Discrete mathematics - eMyTextBooks

Discrete mathematics

Contents

• Introduction

Introductory discrete mathematics

• Set theory
• Functions and relations
• Number theory
• Logic
• Enumeration
• Graph theory
• Recursion

Upper-level discrete mathematics

Upper-level set theory

• Axiomatic set theory
• Zermelo-Frankel Axioms
• Toposes (an alternative foundation)

Upper-level number theory

• Number representations
• Modular arithmetic
• Polynomials and number theory
• Finite fields
• Arithmetic Functions
• Analytic Number Theory

Upper-level logic

• Godel's incompleteness theorem
• Second order logic

Upper-level Combinatorics

Abstract algebra

Abstract algebraic systems

• Groups
• Lattice theory
• Matroids
• Boolean algebra
• Category theory

Algebra over other number systems

• Hypercomplex numbers
• Rings, fields and modules

Others

• Combinatory logic
• Languages and grammars

Automata

• Finite state automata
• Cellular automata

Further problems

• Discrete mathematics:Selected problems

External links

• Companion website to Discrete Mathematics, Fifth Edition, Richard Johnsonbaugh (Prentice-Hall) (http://cwx.prenhall.com/bookbind/pubbooks/johnsonbaugh4/)