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.

82Dxx Specific physical systems

This subtopic introduces the core ideas in specific physical systems, 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

82D05 Gases

Overview

This specific topic studies gases within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Gases

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.) Gases. Available via Amazon search. — Amazon · Bookshop.org

82D10 Plasmas

Overview

This specific topic studies plasmas within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Plasma (physics)

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.) Plasmas. Available via Amazon search. — Amazon · Bookshop.org

82D15 Liquids

Overview

This specific topic studies liquids within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Liquid

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.) Liquids. Available via Amazon search. — Amazon · Bookshop.org

82D30 Random media and composite materials

Overview

This specific topic studies random media and composite materials within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Random media and composite materials

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.) Random media and composite materials. Available via Amazon search. — Amazon · Bookshop.org

82D40 Magnetic materials

Overview

This specific topic studies magnetic materials within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Magnetic materials

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.) Magnetic materials. Available via Amazon search. — Amazon · Bookshop.org

82D50 Superfluids

Overview

This specific topic studies superfluids within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Superfluids

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.) Superfluids. Available via Amazon search. — Amazon · Bookshop.org

82D55 Superconductors

Overview

This specific topic studies superconductors within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Superconductors

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.) Superconductors. Available via Amazon search. — Amazon · Bookshop.org

82D60 Polymers and polyelectrolytes

Overview

This specific topic studies polymers and polyelectrolytes within statistical mechanics and condensed matter physics. It focuses on core models, structural ideas, and standard analytical techniques, 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: Polymers and polyelectrolytes

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.) Polymers and polyelectrolytes. Available via Amazon search. — Amazon · Bookshop.org