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.

60Kxx Special stochastic processes

This subtopic introduces the core ideas in special stochastic processes, 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

60K05 Renewal theory

Overview

Renewal theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K10 Applications of renewal theory

Overview

Applications of renewal theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K15 Markov renewal processes, semi-Markov processes

Overview

Markov renewal processes, semi-Markov processes. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K20 Applications of Markov renewal processes

Overview

Applications of Markov renewal processes. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K25 Queueing theory

Overview

Queueing theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K30 Applications of queueing theory

Overview

Applications of queueing theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K35 Interacting random processes; statistical mechanics type models; percolation theory

Overview

Interacting random processes; statistical mechanics type models; percolation theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K37 Processes in random environments

Overview

Processes in random environments. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K40 Other physical applications of random processes

Overview

Other physical applications of random processes. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K50 Anomalous diffusion models, Lévy flights

Overview

Anomalous diffusion models, Lévy flights. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks

60K99 None of the above

Overview

None of the above. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.

Related Wikipedia Page

Wikipedia: Queueing theory

Useful Links

Key Ideas

  • model-specific stochastic dynamics
  • interacting and structured randomness
  • exact and asymptotic process analysis

Typical Uses

Used for canonical stochastic models where specialized structure permits deeper analysis.

Applications

  • Communication networks
  • Population and epidemic modeling
  • Reliability and service systems

References

Recommended Textbooks