Discrete Mathematics is an ideal resource for discovering the fundamentals of discrete math. Distinct for the depth with which it covers logic, this text emphasizes problem solving and the application of theory as it carefully guides the reader from basic to more complex topics. Discrete Mathematics, Second Edition illustrates the relationships between key concepts through its thematic organization and provides a seamless transition between subjects. View: 918 Winner at the 46th Annual New England Book Show (2003) in the 'College Covers & Jackets' category This introduction to discrete mathematics prepares future computer scientists, engineers, and mathematicians for success by providing extensive and concentrated coverage of logic, functions, algorithmic analysis, and algebraic structures.
This book differs in several ways from current books about discrete mathematics.It presents an elementary and unified introduction to a collection of topics that has not been available in a single source.A major feature of the book is the.
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1 Puzzles, Patterns, and Mathematical Language 1 1.1 First Examples 1 1.2 Number Puzzles and Sequences 9 1.3 Truth-tellers, Liars, and Propositional Logic 24 1.4 Predicates 40 1.5 Implications 53 1.6 Excursion Validity of Arguments 68 2 A Primer of Mathematical Writing 81 2.1 Mathematical Writing 82 2.2 Proofs about Numbers 98 2.3 Mathematical Induction 110 2.4 More about Induction 122 2.5 Contradiction and the Pigeonhole Principle 132 2.6 Excursion Representations of Numbers 150 2.7 Excursion Modular Arithmetic and Cryptography 166 3 Sets and Boolean Algebra 181 3.1 Set Definitions and Operations 181 3.2 More Operations on Sets 198 3.3 Proving Set Properties 210 3.4 Boolean Algebra 221 3.5 Excursion Logic Circuits 229 4 Functions and Relations 248 4.1 Definitions, Diagrams, and Inverses 249 4.2 The Composition Operation 268 4.3 Properties of Functions and Set Cardinality 283 4.4 Properties of Relations 301 4.5 Equivalence Relations 313 4.6 Numerical Functions in Discrete Math 324 4.7 Excursion Iterated Functions and Chaos 334 4.8 Excursion Growth of Functions 345 5 Combinatorics 368 5.1 Introduction 369 5.2 Basic Rules for Counting 386 5.3 Combinations and the Binomial Theorem 398 5.4 Binary Sequences 408 5.5 Recursive Counting 418 5.6 Excursion Solving Recurrence Relations 423 6 Probability 440 6.1 Introduction 440 6.2 Sum and Product Rules for Probability 448 6.3 Probability in Games of Chance 460 6.4 Expected Value in Games of Chance 466 6.5 Excursion Recursion Revisited 475 6.6 Excursion Matrices and Markov Chains 482 7 Graphs and Trees 505 7.1 Graph Theory 506 7.2 Proofs about Graphs and Trees 519 7.3 Isomorphism and Planarity 533 7.4 Connections to Matrices and Relations 546 7.5 Graphs in Puzzles and Games 567 7.6 Excursion Binary Trees 581 7.Discrete Mathematics With Applications 4e Discrete Mathematics With Applications 4th Edition Pdf Free The main themes of a first course in discrete mathematics are logic and proof, induction and recursion, discrete structures, combinatorics and discrete probability, algorithms and their analysis.
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