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.

68Pxx Data structures and information storage

This subtopic introduces the core ideas in data structures and information storage, 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

68P01 General topics in data structures

Overview

This topic examines general topics in data structures within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P05 Data structures

Overview

This topic examines data structures within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P10 Searching and sorting

Overview

This topic examines searching and sorting within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P12 Computational aspects of data structures

Overview

This topic examines computational aspects of data structures within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P15 Database theory

Overview

This topic examines database theory within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P20 Information storage and retrieval

Overview

This topic examines information storage and retrieval within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P25 Data encryption

Overview

This topic examines data encryption within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P30 Coding and information theory

Overview

This topic examines coding and information theory within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks

68P99 None of the above

Overview

This topic examines none of the above within data structures, storage, retrieval, and information organization, focusing on the conceptual models, algorithmic structures, and evaluative criteria used in modern research and practice. It provides a practical bridge between formal theory and deployable computational methods.

Related Wikipedia Page

Data structure (Wikipedia)

Useful Links

Key Ideas

  • Representation and indexing choices for efficient operations
  • Trade-offs between time complexity, memory usage, and persistence
  • Storage and retrieval models for large-scale information systems

Typical Uses

Used to design efficient storage and query pipelines in databases, search systems, and secure data services.

Applications

  • Database engines and query systems
  • Search and recommendation systems
  • Secure storage and coding pipelines

References

Recommended Textbooks