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.

83Cxx General relativity

This subtopic introduces the core ideas in general relativity, 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

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with einstein's equations (general structure, canonical formalism, cauchy problems). It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Einstein's equations (general structure, canonical formalism, Cauchy problems)

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C10 Equations of motion

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with equations of motion. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Equations of motion

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C15 Exact solutions

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with exact solutions. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Exact solutions

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C20 Classes of solutions; algebraically special solutions, metrics with symmetries

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with classes of solutions; algebraically special solutions, metrics with symmetries. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Classes of solutions; algebraically special solutions, metrics with symmetries

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C25 Approximation procedures, weak fields

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with approximation procedures, weak fields. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Approximation procedures, weak fields

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C35 Gravitational waves

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with gravitational waves. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Gravitational waves

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C40 Gravitational energy and conservation laws; groups of motions

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with gravitational energy and conservation laws; groups of motions. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Gravitational energy and conservation laws; groups of motions

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C57 Black holes

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with black holes. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Black holes

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study

83C75 Space-time singularities, cosmic censorship

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with space-time singularities, cosmic censorship. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Space-time singularities, cosmic censorship

Useful Links

Key Ideas

  • Core definitions and equivalent formulations
  • Representative examples and typical counterexamples
  • Connections to neighboring ideas and methods

Typical Uses

This topic is commonly used to frame precise research questions, choose appropriate tools, and organize calculations or constructions within the parent subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic workflows where relevant

References

  • General survey articles and reference works on the surrounding topic
  • Standard monographs and review chapters in the relevant area

Recommended Textbooks

  • An introductory text on the surrounding subtopic
  • An advanced monograph for deeper study