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 studies hydrology, hydrography, oceanography within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia: Hydrology

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Hydrology, hydrography, oceanography. Available via Amazon search. — Amazon · Bookshop.org

86A10 Meteorology and atmospheric physics

Overview

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

Related Wikipedia Page

Wikipedia search: Meteorology and atmospheric physics

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Meteorology and atmospheric physics. Available via Amazon search. — Amazon · Bookshop.org

86A15 Seismology, including tsunami and solitons

Overview

This specific topic studies seismology, including tsunami and solitons within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia: Seismology

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Seismology, including tsunami and solitons. Available via Amazon search. — Amazon · Bookshop.org

86A20 Potentials, prospecting

Overview

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

Related Wikipedia Page

Wikipedia: Potential

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Potentials, prospecting. Available via Amazon search. — Amazon · Bookshop.org

86A22 Inverse problems

Overview

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

Related Wikipedia Page

Wikipedia: Inverse problem

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Inverse problems. Available via Amazon search. — Amazon · Bookshop.org

86A25 Geo-electricity and geomagnetism

Overview

This specific topic studies geo-electricity and geomagnetism within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Geo-electricity and geomagnetism

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Geo-electricity and geomagnetism. Available via Amazon search. — Amazon · Bookshop.org

86A32 Geostatistics

Overview

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

Related Wikipedia Page

Wikipedia: Geostatistics

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Geostatistics. Available via Amazon search. — Amazon · Bookshop.org

86A40 Glaciology

Overview

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

Related Wikipedia Page

Wikipedia: Glaciology

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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Glaciology. Available via Amazon search. — Amazon · Bookshop.org

86A60 Geological problems

Overview

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

Related Wikipedia Page

Wikipedia search: Geological 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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) Geological problems. Available via Amazon search. — Amazon · Bookshop.org

86A99 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

  • Rudin, W. (1976) Principles of Mathematical Analysis. 3rd edn. New York, NY: McGraw-Hill. — Amazon · Bookshop.org
  • Topic-focused textbook search (n.d.) None of the above. Available via Amazon search. — Amazon · Bookshop.org