Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions. Practical mathematics, in nearly every society, is used for such purposes as accounting, measuring land, or predicting astronomical events. Mathematical discovery or research often involves discovering and cataloging patterns, without regard for application. Today, the natural sciences, engineering, economics, and medici ...

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• Mathematics - History
• Mathematics - Inspiration pure and applied mathematics and aesthetics
• Mathematics - Notation language and rigor
• Mathematics - Is mathematics a science?
• Mathematics - Overview of fields of mathematics
• Mathematics - Major themes in mathematics
• Mathematics - Quantity
• Mathematics - Structure
• Mathematics - Space
• Mathematics - Change
• Mathematics - Foundations and methods
• Mathematics - Discrete mathematics
• Mathematics - Applied mathematics
• Mathematics - Important theorems
• Mathematics - Important conjectures
• Mathematics - History and the world of mathematicians
• Mathematics - Mathematics and other fields
• Mathematics - Common misconceptions

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Mathematics, Mathematics - History, Mathematics - Inspiration pure and applied mathematics and aesthetics, Mathematics - Notation language and rigor, Mathematics - Is mathematics a science?, Mathematics - Overview of fields of mathematics, Mathematics - Major themes in mathematics, Mathematics - Quantity, Mathematics - Structure, Mathematics - Space, Mathematics - Change, Mathematics - Foundations and methods, Mathematics - Discrete mathematics, Mathematics - Applied mathematics, Mathematics - Important theorems, Mathematics - Important conjectures, Mathematics - History and the world of mathematicians, Mathematics - Mathematics and other fields, Mathematics - Mathematical tools, Mathematics - Common misconceptions

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Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". If one considers science to be strictly about the physical world, then mathematics, or at least pure mathematics, is not a science. An alternative view is that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In fact, the theoretical physicist, J. M. Ziman, proposed that science is < ...

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Mathematics, Mathematics - History, Mathematics - Inspiration pure and applied mathematics and aesthetics, Mathematics - Notation language and rigor, Mathematics - Is mathematics a science?, Mathematics - Overview of fields of mathematics, Mathematics - Major themes in mathematics, Mathematics - Quantity, Mathematics - Structure, Mathematics - Space, Mathematics - Change, Mathematics - Foundations and methods, Mathematics - Discrete mathematics, Mathematics - Applied mathematics, Mathematics - Important theorems, Mathematics - Important conjectures, Mathematics - History and the world of mathematicians, Mathematics - Mathematics and other fields, Mathematics - Mathematical tools, Mathematics - Common misconceptions

Read more here: » Mathematics: Encyclopedia II - Mathematics - Is mathematics a science?

The mathematics of humour, or the humour of mathematics? You're kidding. They're as different as chalk and cheese. Or are they?

We're familiar with those witty mathematical puzzles which delight children of all ages. We speak of a comedian's sense of 'timing', a term suggestive of arithmetical calibration. We talk of jokes that 'click', like tumblers falling into place in a numerical combination lock.

(See also: Mathematics, Faith and Belief, Spiritual Guidance, God and Religion, Peace on Earth, Peace of Mind, Love and Happiness, Life and Beyond, Body Mind and Soul)

In mathematics, null usually means zero. For example, in a vector space the null vector, is the zero vector, in set theory, the null set, is the set with zero elements, and in measure theory, a null set, is a set with zero measure. A mathematical mapping is said to be null potent (or nilpotent) if repeated application can map the whole domain into the null element. A null space of a mapping is the part of the domain that is mapped into the null element of the image (the i ...

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Null Mathematics, Null Mathematics - Mathematics, Null Mathematics - Statistics

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An alphabetical and subclassified list of mathematics articles is available. The following list of themes and links gives just one possible view. For a fuller treatment, see areas of mathematics or the list of mathematics lists. Mathematics - Quantity. This starts from explicit measurements of sizes of numbers or sets, or ways to find such measurements. See also:

Mathematics, Mathematics - History, Mathematics - Inspiration pure and applied mathematics and aesthetics, Mathematics - Notation language and rigor, Mathematics - Is mathematics a science?, Mathematics - Overview of fields of mathematics, Mathematics - Major themes in mathematics, Mathematics - Quantity, Mathematics - Structure, Mathematics - Space, Mathematics - Change, Mathematics - Foundations and methods, Mathematics - Discrete mathematics, Mathematics - Applied mathematics, Mathematics - Important theorems, Mathematics - Important conjectures, Mathematics - History and the world of mathematicians, Mathematics - Mathematics and other fields, Mathematics - Common misconceptions

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The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. Arithmetic (e.g., addition, subtraction, mul ...

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Mathematics, Mathematics - History, Mathematics - Inspiration pure and applied mathematics and aesthetics, Mathematics - Notation language and rigor, Mathematics - Is mathematics a science?, Mathematics - Overview of fields of mathematics, Mathematics - Major themes in mathematics, Mathematics - Quantity, Mathematics - Structure, Mathematics - Space, Mathematics - Change, Mathematics - Foundations and methods, Mathematics - Discrete mathematics, Mathematics - Applied mathematics, Mathematics - Important theorems, Mathematics - Important conjectures, Mathematics - History and the world of mathematicians, Mathematics - Mathematics and other fields, Mathematics - Mathematical tools, Mathematics - Common misconceptions

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In mathematics, especially geometry, a configuration is an arrangement of points in a certain way. Other related archivesgeometry, mathematics

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Applied mathematics is a branch of mathematics that concerns itself with the application of mathematical knowledge to other domains. Such applications include numerical analysis, mathematical physics, mathematics of engineering, linear programming, optimization and operations research, continuous modelling, mathematical biology and bioinformatics, information theory, game theory, probability and statistics, mathematical economics, financial mathematics, actuarial science, cryptography and hence combinatorics and even finite geometry to some extent, graph theory as applied to network anal ...

