ISBN-10:
0618415386
ISBN-13:
2900618415389
Pub. Date:
02/05/2008
Publisher:
Cengage Learning
Discrete Mathematics / Edition 1

Discrete Mathematics / Edition 1

by Kevin Ferland

Hardcover

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Product Details

ISBN-13: 2900618415389
Publisher: Cengage Learning
Publication date: 02/05/2008
Edition description: Older Edition
Pages: 720
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

Table of Contents

0. Representing Numbers. Part I. Proofs. 1. Logic and Sets. 1.1 Statement Forms and Logical Equivalences. 1.2 Set Notation. 1.3 Quantifiers. 1.4 Set Operations and Identities. 1.5 Valid Arguments. Chapter 1 Review Problems. 2. Basic Proof Writing. 2.1 Direct Demonstration. 2.2 General Demonstration (Part 1). 2.3 General Demonstration (Part 2). 2.4 Indirect Arguments. 2.5 Splitting into Cases. Chapter 2 Review Problems. 3. Elementary Number Theory. 3.1 Divisors. 3.2 Consequences of Well-Ordering. 3.3 Euclid's Algorithm and Lemma. 3.4 Rational Numbers. 3.5 Irrational Numbers. 3.6 Modular Arithmetic. Chapter 3 Review Problems. 4. Indexed by Integers. 4.1 Sequences, Indexing, and Recursion. 4.2 Sigma Notation. 4.3 Mathematical Induction, an Introduction. 4.4 Induction and Summations. 4.5 Strong Induction. 4.6 The Binomial Theorem. Chapter 4 Review Problems. 5. Relations. 5.1 General Relations. 5.2 Special Relations on Sets. 5.3 Basics of Functions. 5.4 Special Functions. 5.5 General Set Constructions. 5.6 Cardinality. Chapter 5 Review Problems. Part II. Combinatorics. 6. Basic Counting. 6.1 The Multiplication Principle. 6.2 Permutations and Combinations. 6.3 Addition and Subtraction. 6.4 Probability. 6.5 Applications of Combinations. 6.6 Correcting for Overcounting. Chapter 6 Review Problems. 7. More Counting. 7.1 Inclusion-Exclusion. 7.2 Multinomial Coefficients. 7.3 Generating Functions. 7.4 Counting Orbits. 7.5 Combinatorial Arguments. Chapter 7 Review Problems. 8. Basic Graph Theory. 8.1 Motivation and Introduction. 8.2 Matrices and Special Graphs. 8.3 Isomorphisms. 8.4 Invariants. 8.5 Directed Graphs and Markov Chains. Chapter 8 Review Problems. 9. Graph Properties. 9.1 Connectivity. 9.2 Euler Circuits. 9.3 Hamiltonian Cycles. 9.4 Planar Graphs. 9.5 Chromatic Number. Chapter 9 Review Problems. 10. Trees and Algorithms. 10.1 Trees. 10.2 Search Trees. 10.3 Weighted Trees. 10.4 Analysis of Algorithms (Part 1). 10.5 Analysis of Algorithms (Part 2). Chapter 10 Review Problems. Appendix A. Assumed Properties of Z and R. Appendix B. Pseudocode.

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