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Outline of mathematics

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Title: Outline of mathematics  
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Subject: Universal Decimal Classification, Mathematics, Lists of mathematics topics, Areas of mathematics, Bliss bibliographic classification
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Outline of mathematics

The following outline is provided as an overview of and topical guide to mathematics:

Mathematics – the search for fundamental truths in pattern, quantity, and change. For more on the relationship between mathematics and science, refer to the article on science.

Contents

  • Nature of mathematics 1
    • Mathematics is 1.1
    • General reference 1.2
      • Classification systems 1.2.1
      • Reference databases 1.2.2
  • Subjects 2
    • Quantity 2.1
    • Structure 2.2
    • Space 2.3
    • Change 2.4
    • Foundations and philosophy 2.5
    • Mathematical logic 2.6
    • Discrete mathematics 2.7
    • Applied mathematics 2.8
  • History 3
  • Psychology 4
  • Influential mathematicians 5
  • Mathematical notation 6
  • See also 7
  • External links 8

Nature of mathematics

  • Definitions of mathematics – Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions, all of which are controversial.
  • Philosophy of mathematics – its aim is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives.

Mathematics is

  • an academic discipline – branch of knowledge that is taught and researched at the college or university level. Disciplines are defined (in part), and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties to which their practitioners belong.
  • a formal science – branch of knowledge concerned with the properties of formal systems based on definitions and rules of inference. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world.

General reference

Classification systems

Reference databases

  • Mathematical Reviews – journal and online database published by the American Mathematical Society (AMS) that contains brief synopses (and occasionally evaluations) of many articles in mathematics, statistics and theoretical computer science.
  • Zentralblatt MATH – service providing reviews and abstracts for articles in pure and applied mathematics, published by Springer Science+Business Media. It is a major international reviewing service which covers the entire field of mathematics. It uses the Mathematics Subject Classification codes for organizing their reviews by topic.

Subjects

Quantity

Quantity

Structure

Structure

Space

Space

Change

Change

Foundations and philosophy

Foundations of mathematics

Mathematical logic

Mathematical logic

Discrete mathematics

Discrete mathematics

Applied mathematics

Applied mathematics

History

Psychology

Influential mathematicians

See Lists of mathematicians

Mathematical notation

  • ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)

See also

External links

  • MAA Reviews – The Basic Library List – Mathematical Association of America
  • Naoki's Recommended Books, compiled by Naoki Saito, U. C. Davis
  • A List of Recommended Books in Topology, compiled by Allen Hatcher, Cornell U.
  • Books in algebraic geometry in nLab


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