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.

20Axx Foundations

This subtopic studies foundations of group theory, including basic definitions, constructions, and the abstract principles underlying group-based algebra.

Specific topics

20A05 Axiomatics and elementary properties of groups

Overview

20A05 studies axiomatics and elementary properties of groups in foundations. It examines the logical and axiomatic foundations of group theory and how formal methods shape group-theoretic arguments.

Related Wikipedia Page

Foundations (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for axiomatics and elementary properties of groups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to frame axioms, logic, and formal reasoning in group theory.

Applications

  • Axioms and formal properties
  • Logic in group theory
  • Foundational approaches to groups

References

Recommended Textbooks

20A10 Metamathematical considerations in group theory

Overview

20A10 studies metamathematical considerations in group theory in foundations. It examines the logical and axiomatic foundations of group theory and how formal methods shape group-theoretic arguments.

Related Wikipedia Page

Foundations (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for metamathematical considerations in group theory
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to frame axioms, logic, and formal reasoning in group theory.

Applications

  • Axioms and formal properties
  • Logic in group theory
  • Foundational approaches to groups

References

Recommended Textbooks

20A15 Applications of logic to group theory

Overview

20A15 studies applications of logic to group theory in foundations. It examines the logical and axiomatic foundations of group theory and how formal methods shape group-theoretic arguments.

Related Wikipedia Page

Foundations (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for applications of logic to group theory
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to frame axioms, logic, and formal reasoning in group theory.

Applications

  • Axioms and formal properties
  • Logic in group theory
  • Foundational approaches to groups

References

Recommended Textbooks