Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

68Rxx Discrete mathematics in relation to CS

This subtopic introduces the core ideas in discrete mathematics in relation to cs, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.

Specific topics

68R01 General topics in discrete mathematics in relation to computer science

Overview

This topic examines general topics in discrete mathematics in relation to computer science within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R05 Combinatorics in computer science

Overview

This topic examines combinatorics in computer science within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R07 Extremal combinatorics in computer science

Overview

This topic examines extremal combinatorics in computer science within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R10 Graph theory in computer science

Overview

This topic examines graph theory in computer science within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R12 Hypergraph theory in computer science

Overview

This topic examines hypergraph theory in computer science within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R15 Combinatorics on words

Overview

This topic examines combinatorics on words within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R20 Coding theory

Overview

This topic examines coding theory within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks

68R99 None of the above

Overview

This topic examines none of the above within discrete mathematics and combinatorial methods in computer science, focusing on the main concepts, representational choices, and standard questions used in modern research and practice. It provides a concise starting point for understanding how the topic fits into the wider field.

Related Wikipedia Page

Discrete mathematics (Wikipedia)

Useful Links

Key Ideas

  • Combinatorial structures and finite-state reasoning
  • Graph-theoretic representations and counting methods
  • Algorithmic use of discrete models and transformations

Typical Uses

Used to model, count, and analyze discrete structures that arise in algorithms, networks, and optimization.

Applications

  • Network design and scheduling
  • Combinatorial optimization
  • Finite-state and symbolic computation

References

Recommended Textbooks