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.

62Rxx Statistics on algebraic/topological structures

This subtopic introduces the core ideas in statistics on algebraic/topological structures, 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

62R01 Statistics on manifolds

Overview

Statistics on manifolds. This topic studies statistics on algebraic and topological structures, including manifold-valued, directional, and shape data.

Related Wikipedia Page

Wikipedia: Directional statistics

Useful Links

Key Ideas

  • non-Euclidean sample spaces
  • geometry-aware inference
  • topological and algebraic constraints in data

Typical Uses

Used when observations live on manifolds, groups, graphs, or other structured spaces.

Applications

  • Computer vision and shape analysis
  • Robotics and orientation data
  • Network and topological data analysis

References

Recommended Textbooks

62R07 Statistical aspects of big data and data science

Overview

Statistical aspects of big data and data science. This topic studies statistics on algebraic and topological structures, including manifold-valued, directional, and shape data.

Related Wikipedia Page

Wikipedia: Directional statistics

Useful Links

Key Ideas

  • non-Euclidean sample spaces
  • geometry-aware inference
  • topological and algebraic constraints in data

Typical Uses

Used when observations live on manifolds, groups, graphs, or other structured spaces.

Applications

  • Computer vision and shape analysis
  • Robotics and orientation data
  • Network and topological data analysis

References

Recommended Textbooks

62R10 Functional data analysis

Overview

Functional data analysis. This topic studies statistics on algebraic and topological structures, including manifold-valued, directional, and shape data.

Related Wikipedia Page

Wikipedia: Directional statistics

Useful Links

Key Ideas

  • non-Euclidean sample spaces
  • geometry-aware inference
  • topological and algebraic constraints in data

Typical Uses

Used when observations live on manifolds, groups, graphs, or other structured spaces.

Applications

  • Computer vision and shape analysis
  • Robotics and orientation data
  • Network and topological data analysis

References

Recommended Textbooks

62R20 Statistics on metric spaces

Overview

Statistics on metric spaces. This topic studies statistics on algebraic and topological structures, including manifold-valued, directional, and shape data.

Related Wikipedia Page

Wikipedia: Directional statistics

Useful Links

Key Ideas

  • non-Euclidean sample spaces
  • geometry-aware inference
  • topological and algebraic constraints in data

Typical Uses

Used when observations live on manifolds, groups, graphs, or other structured spaces.

Applications

  • Computer vision and shape analysis
  • Robotics and orientation data
  • Network and topological data analysis

References

Recommended Textbooks

62R40 Topological data analysis

Overview

Topological data analysis. This topic studies statistics on algebraic and topological structures, including manifold-valued, directional, and shape data.

Related Wikipedia Page

Wikipedia: Directional statistics

Useful Links

Key Ideas

  • non-Euclidean sample spaces
  • geometry-aware inference
  • topological and algebraic constraints in data

Typical Uses

Used when observations live on manifolds, groups, graphs, or other structured spaces.

Applications

  • Computer vision and shape analysis
  • Robotics and orientation data
  • Network and topological data analysis

References

Recommended Textbooks