Outline of mathematics

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

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

• Mathematics in the Dewey Decimal Classification system
• Mathematics Subject Classification – alphanumerical classification scheme collaboratively produced by staff of and based on the coverage of the two major mathematical reviewing databases, Mathematical Reviews and Zentralblatt MATH.

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 organising their reviews by topic.

Subjects

Quantity

Quantity –

• Arithmetic –
• Natural numbers –
• Integers –
• Rational numbers –
• Real numbers –
• Complex numbers –
• Infinity –

Structure

Structure –

• Abstract algebra –
• Linear algebra –
• Number theory –
• Order theory –
• Function (mathematics) –

Space

Space –

• Geometry –
• Algebraic geometry –
• Trigonometry –
• Differential geometry –
• Topology –
• Fractal geometry –

Change

Change –

• Calculus –
• Vector calculus –
• Differential equations –
• Dynamical systems –
• Chaos theory –
• Analysis –

Foundations and philosophy

Foundations of mathematics –

• Philosophy of mathematics –
• Category theory –
• Set theory –

Mathematical logic

Mathematical logic –

• Model theory –
• Proof theory –
• Recursion theory –
• Set theory –

Discrete mathematics

Discrete mathematics –

• Combinatorics
• Theory of computation
• Cryptography
• Graph theory

Applied mathematics

Applied mathematics –

• Mathematical physics –
• Analytical mechanics –
• Mathematical fluid dynamics –
• Numerical analysis –
• Mathematical optimization –
• Probability –
• Statistics –
• Mathematical economics –
• Financial mathematics –
• Game theory –
• Mathematical biology –
• Cryptography –
• Operations research –
• Information theory –
• Control theory –
• Dynamical systems –

History

Main article: History of mathematics

• Babylonian mathematics
• Egyptian mathematics
• Indian mathematics
• Greek mathematics
• Chinese mathematics
  • Abacus
• History of the Hindu-Arabic numeral system
• Islamic mathematics
• Japanese mathematics
• History of algebra
• History of geometry
• History of mathematical notation
• History of trigonometry
• History of writing numbers

General concepts

• Algebra
• Area
• Computation
• Coordinate system
• Derivative
• Equation
• Fractal
• Integral
• Length
• Limit
• Logarithm
• Logic
• Matrix
• Pi
• Power
• Proof
• Series
• Set
• Vector space
• Vector (geometric)
• Volume

Influential mathematicians

• Leonhard Euler
• Pythagoras
• Fibonacci

See also

• Lists of mathematics topics

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