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.

93Bxx Controllability and observability

This subtopic introduces the core ideas in controllability and observability, 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

93B03 Attainable sets, reachability

Overview

This specific topic studies attainable sets, reachability within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Attainable sets, reachability

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B05 Controllability

Overview

This specific topic studies controllability within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Controllability

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B07 Observability

Overview

This specific topic studies observability within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Observability

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B10 Canonical forms

Overview

This specific topic studies canonical forms within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Canonical forms

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B11 System structure simplification

Overview

This specific topic studies system structure simplification within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: System structure simplification

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B12 Variable structure systems

Overview

This specific topic studies variable structure systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Variable structure systems

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B15 Realizations from input-output data

Overview

This specific topic studies realizations from input-output data within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Realizations from input-output data

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B17 Transformations

Overview

This specific topic studies transformations within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Transformations

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B18 Linearizations

Overview

This specific topic studies linearizations within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Linearizations

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B20 Minimal systems representations

Overview

This specific topic studies minimal systems representations within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Minimal systems representations

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B25 Algebraic methods in control theory

Overview

This specific topic studies algebraic methods in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Algebraic methods in control theory

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B27 Geometric methods in systems theory

Overview

This specific topic studies geometric methods in systems theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Geometric methods in systems theory

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B28 Operator-theoretic methods

Overview

This specific topic studies operator-theoretic methods within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Operator-theoretic methods

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B30 System identification

Overview

This specific topic studies system identification within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: System identification

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B35 Sensitivity (robustness)

Overview

This specific topic studies sensitivity (robustness) within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Sensitivity (robustness)

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B36 $H^\infty$-control

Overview

This specific topic studies $h^\infty$-control within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: $H^\infty$-control

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B40 Computational methods in systems theory

Overview

This specific topic studies computational methods in systems theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Computational methods in systems theory

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B45 Model predictive control

Overview

This specific topic studies model predictive control within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Model predictive control

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B50 Synthesis problems

Overview

This specific topic studies synthesis problems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Synthesis problems

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B51 Design techniques (robust design, computer-aided design, etc.)

Overview

This specific topic studies design techniques (robust design, computer-aided design, etc.) within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Design techniques (robust design, computer-aided design, etc.)

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B52 Feedback control

Overview

This specific topic studies feedback control within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Feedback control

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B53 Observers

Overview

This specific topic studies observers within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Observers

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B55 Pole and zero placement problems

Overview

This specific topic studies pole and zero placement problems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Pole and zero placement problems

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B60 Eigenvalue problems in control theory

Overview

This specific topic studies eigenvalue problems in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Eigenvalue problems in control theory

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks

93B70 Linearizations

Overview

This specific topic studies linearizations within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Linearizations

Useful Links

Key Ideas

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

Typical Uses

Used to frame precise research questions and choose suitable analytical or computational methods.

Applications

  • Theoretical research and classification work
  • Modeling and abstraction in adjacent mathematical fields
  • Computational workflows where relevant

References

Recommended Textbooks