{"product_id":"discrete-mathematics-isbn-9780471476023","title":"Discrete Mathematics","description":"These active and well-known authors have come together to create a fresh, innovative, and timely approach to Discrete Math.  One innovation uses several major threads to help weave core topics into a cohesive whole.  Throughout the book the application of mathematical reasoning is emphasized to solve problems while the authors guide the student in thinking about, reading, and writing proofs in a wide variety of contexts.  Another important content thread, as the sub-title implies, is the focus on mathematical puzzles, games and magic tricks to engage students. \u003cp\u003e\u003cb\u003e1 Puzzles, Patterns, and Mathematical Language 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 First Examples 1\u003c\/p\u003e \u003cp\u003e1.2 Number Puzzles and Sequences 9\u003c\/p\u003e \u003cp\u003e1.3 Truth-tellers, Liars, and Propositional Logic 24\u003c\/p\u003e \u003cp\u003e1.4 Predicates 40\u003c\/p\u003e \u003cp\u003e1.5 Implications 53\u003c\/p\u003e \u003cp\u003e1.6 Excursion Validity of Arguments 68\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 A Primer of Mathematical Writing 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Mathematical Writing 82\u003c\/p\u003e \u003cp\u003e2.2 Proofs about Numbers 98\u003c\/p\u003e \u003cp\u003e2.3 Mathematical Induction 110\u003c\/p\u003e \u003cp\u003e2.4 More about Induction 122\u003c\/p\u003e \u003cp\u003e2.5 Contradiction and the Pigeonhole Principle 132\u003c\/p\u003e \u003cp\u003e2.6 Excursion Representations of Numbers 150\u003c\/p\u003e \u003cp\u003e2.7 Excursion Modular Arithmetic and Cryptography 166\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Sets and Boolean Algebra 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Set Definitions and Operations 181\u003c\/p\u003e \u003cp\u003e3.2 More Operations on Sets 198\u003c\/p\u003e \u003cp\u003e3.3 Proving Set Properties 210\u003c\/p\u003e \u003cp\u003e3.4 Boolean Algebra 221\u003c\/p\u003e \u003cp\u003e3.5 Excursion Logic Circuits 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Functions and Relations 248\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Definitions, Diagrams, and Inverses 249\u003c\/p\u003e \u003cp\u003e4.2 The Composition Operation 268\u003c\/p\u003e \u003cp\u003e4.3 Properties of Functions and Set Cardinality 283\u003c\/p\u003e \u003cp\u003e4.4 Properties of Relations 301\u003c\/p\u003e \u003cp\u003e4.5 Equivalence Relations 313\u003c\/p\u003e \u003cp\u003e4.6 Numerical Functions in Discrete Math 324\u003c\/p\u003e \u003cp\u003e4.7 Excursion Iterated Functions and Chaos 334\u003c\/p\u003e \u003cp\u003e4.8 Excursion Growth of Functions 345\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Combinatorics 368\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 369\u003c\/p\u003e \u003cp\u003e5.2 Basic Rules for Counting 386\u003c\/p\u003e \u003cp\u003e5.3 Combinations and the Binomial Theorem 398\u003c\/p\u003e \u003cp\u003e5.4 Binary Sequences 408\u003c\/p\u003e \u003cp\u003e5.5 Recursive Counting 418\u003c\/p\u003e \u003cp\u003e5.6 Excursion Solving Recurrence Relations 423\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Probability 440\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 440\u003c\/p\u003e \u003cp\u003e6.2 Sum and Product Rules for Probability 448\u003c\/p\u003e \u003cp\u003e6.3 Probability in Games of Chance 460\u003c\/p\u003e \u003cp\u003e6.4 Expected Value in Games of Chance 466\u003c\/p\u003e \u003cp\u003e6.5 Excursion Recursion Revisited 475\u003c\/p\u003e \u003cp\u003e6.6 Excursion Matrices and Markov Chains 482\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Graphs and Trees 505\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Graph Theory 506\u003c\/p\u003e \u003cp\u003e7.2 Proofs about Graphs and Trees 519\u003c\/p\u003e \u003cp\u003e7.3 Isomorphism and Planarity 533\u003c\/p\u003e \u003cp\u003e7.4 Connections to Matrices and Relations 546\u003c\/p\u003e \u003cp\u003e7.5 Graphs in Puzzles and Games 567\u003c\/p\u003e \u003cp\u003e7.6 Excursion Binary Trees 581\u003c\/p\u003e \u003cp\u003e7.7 Excursion Hamiltonian Cycles and the TSP 596\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Rules of the Game 613\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eCards 613\u003c\/p\u003e \u003cp\u003eSports 614\u003c\/p\u003e \u003cp\u003eMiscellaneous Games 615\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Matrices and Their Operations 618\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eMatrix Operations 618\u003c\/p\u003e \u003cp\u003eMatrix Arithmetic with Technology 620\u003c\/p\u003e \u003cp\u003eSelected Answers and Hints 625\u003c\/p\u003e \u003cp\u003eReferences and Further Reading 682\u003c\/p\u003e  \u003cb\u003eDoug Ensley\u003c\/b\u003e is a full professor at Shippenshburg University with a Ph.D. from Carnegie Mellon.  He is an active participant in national and regional committees determining the future of the discrete math curriculum, and he regularly speaks at Joint Math and MathFest.  \u003cp\u003e\u003cb\u003eWinston Crawley\u003c\/b\u003e is a full professor and chair of the math department at Shippensburg University.  He has a Ph.D. from University of Tennessee-Knoxville.  Crawley developed the undergraduate computer science curriculum at Shippensburg.\u003c\/p\u003e  Did you know that games and puzzles have given birth to many of today’s deepest mathematical subjects? Now, with Douglas Ensley and Winston Crawley’s \u003ci\u003eIntroduction to Discrete Mathematics\u003c\/i\u003e, you can explore mathematical writing, abstract structures, counting, discrete probability, and graph theory, through games, puzzles, patterns, magic tricks, and real-world problems. You will discover how new mathematical topics can be applied to everyday situations, learn how to work with proofs, and develop your problem-solving skills along the way.  \u003cp\u003e\u003cb\u003eOnline applications help improve your mathematical reasoning.\u003cbr\u003e \u003c\/b\u003eHighly intriguing, interactive Flash-based applications illustrate key mathematical concepts and help you develop your ability to reason mathematically, solve problems, and work with proofs. \u003ci\u003eExplore More\u003c\/i\u003e icons in the text direct you to online activities at www.wiley.com\/college\/ensley.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eImprove your grade with the Student Solutions Manual.\u003c\/b\u003e\u003cbr\u003e A supplementary Student Solutions Manual contains more detailed solutions to selected exercises in the text.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"New","offer_id":44813446709477,"sku":"NP9780471476023","price":194.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780471476023.jpg?v=1761780867","url":"https:\/\/k12savings.com\/products\/discrete-mathematics-isbn-9780471476023","provider":"K12savings","version":"1.0","type":"link"}