Outline of mathematics
Mathematics is a field of study that investigates topics such as number, space, structure, and change. More on the relationship between mathematics and science can be found at Mathematics and science.
- 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.
- 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.
- Mathematical object — an abstract concept in mathematics; an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Each branch of mathematics has its own objects.[a][b]
- Mathematical structure — a set endowed with some additional features on the set (e.g., operation, relation, metric, topology). A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories.
Branches and subjectsEdit
- Arithmetic — (from the Greek ἀριθμός arithmos, 'number' and τική [τέχνη], tiké [téchne], 'art') is a branch of mathematics that consists of the study of numbers and the properties of the traditional mathematical operations on them.
- List of types of numbers
- List of numbers in various languages
- Numeral system, Numeral prefix, List of numeral systems, List of numeral system topics
- Radix, Radix economy, Base (exponentiation), Table of bases
- Mathematical notation, Scientific notation, Positional notation, Notation in probability and statistics, History of mathematical notation, List of mathematical notation systems
- Counting, Measurement
- Operation (mathematics) — an operation is a mathematical function which takes zero or more input values called operands, to a well-defined output value. The number of operands is the arity of the operation.
Foundations and philosophyEdit
- Model theory
- Proof theory
- Set theory
- Type theory
- Recursion theory
- Theory of Computation
- List of logic symbols
- Mathematical chemistry
- Mathematical physics
- Analytical mechanics
- Mathematical fluid dynamics
- Numerical analysis
- Control theory
- Dynamical systems
- Mathematical optimization
- Operations research
- Game theory
- Engineering mathematics
- Mathematical economics
- Financial mathematics
- Information theory
- Mathematical biology
- Babylonian mathematics
- Egyptian mathematics
- Indian mathematics
- Greek mathematics
- Chinese mathematics
- History of the Hindu–Arabic numeral system
- Islamic mathematics
- Japanese mathematics
- History of combinatorics
- History of arithmetic
- History of algebra
- History of geometry
- History of calculus
- History of logic
- History of mathematical notation
- History of trigonometry
- History of writing numbers
- History of statistics
- History of probability
- History of group theory
- History of the function concept
- History of logarithms
- History of the Theory of Numbers
- History of Grandi's series
- History of manifolds and varieties
- 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
- List 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)
- 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.
Journals and databasesEdit
- 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.
- "The Definitive Glossary of Higher Mathematical Jargon — Mathemaical Structure". Math Vault. 2019-08-01. Retrieved 2019-12-09.
- "The Definitive Glossary of Higher Mathematical Jargon — Operation". Math Vault. 2019-08-01. Retrieved 2019-12-10.