subjects(Reference)

Quantity

edit Main article: Quantity See also: Outline of arithmetic and History of arithmetic Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. 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. Elementary arithmetic is the part of arithmetic which deals with basic operations of addition, subtraction, multiplication, and division. Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. Second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. Peano axioms also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19^th century Italian mathematician Giuseppe Peano. Floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. Numbers — a mathematical object used to count, measure, and label. List of types of numbers Natural number, Integer, Rational number, Real number, Irrational number, Transcendental number, Imaginary number, Complex number, Hypercomplex number, p-adic number Negative number, Positive number, Parity (mathematics) Prime number, Composite number Non-standard numbers, including: Infinity, transfinite number, ordinal number, cardinal number, hyperreal number, surreal number, infinitesimal List of numbers in various languages Numeral system, Unary numeral system, Numeral prefix, List of numeral systems, List of numeral system topics Counting, Number line, Numerical digit, Zero Radix, Radix economy, Base (exponentiation), Table of bases Mathematical notation, Infix notation, Scientific notation, Positional notation, Notation in probability and statistics, History of mathematical notation, List of mathematical notation systems Fraction, Decimal, Decimal separator 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. Calculation, Computation, Expression (mathematics), Order of operations, Algorithm Types of Operations: Binary operation, Unary operation, Nullary operation Operands: Order of operations, Addition, Subtraction, Multiplication, Division, Exponentiation, Logarithm, Root Function (mathematics), Inverse function Commutative property, Anticommutative property, Associative property, Additive identity, Distributive property Summation, Product (mathematics), Divisor, Quotient, Greatest common divisor, Quotition and partition, Remainder, Fractional part Subtraction without borrowing, Long division, Short division, Modulo operation, Chunking (division), Multiplication and repeated addition, Euclidean division, Division by zero Plus and minus signs, Multiplication sign, Division sign, Equals sign Equality (mathematics), Inequality (mathematics), Logical equivalence Ratio Variable (mathematics), Constant (mathematics) Measurement

Structure

• algebra
• abstract algebra
• linear algebra
• number theory
• order theory
• function

Space

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

Change

• calculus
• vector calculus
• Differential equations
• chaos theory
• analysis

Philosophy

• philosophy of mathematics
• category theory
• set theory
• Type theory

Logic

• model theory
• proof theory
• set theory
• Type theory
• recursion theory
• Theory of computation
• list of logic symbols
• second-order arithmetic
• peono axioms

Discrete mathematics

• combinatorics
• cryptography
• graph theory
• number theory

Applied mathematics

See also: Outline of probability 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

Psychology

Mathematics education Numeracy Numerical cognition Subitizing Mathematical anxiety Dyscalculia Acalculia Ageometresia Number sense Numerosity adaptation effect Approximate number system Mathematical maturity