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.

80Mxx Basic methods

This subtopic introduces the core ideas in basic 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

80M10 Finite element, Rayleigh-Ritz and Galerkin methods

Overview

This specific topic studies finite element, rayleigh-ritz and galerkin methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: Finite element, Rayleigh-Ritz and Galerkin methods

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Finite element, Rayleigh-Ritz and Galerkin methods. Available via Amazon search. — Amazon · Bookshop.org

80M12 Finite volume methods

Overview

This specific topic studies finite volume methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia: Finite volume method

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Finite volume methods. Available via Amazon search. — Amazon · Bookshop.org

80M20 Finite difference methods

Overview

This specific topic studies finite difference methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia: Finite difference method

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Finite difference methods. Available via Amazon search. — Amazon · Bookshop.org

80M22 Spectral methods

Overview

This specific topic studies spectral methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia: Spectral method

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Spectral methods. Available via Amazon search. — Amazon · Bookshop.org

80M25 Other numerical methods

Overview

This specific topic studies other numerical methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: Other numerical methods

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Other numerical methods. Available via Amazon search. — Amazon · Bookshop.org

80M30 Variational methods

Overview

This specific topic studies variational methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: Variational methods

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Variational methods. Available via Amazon search. — Amazon · Bookshop.org

80M35 Asymptotic methods

Overview

This specific topic studies asymptotic methods within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: Asymptotic methods

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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.) Asymptotic methods. Available via Amazon search. — Amazon · Bookshop.org

80M99 None of the above

Overview

This specific topic studies none of the above within the broader mathematical setting of the parent subtopic. It focuses on core definitions, structural properties, and standard methods of analysis, giving a concise entry point to the main ideas, representative examples, and the kinds of questions that are typically addressed in this part of the field.

Related Wikipedia Page

Wikipedia search: None of the above

Useful Links

Key Ideas

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

Typical Uses

This topic is commonly used to frame precise research questions, organize proofs or calculations, and choose the appropriate tools for work in the surrounding subtopic.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational or algorithmic 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