| List of Algorithms | |
| Instructor's Preface | p. ix |
| Student's Preface | p. xiv |
| Chapter Summaries | p. xvii |
| Pathways Through the Book | p. xx |
| Problem Difficulty Rating | p. xxii |
| Symbols, Notation, Abbreviations and Conventions | p. xxiii |
| Prologue: What Is Discrete Algorithmic Mathematics? | p. 1 |
| Mathematical Preliminaries | p. 9 |
| Sets, Relations, and Functions | p. 9 |
| Some Important Functions | p. 20 |
| Growth Rates and Order Notation | p. 30 |
| Summation and Product Notation | p. 40 |
| Matrix Algebra | p. 50 |
| The Language and Methods of Reasoning | p. 56 |
| Supplementary Problems | p. 69 |
| Algorithms | p. 73 |
| Some Examples of Algorithms | p. 73 |
| Aspects of AL | p. 88 |
| Recursive Algorithms | p. 94 |
| Algorithmic Language: Procedures and Functions | p. 105 |
| The Analysis of Algorithms | p. 117 |
| Supplementary Problems | p. 131 |
| Mathematical Induction | p. 135 |
| Introduction | p. 135 |
| First Examples | p. 137 |
| Strong Induction and Other Variants | p. 151 |
| Induction and Recursive Algorithms | p. 158 |
| Induction and Iterative Algorithms | p. 168 |
| How to Conjecture What to Prove | p. 180 |
| Inductive Definitions | p. 194 |
| Faulty Inductions | p. 201 |
| Supplementary Problems | p. 210 |
| Graphs and Trees | p. 217 |
| Examples and Terminology | p. 217 |
| Paths, Cycles and the Adjacency Matrix | p. 236 |
| Eulerian and Hamiltonian Paths and Cycles | p. 250 |
| Shortest Paths | p. 266 |
| Breadth First Search and Depth First Search | p. 278 |
| Coloring Problems | p. 285 |
| Trees | p. 296 |
| Supplementary Problems | p. 311 |
| Fundamental Counting Methods | p. 321 |
| Introduction | p. 321 |
| First Examples: The Sum and Product Rules | p. 322 |
| Subtler Examples and Further Rules | p. 329 |
| Permutations and Combinations | p. 341 |
| Combinatorial Identities and Combinatorial Arguments | p. 348 |
| The Binomial Theorem | p. 355 |
| Four Common Problems with Balls and Urns | p. 365 |
| Generating Functions | p. 375 |
| Combinatorial Algorithms | p. 385 |
| Algorithmic Pigeonholes | p. 399 |
| Supplementary Problems | p. 406 |
| Difference Equations | p. 411 |
| Introduction | p. 411 |
| Modeling with Difference Equations | p. 413 |
| Getting Information from Difference Equations | p. 426 |
| Terminology and a Fundamental Theorem | p. 433 |
| Constant Coefficient Homogeneous Linear Difference Equations | p. 439 |
| Qualitative Analysis | p. 451 |
| Nonhomogeneous Difference Equations | p. 457 |
| Applications to Algorithms | p. 462 |
| Variable Coefficients, Sums, and Recent Advances in Computer Algebra | p. 479 |
| Nonlinear Difference Equations | p. 484 |
| Finite Differences | p. 495 |
| Supplementary Problems | p. 508 |
| Probability | p. 513 |
| Introduction | p. 513 |
| Probability Space | p. 517 |
| Conditional Probability, Independence, and Bayes' Theorem | p. 527 |
| Random Variables and Distributions | p. 539 |
| Expected Value | p. 557 |
| Variance | p. 569 |
| Statistical Estimation | p. 577 |
| Applications to Algorithms: Proofs of Prior Claims | p. 586 |
| Recursive Methods in Probability | p. 595 |
| Supplementary Problems | p. 606 |
| An Introduction to Mathematical Logic | p. 611 |
| Introduction and Terminology | p. 611 |
| The Propositional Calculus | p. 616 |
| Validity and Tautology | p. 630 |
| Algorithm Verification | p. 637 |
| Boolean Algebra | p. 643 |
| The Predicate Calculus | p. 663 |
| Algorithm Verification Using the Predicate Calculus | p. 676 |
| Theorems and Proofs | p. 682 |
| Supplementary Problems | p. 689 |
| Epilogue: Coming Full Circle with Biology and Minimax Theorems | p. 691 |
| DNA Matching | p. 691 |
| Algorithmic Mathematics and Minimax Theorems | p. 707 |
| Final Problems | p. 717 |
| References | p. 723 |
| Limits | p. 729 |
| Hints and Answers | p. 733 |
| Index | p. 761 |
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