{"product_id":"combinatorial-reasoning-an-introduction-to-the-art-of-counting-hardback-9781118652183","title":"Combinatorial Reasoning; An Introduction to the Art of Counting (Hardback) 9781118652183","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eCombinatorial Reasoning\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Introduction to the Art of Counting\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eDuane DeTemple (Author), William Webb (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781118652183, Wiley\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 25 April 2014\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e496 pages\u003cbr\u003e24.3 x 16.1 x 3.2 cm, 0.798 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\u003eWritten by two well-known scholars in the field, \u003ci\u003eCombinatorial Reasoning: An Introduction to the Art of Counting\u003c\/i\u003e presents a clear and comprehensive introduction to the concepts and methodology of beginning combinatorics. Focusing on modern techniques and applications, the book develops a variety of effective approaches to solving counting problems.\u003c\/p\u003e \u003cp\u003eBalancing abstract ideas with specific topical coverage, the book utilizes real world examples with problems ranging from basic calculations that are designed to develop fundamental concepts to more challenging exercises that allow for a deeper exploration of complex combinatorial situations. Simple cases are treated first before moving on to general and more advanced cases. Additional features of the book include:\u003c\/p\u003e \u003cp\u003e• Approximately 700 carefully structured problems designed for readers at multiple levels, many with hints and\/or short answers\u003cbr\u003e • Numerous examples that illustrate problem solving using both combinatorial reasoning and sophisticated algorithmic methods\u003cbr\u003e • A novel approach to the study of recurrence sequences, which simplifies many proofs and calculations\u003cbr\u003e • Concrete examples and diagrams interspersed throughout to further aid comprehension of abstract concepts\u003cbr\u003e • A chapter-by-chapter review to clarify the most crucial concepts covered\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCombinatorial Reasoning: An Introduction to the Art of Counting\u003c\/i\u003e is an excellent textbook for upper-undergraduate and beginning graduate-level courses on introductory combinatorics and discrete mathematics.\u003c\/p\u003e\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I The Basics of Enumerative Combinatorics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Initial EnCOUNTers with Combinatorial Reasoning 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction, 3\u003c\/p\u003e \u003cp\u003e1.2 The Pigeonhole Principle, 3\u003c\/p\u003e \u003cp\u003e1.3 Tiling Chessboards with Dominoes, 13\u003c\/p\u003e \u003cp\u003e1.4 Figurate Numbers, 18\u003c\/p\u003e \u003cp\u003e1.5 Counting Tilings of Rectangles, 24\u003c\/p\u003e \u003cp\u003e1.6 Addition and Multiplication Principles, 33\u003c\/p\u003e \u003cp\u003e1.7 Summary and Additional Problems, 46\u003c\/p\u003e \u003cp\u003eReferences, 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Selections, Arrangements, and Distributions 51\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Introduction, 51\u003c\/p\u003e \u003cp\u003e2.2 Permutations and Combinations, 52\u003c\/p\u003e \u003cp\u003e2.3 Combinatorial Models, 64\u003c\/p\u003e \u003cp\u003e2.4 Permutations and Combinations with Repetitions, 77\u003c\/p\u003e \u003cp\u003e2.5 Distributions to Distinct Recipients, 86\u003c\/p\u003e \u003cp\u003e2.6 Circular Permutations and Derangements, 100\u003c\/p\u003e \u003cp\u003e2.7 Summary and Additional Problems, 109\u003c\/p\u003e \u003cp\u003eReference, 112\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Binomial Series and Generating Functions 113\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction, 113\u003c\/p\u003e \u003cp\u003e3.2 The Binomial and Multinomial Theorems, 114\u003c\/p\u003e \u003cp\u003e3.3 Newton’s Binomial Series, 122\u003c\/p\u003e \u003cp\u003e3.4 Ordinary Generating Functions, 131\u003c\/p\u003e \u003cp\u003e3.5 Exponential Generating Functions, 147\u003c\/p\u003e \u003cp\u003e3.6 Summary and Additional Problems, 163\u003c\/p\u003e \u003cp\u003eReferences, 