algebraic and Order Properties of Number Systems\u003c\/p\u003e \u003cp\u003eChapter 2: PROOFS\u003cbr\u003e 2.1 Proof Format I: Direct Proofs\u003cbr\u003e 2.2 Proof Format II: Contrapositive and Contradition\u003cbr\u003e 2.3 Proof Format III: Existence, Uniqueness, Or\u003cbr\u003e 2.4 Proof Format IV: Mathematical Induction\u003cbr\u003e The Fundamental Theorem of Arithmetic\u003cbr\u003e 2.5 Further Advice and Practice in Proving\u003cbr\u003e Proof Formats\u003c\/p\u003e \u003cp\u003eChapter 3: FUNCTIONS\u003cbr\u003e 3.1 Definitions\u003cbr\u003e 3.2 Composition, One-to-One, Onto, and Inverses\u003cbr\u003e 3.3 Images and Pre-Images of Sets\u003cbr\u003e Definitions from Chapter 3\u003c\/p\u003e \u003cp\u003eChapter 4: RELATIONS\u003cbr\u003e 4.1 Relations\u003cbr\u003e 4.2 Equivalence Relations\u003cbr\u003e 4.3 Partitions and Equivalence Relations\u003cbr\u003e 4.4 Partial Orders\u003cbr\u003e Definitions from Chapter 4\u003c\/p\u003e \u003cp\u003ePART II\u003c\/p\u003e \u003cp\u003eChapter 5: INFINTE SETS\u003cbr\u003e 5.1 The Sizes of Sets\u003cbr\u003e 5.2 Countable Sets\u003cbr\u003e 5.3 Uncountable Sets\u003cbr\u003e 5.4 The Axiom of Choice and Its Equivalents\u003cbr\u003e Definitions from Chapter 5\u003c\/p\u003e \u003cp\u003eChapter 6: INTRODUCTION TO DISCRETE MATHEMATICS\u003cbr\u003e 6.1 Graph Theory\u003cbr\u003e 6.2 Trees and Algorithms\u003cbr\u003e 6.3 Counting Principles I\u003cbr\u003e 6.4 Counting Principles II\u003cbr\u003e Definitions from Chapter 6\u003c\/p\u003e \u003cp\u003eChapter 7: INTRODUCTION TO ABSTRACT ALGEBRA\u003cbr\u003e 7.1 Operations and Properties\u003cbr\u003e 7.2 Groups\u003cbr\u003e Groups in Geometry\u003cbr\u003e 7.3 Rings and Fields\u003cbr\u003e 7.4 Lattices\u003cbr\u003e 7.5 Homomorphisms\u003cbr\u003e Definitions from Chapter 7\u003c\/p\u003e \u003cp\u003eChapter 8: INTRODUCTION TO ANALYSIS\u003cbr\u003e 8.1 Real Numbers, Approximations, and Exact Values\u003cbr\u003e Zeno’s Paradoxes\u003cbr\u003e 8.2 Limits of Functions\u003cbr\u003e 8.3 Continuous Functions and Counterexamples\u003cbr\u003e Counterexamples in Rational Analysis\u003cbr\u003e 8.4 Sequences and Series\u003cbr\u003e 8.5 Discrete Dynamical Systems\u003cbr\u003e The Intermediate Value Theorem\u003cbr\u003e Definitions for Chapter 8\u003c\/p\u003e \u003cp\u003eChapter 9: METAMATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS\u003cbr\u003e 9.1 Metamathematics\u003cbr\u003e 9.2 The Philosophy of Mathematics\u003cbr\u003e Definitions for Chapter 9\u003c\/p\u003e \u003cp\u003eAppendix: THE GREEK ALPHABET\u003cbr\u003e Answers: SELECTED ANSWERS\u003c\/p\u003e \u003cp\u003eIndex\u003cbr\u003e List of Symbols\u003cbr\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: 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":"Wiley","offers":[{"title":"Brand New","offer_id":52257032929560,"sku":"9780470085011","price":160.29,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9780470085011.jpg?v=1781275914","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/the-foundations-of-mathematics-hardback-9780470085011","provider":"Freshly Printed Books","version":"1.0","type":"link"}