Mathematics is a field of study that investigates topics such as

number A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers ...

space Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually con ...

, structure, and change.

Philosophy

Nature

Definitions of mathematics Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions. All proposed definitions are controversial in their own ways. Early definitions Pythago ...

– Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions, all of which are controversial. *

Language of mathematics The language of mathematics or mathematical language is an extension of the natural language (for example English) that is used in mathematics and in science for expressing results (scientific laws, theorems, proofs, logical deductions, etc) wi ...

is the system used by

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

s to communicate

mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

ideas among themselves, and is distinct from natural languages in that it aims to communicate abstract, logical ideas with precision and unambiguity. *

Philosophy of mathematics The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in peopl ...

– 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. :* Classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premis ...

and ZFC set theory. :*

Constructive mathematics In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists. Contrastingly, in classical mathematics, one can prove t ...

asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. In classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption. :*

Predicative mathematics In mathematics, logic and philosophy of mathematics, something that is impredicative is a self-referencing definition. Roughly speaking, a definition is impredicative if it invokes (mentions or quantifies over) the set being defined, or (more co ...

Mathematics is

* An

academic discipline An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membershi ...

– 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 Formal science is a branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, gam ...

– 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.

Concepts

Mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical ...

abstract concept Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by sev ...

in mathematics; an ''object'' is anything that has been (or could be) formally defined, and with which one may do

deductive reasoning Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. if it is impossible for the premises to be true and the conclusion to be false ...

and

mathematical proof A mathematical proof is an Inference, inferential Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previo ...

s. Each branch of mathematics has its own objects. *

Mathematical structure In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additi ...

a set endowed with some additional features on the set (e.g.,

operation Operation or Operations may refer to: Arts, entertainment and media * ''Operation'' (game), a battery-operated board game that challenges dexterity * Operation (music), a term used in musical set theory * ''Operations'' (magazine), Multi-Man ...

, relation,

metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement * An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement Mathematics In mathem ...

topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

). A partial list of possible structures are

measures Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Mea ...

algebraic structure In mathematics, an algebraic structure consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplication), and a finite set ...

s (

group A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic ide ...

field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grass ...

s, etc.),

topologies In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...

, metric structures (

geometries This is a list of geometry topics. Types, methodologies, and terminologies of geometry. * Absolute geometry * Affine geometry * Algebraic geometry * Analytic geometry * Archimedes' use of infinitesimals * Birational geometry * Complex geomet ...

orders Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of ...

events Event may refer to: Gatherings of people * Ceremony, an event of ritual significance, performed on a special occasion * Convention (meeting), a gathering of individuals engaged in some common interest * Event management, the organization of ev ...

equivalence relation In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. Each equivalence relatio ...

differential structure In mathematics, an ''n''- dimensional differential structure (or differentiable structure) on a set ''M'' makes ''M'' into an ''n''-dimensional differential manifold, which is a topological manifold with some additional structure that allows for ...

s, and

categories Category, plural categories, may refer to: Philosophy and general uses *Categorization, categories in cognitive science, information science and generally *Category of being * ''Categories'' (Aristotle) *Category (Kant) *Categories (Peirce) *C ...

. :*

Equivalent definitions of mathematical structures In mathematics, equivalent definitions are used in two somewhat different ways. First, within a particular mathematical theory (for example, Euclidean geometry), a notion (for example, ellipse or minimal surface) may have more than one definition. ...

Abstraction Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or " concrete") signifiers, first principles, or other methods. "An a ...

the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent

phenomena A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried ...

Branches and subjects

Quantity

Number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

is a branch of

pure mathematics Pure mathematics is the study of mathematical concepts independently of any application outside mathematics. These concepts may originate in real-world concerns, and the results obtained may later turn out to be useful for practical applications ...

devoted primarily to the study of the

integers An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

and

integer-valued function In mathematics, an integer-valued function is a function whose values are integers. In other words, it is a function that assigns an integer to each member of its domain. Floor and ceiling functions are examples of an integer-valued function of ...

s. *

Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th c ...

(from the

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

ἀριθμός ''arithmos'', 'number' and τική �έχνη ''tiké échne', '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 The operators in elementary arithmetic are addition, subtraction, multiplication, and division. The operators can be applied on both real numbers and imaginary numbers. Each kind of number is represented on a number line designated to the ty ...

is the part of arithmetic which deals with basic operations of addition, subtraction, multiplication, and division. :*

Modular arithmetic In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his bo ...