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The aim of this page is to list all areas of modern mathematics, with a brief explanation about their scope and links to other parts of this encyclopedia, set out in a systematic way. The way research-level mathematics is internally organised is mostly determined by practitioners, and does change over time; this is in contrast with the apparently timeless syllabus divisions used in mathematics education, where calculus can seem to be much the same over a time scale of a century. Calculus itself does not appear as a major heading — m ...

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• Areas of mathematics - Foundations / general
• Areas of mathematics - Algebra
• Areas of mathematics - Analysis
• Areas of mathematics - Geometry
• Areas of mathematics - Applied mathematics
• Areas of mathematics - Probability and statistics
• Areas of mathematics - Computational sciences
• Areas of mathematics - Physical sciences
• Areas of mathematics - Non-physical sciences

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In mathematics, the closure C(X) of an object X is defined to be the smallest object that both includes X as a subset and possesses some given property. (Thus, an object is, among other things, a set.) An object is closed if it is equal to its closure. Typical structural properties of all closure operations are: The closure is increasing or extensive: the closure of an object contains the object. The closure is idempotent: the closure of the closure equals t ...

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• Closure mathematics - Examples

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Ana is a mathematical/geometric term referring to a direction in the fourth spatial dimension. It comes from the Greek word for "up". As the other three dimensions all have counterparts, up/down, north/south, east/west, the counterpart of ana is kata (from the Greek word for "down"). Other related archivesANA, Greek, fourth spatial dimension, geometric, kata, mathematical

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In mathematics, and particularly in applications to set theory and the foundations of mathematics, a universe or universal class (or if a set, universal set) is, roughly speaking, a class that is large enough to contain (in some sense) all of the sets that one may wish to use. Universe mathematics - In a specific context. There are several precise versions of this general idea. Perhaps the simplest is that any set can be a universe, so long as you are studying that particular set. So if ...

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• Universe mathematics - In a specific context
• Universe mathematics - In ordinary mathematics
• Universe mathematics - In set theory
• Universe mathematics - In category theory

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Chess and mathematics have been pursued intellectually for centuries by many researchers and scientists, especially mathematicians. Naturally, the logic and symmetries in chess appeal to mathematicians. The following mathematicians either played or studied chess in their life: George Airy Adolf Anderssen George Atwood Harry Bateman Jacob Bronowski Max Black Jerome Cardan Lewis Carroll Henry Dudeney Albert Einstein Noam Elkies

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Analysis is the generic name given to any branch of mathematics which depends upon the concepts of limits and convergence, and studies closely related topics such as continuity, integration, differentiability and transcendental functions. These topics are often studied in the context of real numbers, complex numbers, and their functions. However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or "distance" (a metric space). Mathematical analysis ...

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• Mathematical analysis - History
• Mathematical analysis - Subdivisions

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There are several meanings of the word character in mathematics, although all are related to the idea of using complex numbers to study a more abstract algebraic structure. Character mathematics - External link. Character of a group representation on PlanetMath. Other related archivesPlanetMath, complex numbers

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The Annals of Mathematics (ISSN 0003-486X), often just called Annals, is a bimonthly mathematics research journal published by Princeton University and the Institute for Advanced Study. It ranks amongst the most prestigious mathematics journals in the world by criteria such as refereeing intensity. It started out as The Analyst in 1874, but was discontinued in 1883 and renamed in 1884 under the new direction of Ormond Stone of the University of Virginia. It moved to Harvard in ...

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• Annals of Mathematics - External link

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Commensurability mathematics - Commensurability in general. Generally, two quantities are commensurable if both can be measured in the same units. For example, a distance measured in miles and a quantity of water measured in gallons are incommensurable. A time measured in weeks and a time measured in minutes are commensurable because a week is a constant number of minutes (10080), so that one can convert between the two units by multiplying or dividing by 10080. Commensurabilit ...

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• Commensurability mathematics - Commensurability in general
• Commensurability mathematics - Commensurability in mathematics

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In mathematics, more particularly in functional analysis and differential topology, a current in the sense of Georges de Rham is a functional on the space of compactly supported differential forms, on a smooth manifold M. Formally currents behave like Schwartz distributions with values in differential forms. In a geometric sense they can represent quite singular versions of submanifolds: Dirac delta functions or even multipoles (directional derivatives of delta functions) spread out along subsets of M. ...

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• Current mathematics - Topology
• Current mathematics - Examples

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In mathematics, a sheaf F on a topological space X is something that assigns a structure F(U) (such as a set, group, or ring) to each open set U of X. The structures F(U) are compatible with the operations of restricting the open set to smaller subsets and gluing smaller open sets to obtain a bigger one. A presheaf is similar to a sheaf, but it may not be possible to glue. Sheaves enable one to discuss in a refined way what is a local property, as appl ...

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• Sheaf mathematics - Introduction
• Sheaf mathematics - The formal definition
• Sheaf mathematics - Definition of a presheaf
• Sheaf mathematics - The gluing axiom
• Sheaf mathematics - Examples
• Sheaf mathematics - Morphisms of sheaves
• Sheaf mathematics - Stalks of a sheaf at a point and germs of functions
• Sheaf mathematics - The étale space of a sheaf
• Sheaf mathematics - Generalizations
• Sheaf mathematics - History

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