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.

80Axx Thermodynamics and heat transfer fundamentals

This subtopic introduces the core ideas in thermodynamics and heat transfer fundamentals, 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

80A05 Foundations of thermodynamics and heat transfer

Overview

This specific topic studies foundations of thermodynamics and heat transfer 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: Foundations of thermodynamics and heat transfer

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

80A10 Classical thermodynamics, including relativistic thermodynamics

Overview

This specific topic studies classical thermodynamics, including relativistic thermodynamics 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: Classical thermodynamics, including relativistic thermodynamics

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

80A17 Thermodynamics of continua

Overview

This specific topic studies thermodynamics of continua 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: Thermodynamics of continua

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

80A20 Heat and mass transfer, heat flow

Overview

This specific topic studies heat and mass transfer, heat flow 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: Heat and mass transfer, heat flow

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

80A22 Stefan problems, phase changes, etc.

Overview

This specific topic studies stefan problems, phase changes, etc. 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: Stefan problems, phase changes, etc.

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

80A25 Combustion

Overview

This specific topic studies combustion 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: Combustion

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

80A30 Chemical kinetics

Overview

This specific topic studies chemical kinetics 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: Chemical kinetics

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

80A50 Chemistry (general)

Overview

This specific topic studies chemistry (general) 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: Chemistry (general)

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