Second-order arithmetic In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. A precu ...

is a collection of axiomatic systems that formalize the natural numbers and their subsets. :*

Peano axioms In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. These axioms have been used nearly ...

also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano. :*

Floating-point arithmetic In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can b ...

is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. *

Numbers A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers ca ...

mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical ...

used to count, measure, and label. :*

List of types of numbers Numbers can be classified according to how they are represented or according to the properties that they have. Main types * Natural numbers (\mathbb): The counting numbers are commonly called natural numbers; however, other definitions inclu ...

::*

Natural number In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called '' cardinal ...

Integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...

Rational number In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ra ...

Real number In mathematics, a real number is a number that can be used to measurement, measure a ''continuous'' one-dimensional quantity such as a distance, time, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small var ...

Irrational number In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two inte ...

Transcendental number In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are and . Though only a few classe ...

Imaginary number An imaginary number is a real number multiplied by the imaginary unit , is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property . The square of an imaginary number is . Fo ...

Complex number In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the for ...

Hypercomplex number In mathematics, hypercomplex number is a traditional term for an element of a finite-dimensional unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th century forms the basis of modern group represe ...

p-adic number In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The exte ...

::*

Negative number In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is inequality (mathematics), less than 0 (number), zero. Negative numbers are often used to represent the magnitude of a loss ...

Positive number In mathematics, the sign of a real number is its property of being either positive, negative, or zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also se ...

Parity (mathematics) In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not.. For example, −4, 0, 82 are even because \begin -2 \cdot 2 &= -4 \\ 0 \cdot 2 &= 0 \\ 41 ...

::*

Prime number A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only way ...

Composite number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, ...

::*Non-standard numbers, including:

Infinity Infinity is that which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol . Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions am ...

transfinite number In mathematics, transfinite numbers are numbers that are " infinite" in the sense that they are larger than all finite numbers, yet not necessarily absolutely infinite. These include the transfinite cardinals, which are cardinal numbers used to q ...

, ordinal number,

cardinal number In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality (size) of sets. The cardinality of a finite set is a natural number: the number of elements in the set. T ...

hyperreal number In mathematics, the system of hyperreal numbers is a way of treating infinite and infinitesimal (infinitely small but non-zero) quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbe ...

surreal number In mathematics, the surreal number system is a totally ordered proper class containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surrea ...

, infinitesimal :*

List of numbers in various languages A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby union ...

Numeral system A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symb ...

Unary numeral system The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number ''N'', a symbol representing 1 is repeated ''N'' times. In the unary system, the number 0 (zero) is represented by the empty string, th ...

Numeral prefix Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: * unicycle, bicycle, tricycle (1-cycle, 2-cycle, 3-cyc ...

List of numeral systems There are many different numeral systems, that is, writing systems for expressing numbers. By culture / time period By type of notation Numeral systems are classified here as to whether they use positional notation (also known as place-value ...

List of numeral system topics This is a list of Wikipedia articles on topics of numeral system and "numeric representations" See also: computer numbering formats and number names. Arranged by base * Radix, radix point, mixed radix, base (mathematics) * Unary numeral syste ...

Counting Counting is the process of determining the number of elements of a finite set of objects, i.e., determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every elem ...

Number line In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a po ...

Numerical digit A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin ...

Zero 0 (zero) is a number representing an empty quantity. In place-value notation such as the Hindu–Arabic numeral system, 0 also serves as a placeholder numerical digit, which works by multiplying digits to the left of 0 by the radix, usu ...

::* Radix,

Radix economy The radix economy of a number in a particular base (or radix) is the number of digits needed to express it in that base, multiplied by the base (the number of possible values each digit could have). This is one of various proposals that have been ...

Base (exponentiation) In exponentiation, the base is the number b in an expression of the form bn. Related terms The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more comm ...

Table of bases This table of bases gives the values of 0 to 256 in bases 2 to 36, using A−Z for 10−35. "Base" (or "radix") is a term used in discussions of numeral systems which use place-value notation for representing numbers. Base 10 is in bold. ...

Mathematical notation Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas. Mathematical notation is widely used in mathe ...

Infix notation Infix notation is the notation commonly used in arithmetical and logical formulae and statements. It is characterized by the placement of operators between operands—"infixed operators"—such as the plus sign in . Usage Binary relations are ...

