Preface | |
The MathZone Companion Website To the Student | |
The Foundations: Logic and Proofs | |
Propositional Logic | |
Propositional Equivalences | |
Predicates and Quantifiers | |
Nested Quantifiers | |
Rules of Inference | |
Introduction to Proofs | |
Proof Methods and Strategy End-of-Chapter Material | |
Basic Structures: Sets, Functions, Sequences and Sums | |
Sets | |
Set Operations | |
Functions | |
Sequences and Summations End-of-Chapter Material | |
The Fundamentals: Algorithms, the Integers, and Matrices | |
Algorithms | |
The Growth of Functions | |
Complexity of Algorithms | |
The Integers and Division | |
Primes and Greatest Common Divisors | |
Integers and Algorithms | |
Applications of Number Theory | |
Matrices End-of-Chapter Material | |
Induction and Recursion | |
Mathematical Induction | |
Strong Induction and Well-Ordering | |
Recursive Definitions and Structural Induction | |
Recursive Algorithms | |
Program Correctness End-of-Chapter Material | |
Counting | |
The Basics of Counting | |
The Pigeonhole Principle | |
Permutations and Combinations | |
Binomial Coefficients | |
Generalized Permutations and Combinations | |
Generating Permutations and Combinations End-of-Chapter Material | |
Discrete Probability | |
An Introduction to Discrete Probability | |
Probability Theory | |
Bayes’ Theorem | |
Expected Value and Variance End-of-Chapter Material | |
Advanced Counting Techniques | |
Recurrence Relations | |
Solving Linear Recurrence Relations | |
Divide-and-Conquer Algorithms and Recurrence elations | |
Generating Functions | |
Inclusion-Exclusion | |
Applications of Inclusion-Exclusion End-of-Chapter Material | |
Relations | |
Relations and Their Properties | |
n-ary Relations and Their Applications | |
Representing Relations | |
Closures of Relations | |
Equivalence Relations | |
Partial Orderings End-of-Chapter Material | |
Graphs | |
Graphs and Graph Models | |
Graph Terminology and Special Types of Graphs | |
Representing Graphs and Graph Isomorphism | |
Connectivity | |
Euler and Hamilton Paths | |
Shortest-Path Problems | |
Planar Graphs | |
Graph Coloring End-of-Chapter Material | |
Trees | |
Introduction to Trees | |
Applications of Trees | |
Tree Traversal | |
Spanning Trees | |
Minimum Spanning Trees End-of-Chapter Material | |
Boolean Algebra | |
Boolean Functions | |
Representing Boolean Functions | |
Logic Gates | |
Minimization of Circuits End-of-Chapter Material | |
Modeling Computation | |
Languages and Grammars | |
Finite-State Machines with Output | |
Finite-State Machines with No Output | |
Language Recognition | |
Turing Machines End-of-Chapter Material | |
Appendixes | |
Axioms for the Real Numbers and the Positive Integers | |
Exponential and Logarithmic Functions | |
Pseudocode Suggested Readings | |
Answers to Odd-Numbered Exercises | |
Photo Credits | |
Index of Biographies | |
Index | |
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