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.

93Cxx System structure and realization

This subtopic introduces the core ideas in system structure and realization, 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

93C05 Linear systems in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Linear systems 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

93C10 Nonlinear systems in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Nonlinear systems 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

93C15 Systems governed by ODEs in control theory

Overview

This specific topic studies systems governed by odes in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Systems governed by ODEs 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

93C20 Systems governed by PDEs in control theory

Overview

This specific topic studies systems governed by pdes in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Systems governed by PDEs 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

93C23 Systems governed by functional-differential equations in control theory

Overview

This specific topic studies systems governed by functional-differential equations in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Systems governed by functional-differential equations 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

93C25 Systems in abstract spaces in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Systems in abstract spaces 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

93C28 Dynamical systems in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Dynamical systems 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

93C30 Systems governed by functional relations other than differential equations in control theory

Overview

This specific topic studies systems governed by functional relations other than differential equations in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Systems governed by functional relations other than differential equations 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

93C35 Multivariable systems in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Multivariable systems 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

93C40 Adaptive control/observation systems

Overview

This specific topic studies adaptive control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Adaptive control/observation 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

93C41 Problems with incomplete information in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Problems with incomplete information 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

93C42 Fuzzy control/observation systems

Overview

This specific topic studies fuzzy control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Fuzzy control/observation 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

93C43 Delay control/observation systems

Overview

This specific topic studies delay control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Delay control/observation 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

93C48 Hybrid systems

Overview

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

Related Wikipedia Page

Wikipedia search: Hybrid 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

93C55 Discrete-time control/observation systems

Overview

This specific topic studies discrete-time control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Discrete-time control/observation 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

93C57 Sampled-data control/observation systems

Overview

This specific topic studies sampled-data control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Sampled-data control/observation 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

93C62 Digital control/observation systems

Overview

This specific topic studies digital control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Digital control/observation 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

93C65 Discrete event control/observation systems

Overview

This specific topic studies discrete event control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Discrete event control/observation 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

93C70 Time-scale analysis and singular perturbations in control theory

Overview

This specific topic studies time-scale analysis and singular perturbations in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Time-scale analysis and singular perturbations 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

93C73 Perturbations in control/observation systems

Overview

This specific topic studies perturbations in control/observation systems within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Perturbations in control/observation 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

93C80 Frequency-response methods in control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Frequency-response 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

93C83 Control/observation systems involving computers (process control, etc.)

Overview

This specific topic studies control/observation systems involving computers (process control, etc.) within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Control/observation systems involving computers (process control, 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

93C85 Automated systems (robots, etc.) in control theory

Overview

This specific topic studies automated systems (robots, etc.) in control theory within its parent subtopic, emphasizing core definitions, structural results, and standard techniques.

Related Wikipedia Page

Wikipedia search: Automated systems (robots, etc.) 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

93C95 Applications of control theory

Overview

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

Related Wikipedia Page

Wikipedia search: Applications of 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