Mathematics Branches, Topics, and Sub-Topics

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Search by code, branch, topic, subtopic, or a keyword from the descriptions.

68Nxx Software and programming theory

This subtopic introduces the core ideas in software and programming theory, 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

68N01 General topics in software

Overview

This topic examines general topics in software within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N15 Theory of programming languages

Overview

This topic examines theory of programming languages within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N17 Logic programming

Overview

This topic examines logic programming within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N18 Functional programming and lambda calculus

Overview

This topic examines functional programming and lambda calculus within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N19 Other programming paradigms

Overview

This topic examines other programming paradigms within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N20 Compilers and interpreters

Overview

This topic examines compilers and interpreters within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N25 Operating systems

Overview

This topic examines operating systems within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N27 Abstract data types; algebraic specification

Overview

This topic examines abstract data types; algebraic specification within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N28 Formal aspects of software

Overview

This topic examines formal aspects of software within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N30 Mathematical aspects of software engineering

Overview

This topic examines mathematical aspects of software engineering within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks

68N99 None of the above

Overview

This topic examines none of the above within software, programming languages, and formal software methods, 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

Programming language theory (Wikipedia)

Useful Links

Key Ideas

  • Semantics, type systems, and program correctness principles
  • Language implementation through parsing, compilation, and runtime systems
  • Formal specification and verification for dependable software

Typical Uses

Used to reason about program behavior, language design, tooling correctness, and software lifecycle quality.

Applications

  • Compiler and interpreter development
  • Static analysis and formal verification
  • Reliable software engineering processes

References

Recommended Textbooks