Scientific notation Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, o ...

, Positional notation,

Notation in probability and statistics Probability theory and statistics have some commonly used conventions, in addition to standard mathematical notation and mathematical symbols. Probability theory * Random variables are usually written in upper case roman letters: ''X'', ''Y'', ...

History of mathematical notation The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness. Mathematical ...

List of mathematical notation systems A list is a set of discrete items of information collected and set forth in some format for utility, entertainment, or other purposes. A list may be memorialized in any number of ways, including existing only in the mind of the list-maker, but ...

Fraction A fraction (from la, fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight ...

, Decimal,

Decimal separator A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form (e.g., "." in 12.45). Different countries officially designate different symbols for use as the separator. The ch ...

Operation (mathematics) In mathematics, an operation is a function which takes zero or more input values (also called "'' operands''" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operat ...

an operation is a

mathematical function In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the func ...

which takes zero or more input values called

operand In mathematics, an operand is the object of a mathematical operation, i.e., it is the object or quantity that is operated on. Example The following arithmetic expression shows an example of operators and operands: :3 + 6 = 9 In the above exa ...

s, to a well-defined output value. The number of operands is the

arity Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In ...

of the operation. :*

Calculation A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to t ...

Computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as '' computers''. An esp ...

Expression (mathematics) In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, ...

Order of operations In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For exam ...

Algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

:*Types of Operations:

Binary operation In mathematics, a binary operation or dyadic operation is a rule for combining two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two. More specifically, an internal binary op ...

Unary operation In mathematics, an unary operation is an operation with only one operand, i.e. a single input. This is in contrast to binary operations, which use two operands. An example is any function , where is a set. The function is a unary operation ...

Nullary operation Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. ...

:*Operands:

Addition Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or ''sum'' of ...

Subtraction Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...

Multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being ad ...

Division Division or divider may refer to: Mathematics *Division (mathematics), the inverse of multiplication *Division algorithm, a method for computing the result of mathematical division Military * Division (military), a formation typically consisting ...

Exponentiation Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...

Logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...

Root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...

::*

Function (mathematics) In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the func ...

Inverse function In mathematics, the inverse function of a function (also called the inverse of ) is a function that undoes the operation of . The inverse of exists if and only if is bijective, and if it exists, is denoted by f^ . For a function f\colon ...

::*

Commutative property In mathematics, a binary operation is commutative if changing the order of the operands does not change the result. It is a fundamental property of many binary operations, and many mathematical proofs depend on it. Most familiar as the name of ...

Anticommutative property In mathematics, anticommutativity is a specific property of some non-commutative mathematical Operation (mathematics), operations. Swapping the position of Binary operation, two arguments of an antisymmetric operation yields a result which is the ...

Associative property In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacemen ...

Additive identity In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element ''x'' in the set, yields ''x''. One of the most familiar additive identities is the number 0 from eleme ...

Distributive property In mathematics, the distributive property of binary operations generalizes the distributive law, which asserts that the equality x \cdot (y + z) = x \cdot y + x \cdot z is always true in elementary algebra. For example, in elementary arithmetic ...

::*

Summation In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, m ...

Product (mathematics) In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called ''factors''. For example, 30 is the product of 6 and 5 (the result of multiplication), and x\c ...

Divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...

Quotient In arithmetic, a quotient (from lat, quotiens 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a ...

Greatest common divisor In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers ''x'', ''y'', the greatest common divisor of ''x'' and ''y'' i ...

Quotition and partition In arithmetic, quotition and partition are two ways of viewing fractions and division. In quotition division one asks, "how many parts are there?"; While in partition division one asks, "what is the size of each part?". For example, the expressio ...

Remainder In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division). In algeb ...

Fractional part The fractional part or decimal part of a non‐negative real number x is the excess beyond that number's integer part. If the latter is defined as the largest integer not greater than , called floor of or \lfloor x\rfloor, its fractional part ca ...

::*

Subtraction without borrowing In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (hardware) for addition throughout the whole range. For a given nu ...

Long division In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals ( Positional notation) that is simple enough to perform by hand. It breaks down a division problem into a series of easier steps ...

Short division In arithmetic, short division is a division algorithm which breaks down a division problem into a series of easier steps. It is an abbreviated form of long division — whereby the products are omitted and the partial remainders are notated as sup ...

