Mathematics 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 ...

is a field of study that investigates topics such as number, space,

structure A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such as ...

, 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 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) with ...

is the system used by mathematicians to communicate mathematical 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 – 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 In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. It stands in contrast to other types of mathematics such as constructive m ...

refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory. :* Constructive mathematics 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

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 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, ga ...

– 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 an abstract concept in

mathematics 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 ...

; 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 fals ...

and mathematical proofs. 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 additional ...

set Set, The Set, SET or SETS may refer to: Science, technology, and mathematics Mathematics *Set (mathematics), a collection of elements *Category of sets, the category whose objects and morphisms are sets and total functions, respectively Electro ...

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-Ma ...

relation Relation or relations may refer to: General uses *International relations, the study of interconnection of politics, economics, and law on a global level *Interpersonal relationship, association or acquaintance between two or more people *Public ...

, metric, topology). A partial list of possible structures are measures,

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 of ...

s ( groups, fields, etc.), topologies, 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 geometry ...

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 d ...

, events,

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 relation ...

s, differential structures, and categories. :*

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 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 W ...

Branches and subjects

Quantity

* Number theory 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 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 o ...

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 ...

(from the Greek 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 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 operatio ...

on them. :* Elementary arithmetic is the part of arithmetic which deals with basic operations of addition, subtraction, multiplication, and division. :* Modular arithmetic :* 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 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 be ...

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 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, Hypercomplex number, p-adic number ::*

Negative number In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed m ...

, Positive number, Parity (mathematics) ::* Prime number, Composite number ::*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 amo ...

, transfinite number,

ordinal number In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, th, etc.) aimed to extend enumeration to infinite sets. A finite set can be enumerated by successively labeling each element with the least n ...

, cardinal number, hyperreal number, surreal number,

infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referr ...

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 unio ...

:* Numeral system, Unary numeral system, Numeral prefix, List of numeral systems,

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, Number line, Numerical digit, Zero ::*

Radix In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is t ...

, Radix economy, Base (exponentiation),

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,

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 a ...

, Scientific notation,

Positional notation Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...

, Notation in probability and statistics, History of mathematical notation,

List of mathematical notation systems 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 ...

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 The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

, 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 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 th ...

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 es ...

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, f ...

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 exampl ...

, Algorithm :*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, Nullary operation :*Operands:

Addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol ) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication and Division (mathematics), division. ...

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 additi ...

, Division, Exponentiation, Logarithm, Root ::* Function (mathematics), Inverse function ::* Commutative property,

Anticommutative property In mathematics, anticommutativity is a specific property of some non-commutative mathematical operations. Swapping the position of two arguments of an antisymmetric operation yields a result which is the ''inverse'' of the result with unswapped ...

, Associative property, Additive identity, Distributive property ::*

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, mat ...

, Product (mathematics), Divisor, Quotient, Greatest common divisor,

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,

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 can ...

::* Subtraction without borrowing, Long division,

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, 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) 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 n ...

, Logical equivalence :* Ratio * Variable (mathematics), Constant (mathematics) *

Measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...

Structure

* Algebra * Abstract algebra * Linear algebra (

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 edge ...

) * Number theory * Order theory * Function

Space

* Geometry *

Algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

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 projecti ...

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 *

Differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

* Topology * Fractal geometry

Change

* Calculus * Vector calculus * Differential equations * Dynamical systems *

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 co ...

* Analysis

Foundations and philosophy

* Philosophy of mathematics *

Category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

* Set theory * Type theory

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 s ...

Proof theory Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four correspo ...

* Set theory * Type theory * Recursion theory * Theory of Computation * List of logic symbols * 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 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 appl ...

(

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 edge ...

) * Cryptography * Graph theory * Number theory

Applied mathematics

* Mathematical chemistry * Mathematical physics *

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 * Control theory * Dynamical systems *

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 * Probability *

Statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

Game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appli ...

* Engineering mathematics *

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 an ...

* Financial mathematics *

Information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

* Cryptography *

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 *

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 count ...

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, Brahmagupta ...

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 mathem ...

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 full ...

* Japanese mathematics

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 an ...

* History of algebra * History of geometry *

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 * History of mathematical notation * History of trigonometry *

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 *

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 * History of the function concept * History of logarithms * History of the Theory of Numbers *

History of Grandi's series Geometry and infinite zeros Grandi Guido Grandi (1671–1742) reportedly provided a simplistic account of the series in 1703. He noticed that inserting parentheses into produced varying results: either :(1-1) + (1-1) + \cdots = 0 or :1+(-1+1)+( ...

* History of manifolds and varieties

Psychology

* Mathematics education *

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 bes ...

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 r ...

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 * Acalculia * Ageometresia * Number sense *

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.

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 Zermelo ...

* List of equations * List of mathematical functions *

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 l ...

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 *

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 *

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 * List of theorems * List of theorems called fundamental * List of unsolved problems in mathematics *

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 of ...

* Notation in probability and statistics * List of logic symbols *

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 *

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. Certain ...

* Mathematical alphanumeric symbols * Mathematical operators and symbols in Unicode *

ISO 31-11 ISO 31-11:1992 was the part of international standard ISO 31 that defines ''mathematical signs and symbols for use in physical sciences and technology''. It was superseded in 2009 by ISO 80000-2:2009 and subsequently revised in 2019 as ISO-800 ...

(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 pu ...

'' – 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.

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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