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.

86Axx Geophysical processes and methods

This subtopic introduces the core ideas in geophysical processes and 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

86A05 Hydrology, hydrography, oceanography

Overview

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

Related Wikipedia Page

Wikipedia search: Hydrology, hydrography, oceanography

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

86A10 Meteorology and atmospheric physics

Overview

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

Related Wikipedia Page

Wikipedia search: Meteorology and atmospheric physics

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

86A15 Seismology, including tsunami and solitons

Overview

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

Related Wikipedia Page

Wikipedia search: Seismology, including tsunami and solitons

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

86A20 Potentials, prospecting

Overview

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

Related Wikipedia Page

Wikipedia search: Potentials, prospecting

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

86A22 Inverse problems

Overview

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

Related Wikipedia Page

Wikipedia search: Inverse 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

86A25 Geo-electricity and geomagnetism

Overview

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

Related Wikipedia Page

Wikipedia search: Geo-electricity and geomagnetism

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

86A32 Geostatistics

Overview

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

Related Wikipedia Page

Wikipedia search: Geostatistics

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

86A40 Glaciology

Overview

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

Related Wikipedia Page

Wikipedia search: Glaciology

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

86A60 Geological problems

Overview

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

Related Wikipedia Page

Wikipedia search: Geological 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

86A99 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