Modulo operation In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is ...

Chunking (division) In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method wi ...

Multiplication and repeated addition In mathematics education, there was a debate on the issue of whether the operation of multiplication should be taught as being a form of repeated addition. Participants in the debate brought up multiple perspectives, including axioms of arithmeti ...

Euclidean division In arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than ...

Division by zero In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as \tfrac, where is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is ...

Plus and minus signs The plus and minus signs, and , are mathematical symbols used to represent the notions of positive and negative, respectively. In addition, represents the operation of addition, which results in a sum, while represents subtraction, resul ...

Multiplication sign The multiplication sign, also known as the times sign or the dimension sign, is the symbol , used in mathematics to denote the multiplication operation and its resulting product. While similar to a lowercase X (), the form is properly a fou ...

Division sign The division sign () is a symbol consisting of a short horizontal line with a dot above and another dot below, used in Anglophone countries to indicate mathematical division. However, this usage, though widespread in some countries, is not u ...

Equals sign The equals sign ( British English, Unicode) or equal sign (American English), also known as the equality sign, is the mathematical symbol , which is used to indicate equality in some well-defined sense. In an equation, it is placed between ...

Equality (mathematics) In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality b ...

Inequality (mathematics) In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different ...

Logical equivalence In logic and mathematics, statements p and q are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of p and q is sometimes expressed as p \equiv q, p :: q, \textsfpq, or p \iff q, depending ...

Ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...

Variable (mathematics) In mathematics, a variable (from Latin '' variabilis'', "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of ...

Constant (mathematics) In mathematics, the word constant conveys multiple meanings. As an adjective, it refers to non-variance (i.e. unchanging with respect to some other value); as a noun, it has two different meanings: * A fixed and well-defined number or other non ...

* Measurement

Structure

Algebra Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...

Abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The te ...

Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matric ...

(

Outline Outline or outlining may refer to: * Outline (list), a document summary, in hierarchical list format * Code folding, a method of hiding or collapsing code or text to see content in outline form * Outline drawing, a sketch depicting the outer edg ...

) *

Order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...

Function Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-orie ...

Space

Geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

* Algebraic geometry :*

List of algebraic geometry topics This is a list of algebraic geometry topics, by Wikipedia page. Classical topics in projective geometry *Affine space * Projective space *Projective line, cross-ratio *Projective plane **Line at infinity **Complex projective plane *Complex projec ...

List of algebras {{short description, None This is a list of possibly nonassociative algebras. An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with multiplication-by-scalars from the base ri ...

Trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...

* Differential geometry *

Topology In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...

Fractal geometry In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as ill ...

Change

Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

Vector calculus Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subjec ...

Differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...

s *

Dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

s *

Chaos theory Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have ...

Analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

Foundations and philosophy

* Category theory *

Set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

Type theory In mathematics, logic, and computer science, a type theory is the formal system, formal presentation of a specific type system, and in general type theory is the academic study of type systems. Some type theories serve as alternatives to set theor ...

Mathematical logic

Model theory In mathematical logic, model theory is the study of the relationship between formal theories (a collection of sentences in a formal language expressing statements about a mathematical structure), and their models (those structures in which the ...

* Proof theory *

Recursion theory Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has sinc ...

Theory of Computation In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., ...

List of logic symbols In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the sub ...

is a collection of axiomatic systems that formalize the natural numbers and their subsets. *

also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.

Discrete mathematics

Combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

(

outline Outline or outlining may refer to: * Outline (list), a document summary, in hierarchical list format * Code folding, a method of hiding or collapsing code or text to see content in outline form * Outline drawing, a sketch depicting the outer edg ...

) *

Cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adve ...

Graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

Applied mathematics

Mathematical chemistry Mathematical chemistry is the area of research engaged in novel applications of mathematics to chemistry; it concerns itself principally with the mathematical modeling of chemical phenomena. Mathematical chemistry has also sometimes been called c ...

Mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

Analytical mechanics In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was developed by many scientists and mathematicians during the ...

* Mathematical fluid dynamics *

Numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

Control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

s *

Mathematical optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

Operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve dec ...

Probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

* Statistics * Game theory *

Engineering mathematics Engineering mathematics is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in engineering and industry. Along with fields like engineering physics and engineering geology, both of which may b ...

Mathematical economics Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference a ...