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Alternating Sums, Inclusion-Exclusion Principle, Rook Polynomials, and Fibonacci Nim 167\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Introduction, 167\u003c\/p\u003e \u003cp\u003e4.2 Evaluating Alternating Sums with the DIE Method, 168\u003c\/p\u003e \u003cp\u003e4.3 The Principle of Inclusion–Exclusion (PIE), 179\u003c\/p\u003e \u003cp\u003e4.4 Rook Polynomials, 191\u003c\/p\u003e \u003cp\u003e4.5 (Optional) Zeckendorf Representations and Fibonacci Nim, 202\u003c\/p\u003e \u003cp\u003e4.6 Summary and Additional Problems, 207\u003c\/p\u003e \u003cp\u003eReferences, 210\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Recurrence Relations 211\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction, 211\u003c\/p\u003e \u003cp\u003e5.2 The Fibonacci Recurrence Relation, 212\u003c\/p\u003e \u003cp\u003e5.3 Second-Order Recurrence Relations, 222\u003c\/p\u003e \u003cp\u003e5.4 Higher-Order Linear Homogeneous Recurrence Relations, 233\u003c\/p\u003e \u003cp\u003e5.5 Nonhomogeneous Recurrence Relations, 247\u003c\/p\u003e \u003cp\u003e5.6 Recurrence Relations and Generating Functions, 257\u003c\/p\u003e \u003cp\u003e5.7 Summary and Additional Problems, 268\u003c\/p\u003e \u003cp\u003eReferences, 273\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Special Numbers 275\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction, 275\u003c\/p\u003e \u003cp\u003e6.2 Stirling Numbers, 275\u003c\/p\u003e \u003cp\u003e6.3 Harmonic Numbers, 296\u003c\/p\u003e \u003cp\u003e6.4 Bernoulli Numbers, 306\u003c\/p\u003e \u003cp\u003e6.5 Eulerian Numbers, 315\u003c\/p\u003e \u003cp\u003e6.6 Partition Numbers, 323\u003c\/p\u003e \u003cp\u003e6.7 Catalan Numbers, 335\u003c\/p\u003e \u003cp\u003e6.8 Summary and Additional Problems, 345\u003c\/p\u003e \u003cp\u003eReferences, 352\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II Two Additional Topics in Enumeration\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Linear Spaces and Recurrence Sequences 355\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction, 355\u003c\/p\u003e \u003cp\u003e7.2 Vector Spaces of Sequences, 356\u003c\/p\u003e \u003cp\u003e7.3 Nonhomogeneous Recurrences and Systems of Recurrences, 367\u003c\/p\u003e \u003cp\u003e7.4 Identities for Recurrence Sequences, 378\u003c\/p\u003e \u003cp\u003e7.5 Summary and Additional Problems, 390\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Counting with Symmetries 393\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction, 393\u003c\/p\u003e \u003cp\u003e8.2 Algebraic Discoveries, 394\u003c\/p\u003e \u003cp\u003e8.3 Burnside’s Lemma, 407\u003c\/p\u003e \u003cp\u003e8.4 The Cycle Index and Pólya’s Method of Enumeration, 417\u003c\/p\u003e \u003cp\u003e8.5 Summary and Additional Problems, 430\u003c\/p\u003e \u003cp\u003eReferences, 432\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III Notations Index, Appendices, and Solutions to Selected Odd Problems \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex of Notations 435\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Mathematical Induction 439\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Principle of Mathematical Induction, 439\u003c\/p\u003e \u003cp\u003eA.2 Principle of Strong Induction, 441\u003c\/p\u003e \u003cp\u003eA.3 Well Ordering Principle, 442\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B Searching the Online Encyclopedia of Integer Sequences (OEIS) 443\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eB. 1 Searching a Sequence, 443\u003c\/p\u003e \u003cp\u003eB. 2 Searching an Array, 444\u003c\/p\u003e \u003cp\u003eB. 3 Other Searches, 444\u003c\/p\u003e \u003cp\u003eB. 4 Beginnings of OEIS, 444\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix C Generalized Vandermonde Determinants 445\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eHints, Short Answers, and Complete Solutions to Selected Odd Problems 449\u003c\/p\u003e \u003cp\u003eIndex 467\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":52421358682392,"sku":"9781118652183","price":90.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781118652183.jpg?v=1784592088","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/combinatorial-reasoning-an-introduction-to-the-art-of-counting-hardback-9781118652183","provider":"Freshly Printed Books","version":"1.0","type":"link"}