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.

76Mxx Basic methods and computational fluid mechanics

This subtopic introduces the core ideas in basic methods and computational fluid mechanics, 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

76M10 Finite element methods applied to fluid mechanics

Overview

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

Related Wikipedia Page

Wikipedia search: Finite element methods applied to fluid mechanics

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

76M12 Finite volume methods applied to fluid mechanics

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with finite volume methods applied to fluid mechanics. 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 applied to fluid mechanics

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

76M20 Finite difference methods applied to fluid mechanics

Overview

This specific topic focuses on the core definitions, structural features, and standard questions connected with finite difference methods applied to fluid mechanics. 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 applied to fluid mechanics

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

76M22 Spectral methods applied to fluid mechanics

Overview

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

Related Wikipedia Page

Wikipedia search: Spectral methods applied to fluid mechanics

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

76M28 Particle methods and lattice-gas methods

Overview

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

Related Wikipedia Page

Wikipedia search: Particle methods and lattice-gas 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

76M45 Asymptotic methods, singular perturbations

Overview

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

Related Wikipedia Page

Wikipedia search: Asymptotic methods, singular perturbations

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

76M60 Symmetry analysis, Lie group methods

Overview

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

Related Wikipedia Page

Wikipedia search: Symmetry analysis, Lie group 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