Financial mathematics Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require ...

Information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

Mathematical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development a ...

History

Regional history

Babylonian mathematics Babylonian mathematics (also known as ''Assyro-Babylonian mathematics'') are the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Bab ...

Egyptian mathematics Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c. , from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt. The ancient Egyptians utilized a numeral system for coun ...

Indian mathematics Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupt ...

Greek mathematics Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly extant from the 7th century BC to the 4th century AD, around the shores of the Eastern Mediterranean. Greek math ...

Chinese mathematics Mathematics in China emerged independently by the 11th century BCE. The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system ( base 2 and base 10), algebra, geomet ...

History of the Hindu–Arabic numeral system The Hindu–Arabic numeral system is a decimal place-value numeral system that uses a zero glyph as in "205". Its glyphs are descended from the Indian Brahmi numerals. The full system emerged by the 8th to 9th centuries, and is first described o ...

Islamic mathematics Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built on Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics ( Aryabhata, Brahmagupta). Important progress was made, such as ...

Japanese mathematics denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term ''wasan'', from ''wa'' ("Japanese") and ''san'' ("calculation"), was coined in the 1870s and employed to distinguish native Japanes ...

Subject history

History of combinatorics The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. ...

History of arithmetic The history of arithmetic includes the period from the emergence of counting before the formal definition of numbers and arithmetic operations over them by means of a system of axioms. Arithmetic — the science of numbers, their properties and ...

History of algebra Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until the 19th century, algebra consisted essentially of the theory of equations. For example, the fun ...

History of geometry Geometry (from the grc, γεωμετρία; ''geo-'' "earth", '' -metron'' "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the stud ...

History of calculus Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, a ...

History of logic The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic (or term logic) as found ...

History of trigonometry Early study of triangles can be traced to the 2nd millennium BC, in Egyptian mathematics ( Rhind Mathematical Papyrus) and Babylonian mathematics. Trigonometry was also prevalent in Kushite mathematics. Systematic study of trigonometric function ...

History of writing numbers A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbo ...

History of statistics Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states. In early times, the meaning was restricted to information about states, particularly demographics ...

History of probability Probability has a dual aspect: on the one hand the likelihood of hypotheses given the evidence for them, and on the other hand the behavior of stochastic processes such as the throwing of dice or coins. The study of the former is historically olde ...

History of group theory The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry. Jos ...

History of the function concept The mathematical concept of a function emerged in the 17th century in connection with the development of the calculus; for example, the slope \operatorname\!y/\operatorname\!x of a graph at a point was regarded as a function of the ''x''-coordinat ...

History of logarithms The history of logarithms is the story of a correspondence (in modern terms, a group isomorphism) between multiplication on the positive real numbers and addition on the real number line that was formalized in seventeenth century Europe and was w ...

History of the Theory of Numbers ''History of the Theory of Numbers'' is a three-volume work by L. E. Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. T ...

* History of Grandi's series *

History of manifolds and varieties The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic struc ...

Psychology

Mathematics education In contemporary education, mathematics education, known in Europe as the didactics or pedagogy of mathematics – is the practice of teaching, learning and carrying out scholarly research into the transfer of mathematical knowledge. Although ...

Numeracy Numeracy is the ability to understand, reason with, and to apply simple numerical concepts. The charity National Numeracy states: "Numeracy means understanding how mathematics is used in the real world and being able to apply it to make the be ...

Numerical Cognition Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes ...

Subitizing Subitizing is the rapid, accurate, and confident judgments of numbers performed for small numbers of items. The term was coined in 1949 by E. L. Kaufman et al., and is derived from the Latin adjective '' subitus'' (meaning "sudden") and captures ...

Mathematical anxiety Mathematical anxiety, also known as math phobia, is anxiety about one's ability to do mathematics. Math Anxiety Mark H. Ashcraft defines math anxiety as "a feeling of tension, apprehension, or fear that interferes with math performance" (2002, p.& ...

Dyscalculia Dyscalculia () is a disability resulting in difficulty learning or comprehending arithmetic, such as difficulty in understanding numbers, learning how to manipulate numbers, performing mathematical calculations, and learning facts in mathematics. ...

Acalculia Acalculia is an acquired impairment in which people have difficulty performing simple mathematical tasks, such as adding, subtracting, multiplying and even simply stating which of two numbers is larger. Acalculia is distinguished from dyscalcul ...

