Discrete Mathematics

Key Benefit: This book presents a sound mathematical treatment that increases smoothly in sophistication. Key Topics: The book presents utility-grade discrete math tools so that any reader can understand them, use them, and move on to more advanced mathematical topics. Market: A handy reference for computer scientists.

Sets, Sequences and Functions
Some Warmup Questions
The Natural Numbers
Some Special Sets
Set Operations
Sequences
Functions
Inverses of Functions
Elementary Logic
Informal Introduction
Propositional Calculus
Methods of Proof
Logic in Proofs
Analysis of Arguments
Relations
Relations
Digraphs and Graphs
Matrices
Multiplication of Matrices
Equivalence Relations and Partitions
The Division Algorithm and Z(p)
Induction and Recursion
Loop Invariants
Mathematical Induction
Big-Oh Notation
Recursive Definitions
Recurrence Relations
More Induction
The Euclidean Algorithm
Counting
Basic Counting Techniques
Elementary Probability
Inclusion-Exclusion Principle and Binomial Methods
Counting and Partitions
Pigeon-Hole Principle
Independence in Probability
Introduction to Graphs and Trees
Graphs
Edge Traversal Problems
Trees
Rooted Trees
Vertex Traversal Problems
Minimum Spanning Trees
Recursion, Trees and Algorithms
General Recursion
Recursive Algorithms
Depth-First Search Algorithms
Labeling Algorithms
Polish Notation
Weighted Trees
Digraphs
Digraphs
Weighted Digraphs
Digraph Algorithms
Modifications and Applications of the Algorithms
Boolean Algebra
Boolean Algebras
Isomorphisms of Boolean Algebras
Boolean Expressions
Logic Networks
Karnaugh Maps
More Relations
Partially Ordered Sets
Special Orderings
Properties of General Relations
Closures of Relations
Predicate Calculus and Infinite Sets
Quantifiers
Elementary Predicate Calculus
Infinite Sets
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Table of Contents

Supplemental Materials