Mathematics A Discrete Introduction

This book is an introduction to mathematics--in particular, it is an introduction to discrete mathematics. There are two primary goals for this book: students will learn to reading and writing proofs, and students will learn the fundamental concepts of discrete mathematics.

1. FUNDAMENTALS
Definition
Theorem
Proof
Counterexample
Boolean Algebra
2. COLLECTIONS
Lists
Factorial
Sets I: Introduction, Subsets
Quantifiers
Sets II: Operations
3. COUNTING AND RELATIONS
Relations
Equivalence Relations
Partitions
Binomial Coefficients
Counting Multisets
Inclusion-Exclusion
4. MORE PROOF
Contradiction
Smallest Counterexample
Introduction
5. FUNCTIONS
Functions
The Pigeonhole Principle
Composition
Permutations
Symmetry
Assorted Notation
6. PROBABILITY
Sample Space
Events
Conditional Probability and Independence
Random Variables
Expectation
7. NUMBER THEORY
Dividing
Greatest Common Divisor
Modular Arithmetic
The Chinese Remainder Theorem
Factoring
8. ALGEBRA
Groups
Group Isomorphism
Subgroups
Fermat's Little Theorem
Public-Key Cryptography I: Introduction
Public-Key Cryptography II: Rabin's Method
Public-Key Cryptography III: RSA
9. GRAPHS
Graph Theory Fundamentals
Subgraphs
Connection
Trees
Eulerian Graphs
Coloring
Planar Graphs
10. PARTIALLY ORDERED SETS
Partially Ordered Sets Fundamentals
Max and Min
Linear Orders
Linear Extensions
Dimension
Lattices
APPENDIXES
A
Lots of Hints and Comments; Some Answers
B
Glossary
C
Fundamentals
Index

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Mathematics A Discrete Introduction

Summary

Table of Contents

Supplemental Materials