* Ageometresia *

Number sense In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by Sta ...

Numerosity adaptation effect The numerosity adaptation effect is a perceptual phenomenon in numerical cognition which demonstrates non-symbolic numerical intuition and exemplifies how numerical percepts can impose themselves upon the human brain automatically. This effect ...

Approximate number system The approximate number system (ANS) is a cognitive system that supports the estimation of the magnitude of a group without relying on language or symbols. The ANS is credited with the non-symbolic representation of all numbers greater than four, ...

Mathematical maturity In mathematics, mathematical maturity is an informal term often used to refer to the quality of having a general understanding and mastery of the way mathematicians operate and communicate. It pertains to a mixture of mathematical experience and i ...

Influential mathematicians

See

Lists of mathematicians Lists of mathematicians cover notable mathematicians by nationality, ethnicity, religion, profession and other characteristics. Alphabetical lists are also available (see table to the right). Lists by nationality, ethnicity or religion * List ...

Mathematical notation

List of axioms This is a list of axioms as that term is understood in mathematics. In epistemology, the word ''axiom'' is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system. ZF (the Zermel ...

List of equations This is a list of equations, by Wikipedia page under appropriate bands of maths, science and engineering. Eponymous equations Mathematics * Cauchy–Riemann equations * Chapman–Kolmogorov equation * Maurer–Cartan equation * Pell's equat ...

List of mathematical functions In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed ...

List of types of functions Functions can be identified according to the properties they have. These properties describe the functions' behaviour under certain conditions. A parabola is a specific type of function. Relative to set theory These properties concern the domain, ...

List of mathematical jargon The language of mathematics has a vast vocabulary of specialist and technical terms. It also has a certain amount of jargon: commonly used phrases which are part of the culture of mathematics, rather than of the subject. Jargon often appears in ...

List of mathematical abbreviations This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology. :''This list is limited to abbreviations of two or more letters. The capitalization of some of these abbreviation ...

List of mathematical proofs A list of articles with mathematical proofs: Theorems of which articles are primarily devoted to proving them *Bertrand's postulate and a proof *Estimation of covariance matrices * Fermat's little theorem and some proofs *Gödel's completeness ...

List of long mathematical proofs This is a list of unusually long mathematical proofs. Such proofs often use computational proof methods and may be considered non-surveyable. , the longest mathematical proof, measured by number of published journal pages, is the classification ...

List of mathematical symbols A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula ...

List of mathematical symbols by subject The following list of mathematical symbols by subject features a selection of the most common symbols used in modern mathematical notation within formulas, grouped by mathematical topic. As it is impossible to know if a complete list existing toda ...

List of rules of inference This is a list of rules of inference, logical laws that relate to mathematical formulae. Introduction Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules ...

List of theorems A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby union ...

* List of theorems called fundamental *

List of unsolved problems in mathematics Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Eucl ...

Table of mathematical symbols by introduction date The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. Note that the table can also be ordered alphabetically by clicking on the relevant header title. See also * History o ...

Physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, ...

s *

Greek letters used in mathematics, science, and engineering Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these cont ...

Latin letters used in mathematics Many letters of the Latin alphabet, both capital and small, are used in mathematics, science, and engineering to denote by convention specific or abstracted constants, variables of a certain type, units, multipliers, or physical entities. Certai ...

Mathematical alphanumeric symbols Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts ofte ...

Mathematical operators and symbols in Unicode The Unicode Standard encodes almost all standard characters used in mathematics. Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. Mathematical op ...

ISO 31-11 ISO 31-11:1992 was the part of international standard international standard is a technical standard developed by one or more international standards organizations. International standards are available for consideration and use worldwide. Th ...

(Mathematical signs and symbols for use in physical sciences and technology)

Classification systems

* Mathematics in the Dewey Decimal Classification system *''

Mathematics Subject Classification The Mathematics Subject Classification (MSC) is an 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. ...

'' – 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 databases

*''

Mathematical Reviews ''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also ...

'' – 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 zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastruct ...

'' – 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.

References

Bibliography

Citations

Notes

External links

MAA Reviews – The Basic Library List – Mathematical Association of America
* ttp://www.math.cornell.edu/~hatcher/Other/topologybooks.pdf A List of Recommended Books in Topology, compiled by Allen Hatcher, Cornell U.br>Books in algebraic geometry in nLab
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