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.

78Mxx Basic methods

This subtopic introduces the core ideas in basic methods, 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

78M10 Finite element, Rayleigh-Ritz and Galerkin methods

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with finite element, rayleigh-ritz and galerkin methods. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: Finite element, Rayleigh-Ritz and Galerkin methods

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

78M12 Finite volume methods

Overview

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

Related Wikipedia Page

Wikipedia search: Finite volume methods

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

78M20 Finite difference methods

Overview

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

Related Wikipedia Page

Wikipedia search: Finite difference methods

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

78M22 Spectral methods

Overview

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

Related Wikipedia Page

Wikipedia search: Spectral methods

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

78M25 Other numerical methods

Overview

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

Related Wikipedia Page

Wikipedia search: Other numerical methods

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

78M30 Variational methods

Overview

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

Related Wikipedia Page

Wikipedia search: Variational methods

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

78M35 Asymptotic analysis

Overview

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

Related Wikipedia Page

Wikipedia search: Asymptotic analysis

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

78M99 None of the above

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with none of the above. It provides a concise entry point for understanding how this theme fits into the broader mathematical landscape.

Related Wikipedia Page

Wikipedia search: None of the above

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