Discrete Mathematics

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Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

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

Upper-level number theory

• Number representations
• Modular arithmetic
• Polynomials
• 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
• Pushdown automata
• Turing machines
• Cellular automata

Further problems

• Selected problems

Unordered pages

• Axiom of choice
• Naive set theory
• Sieve of Eratosthenes

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