# Discrete mathematics

Subject classification: this is a mathematics resource. |

Development status: this resource is experimental in nature. |

Completion status: this resource is ~10% complete. |

Educational level: this is a tertiary (university) resource. |

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**Welcome to the Main Page of Discrete Mathematics!**

These are the main topics we are going over in the course:

Welcome to the Topic of Discrete Mathematics, a department of the School of Mathematics and School of Computer Science. Discrete mathematics is very important for studying computer science.

## Why Learn Discrete Mathematics?

[edit | edit source]While many of the topics within Discrete Mathematics have been around for a long time, traditional education typically focused on Continuous Mathematics, such as calculus. With the widespread adoption of computers, the usefulness of discrete mathematics has dramatically increased. From basic logic in circuits, to number theory and cryptography, computer science inevitably relies upon discrete mathematics.

**Learning discrete mathematics will...**

- Develop your critical thinking and formal reasoning skills.
- Provide a foundation for learning computer science.
- Develop your programming abilities (regardless of whether you have programmed before).
- Familiarize you with the many different branches of mathematics.
- Help you to "read mathematics."

## Homework

[edit | edit source]To come.

## Complete List of Subjects

[edit | edit source]Discrete Mathematics is a broad subject encompassing several formal systems for dealing with discrete quantities. If you are studying Discrete Mathematics as part of a related field, you may wish to follow a streamlined set of core topics that you need. A complete list of Discrete Mathematics topics is given below.

- Algorithmics
- Collections
- Combinatorics
- Complexity
- Computability
- Counting
- Digital geometry
- Digital topology
- Functions
- Graph theory
- Information theory
- Linear algebra
- Markov chains
- Number theory
- Partially Ordered Sets
- Probability
- Proofs
- Relations

## Notable Textbooks

[edit | edit source]*Discrete Mathematics With Applications*by Susanna S. Epp- w:
*Concrete Mathematics: A Foundation for Computer Science*by Donald Knuth. - Discrete Mathematics. An Open Introduction 3rd Edition by Oscar Levin

## Off-site courses

[edit | edit source]*Discrete Math*, Michael Damron, New York University, Fall 2008. (Earlier versions: Spring 2007)*Introduction to Contemporary Mathematics*, Larry Bowen, University of Alabama.*Discrete Structures*, Margaret Fleck and Eric Shaffer, Spring 2009*Discrete Mathematics*, Ben Maloney, University of Wollongong, Summer 2010-2011.*Discrete Mathematics I*, Peter G. Binev, University of South Carolina, Fall 2006.