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.

85Axx Astronomy and astrophysics topics

This subtopic introduces the core ideas in astronomy and astrophysics topics, 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

85A04 General questions in astrodynamics

Overview

This specific topic studies general questions in astrodynamics within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: General questions in astrodynamics

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A05 Galactic and stellar dynamics

Overview

This specific topic studies galactic and stellar dynamics within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Galactic and stellar dynamics

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A15 Galactic and stellar structure

Overview

This specific topic studies galactic and stellar structure within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Galactic and stellar structure

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A20 Planetary atmospheres

Overview

This specific topic studies planetary atmospheres within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Planetary atmospheres

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A25 Radiative transfer

Overview

This specific topic studies radiative transfer within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Radiative transfer

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A30 Hydrodynamic and hydromagnetic problems

Overview

This specific topic studies hydrodynamic and hydromagnetic problems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Hydrodynamic and hydromagnetic problems

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A35 Statistical astronomy

Overview

This specific topic studies statistical astronomy within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Statistical astronomy

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A40 Cosmology

Overview

This specific topic studies cosmology within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Cosmology

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks

85A99 None of the above

Overview

This specific topic studies none of the above within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: None of the above

Useful Links

Key Ideas

  • Core definitions and standard formulations
  • Representative examples and structural results
  • Connections to neighboring methods and applications

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

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

References

Recommended Textbooks