Discrete Mathematics

$Discrete$ $Mathematics$

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

Contents

Introduction

Introductory discrete mathematics

1. Set theory
2. Functions and relations
3. Number theory
4. Logic
5. Enumeration
6. Graph theory
7. Recursion
8. Semigroup

Upper-level discrete mathematics

Upper-level set theory

1. Axiomatic set theory
2. Zermelo-Frankel Axioms
3. Topoi

Upper-level number theory

1. Number representations
2. Modular arithmetic
3. Polynomials
4. Finite fields
5. Arithmetic Functions
6. Analytic Number Theory

Upper-level logic

1. Godel's incompleteness theorem
2. Second order logic

Abstract algebra

Abstract algebraic systems

1. Groups
2. Lattice theory
3. Matroids
4. Boolean algebra
5. Category theory

Algebra over other number systems

1. Hypercomplex numbers
2. Rings, fields and modules

Automata

1. Finite state automata
2. Pushdown automata
3. Turing machines
4. Cellular automata

Further problems

1. Selected problems

Unordered pages

1. Combinatory logic
2. Languages and grammars
3. Axiom of choice
4. Naive set theory
5. Sieve of Eratosthenes