Mathematics is a field of study that investigates topics including number, space, structure, and change. For more on the relationship between mathematics and science, refer to the article on science.

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 at all levels of education and researched typically 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 physical 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 organizing their reviews by topic.

Subjects

Quantity

Quantity

Arithmetic

Natural numbers

Integers

Rational numbers

Real numbers

Complex numbers

Hypercomplex numbers

Infinity

Structure

Structure

Algebra

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

Type theory

Mathematical logic

See also: Outline of mathematical logic

Mathematical logic

Model theory

Proof theory

Set theory

Type theory

Recursion theory

Theory of Computation

Discrete mathematics

Discrete mathematics

Combinatorics (outline)

Cryptography

Graph theory

Applied mathematics

Applied mathematics

Mathematical chemistry

Mathematical physics

Analytical mechanics

Mathematical fluid dynamics

Numerical analysis

Control theory

Dynamical systems

Mathematical optimization

Operations research

Probability

Statistics

Game theory

Engineering mathematics

Mathematical economics

Financial mathematics

Information theory

Cryptography

Mathematical biology

History

History of mathematics

Babylonian mathematics

Egyptian mathematics

Indian mathematics

Greek mathematics

Chinese mathematics

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

Psychology

Mathematics education

Numeracy

Numerical Cognition

Subitizing

Mathematical anxiety

Dyscalculia

Acalculia

Ageometresia

Number sense

Numerosity adaptation effect

Approximate number system

Mathematical maturity

Influential mathematicians

See Lists of mathematicians.

Mathematical notation

Mathematical notation

List of mathematical abbreviations

List of mathematical symbols

List of mathematical symbols by subject

Table of mathematical symbols by introduction date

Notation in probability and statistics

Table of logic symbols

Physical constants

Greek letters used in mathematics, science, and engineering

Latin letters used in mathematics

Mathematical alphanumeric symbols

Mathematical operators and symbols in Unicode

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

See also

iconMathematics portal

Lists of mathematics topics

Areas of mathematics

Glossary of areas of mathematics

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

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Hellenica World - Scientific Library

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