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.

76Fxx Turbulence

This subtopic introduces the core ideas in turbulence, 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

76F02 Fundamentals of turbulence

Overview

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

Related Wikipedia Page

Wikipedia search: Fundamentals of turbulence

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

76F05 Isotropic turbulence; homogeneous turbulence

Overview

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

Related Wikipedia Page

Wikipedia search: Isotropic turbulence; homogeneous turbulence

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

76F10 Shear flows and turbulence

Overview

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

Related Wikipedia Page

Wikipedia search: Shear flows and turbulence

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

76F25 Turbulent transport, mixing

Overview

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

Related Wikipedia Page

Wikipedia search: Turbulent transport, mixing

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

76F35 Convective turbulence

Overview

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

Related Wikipedia Page

Wikipedia search: Convective turbulence

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

76F55 Statistical turbulence modeling

Overview

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

Related Wikipedia Page

Wikipedia search: Statistical turbulence modeling

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

76F65 Direct numerical and large eddy simulation

Overview

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

Related Wikipedia Page

Wikipedia search: Direct numerical and large eddy simulation

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