* ADE classification, a mathematics classification

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below.

The classification theorem has applications in many branches of mathematics, as questions about the structure of finite groups ( and their action on other mathematical objects ) can sometimes be reduced to questions about finite simple groups.

It is interdisciplinary in nature, borrowing, adapting and enhancing method and theory from numerous other disciplines such as computer science ( e. g. algorithm and software design, database design and theory ), geoinformation science ( spatial statistics and modeling, geographic information systems ), artificial intelligence research ( supervised classification, fuzzy logic ), ecology ( point pattern analysis ), applied mathematics ( graph theory, probability theory ) and statistics.

Special types of buildings are studied in discrete mathematics, and the idea of a geometric approach to characterizing simple groups proved very fruitful in the classification of finite simple groups.

Further, the classification scheme for root systems, by Dynkin diagrams, occurs in parts of mathematics with no overt connection to Lie theory ( such as singularity theory ).

One of the important unsolved problems in mathematics is the description of the unitary dual, the effective classification of irreducible unitary representations of all real reductive Lie groups.

In mathematics and theoretical physics, Wigner's classification

Cambridge did not divide its examination classification in mathematics into 2: 1s and 2: 2s until 1995 but now there are Senior Optimes Division 1 and Senior Optimes Division 2.

Concerning the mathematics, it should be noted that presently, i. e. in 2011, the Yang – Mills theory is a very active field of research, yielding e. g. a classification of differentiable structures of four-dimensional manifolds by Simon Donaldson.

In mathematics the Karoubi envelope ( or Cauchy completion or idempotent splitting ) of a category C is a classification of the idempotents of C, by means of an auxiliary category.

If the domain is unclear, but reasonably believed to exist, it is better to put the page into the root: category: mathematics, where it will have a better chance of spotting and classification.

This classification, though it is of high value in the clearing up of our conceptions of the essential contrasted with the accidental, the relation of genus, differentia and definition and so forth, is of more significance in connection with abstract sciences, especially mathematics, than for the physical sciences.

In addition, as mathematics evolves, these classification schemes must evolve as well to account for newly created areas or newly discovered links between different areas.

He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in putting together the classification proof, the largest collaborative piece of pure mathematics ever attempted.

In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface.

It is most often applied in studying exact solutions of Einstein's field equations, but strictly speaking the classification is a theorem in pure mathematics applying to any Lorentzian manifold, independent of any physical interpretation.

Abstraction in mathematics is the process of extracting the underlying essence 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.

" The word " mathematics " may have originally been plural in concept, referring to mathematic endeavors, but metonymic shift — that is, the shift in concept from " the endeavors " to " the whole set of endeavors "— produced the usage of " mathematics " as a singular entity taking singular verb forms.

This proved to be a fertile approach, which later mathematicians adapted to many other fields of mathematics besides the theory of equations to which Galois originally applied it.

Combinatory logic and lambda calculus were both originally developed to achieve a clearer approach to the foundations of mathematics.

Naive Set Theory is a mathematics textbook by Paul Halmos originally published in 1960.

Stieltjes originally wrote to Hermite concerning celestial mechanics, but the subject quickly turned to mathematics and he began to devote his spare time to mathematical research.

In mathematics, chain complex and cochain complex are constructs originally used in the field of algebraic topology.

The upper-case letter of omicron ( O ) was originally used in mathematics as a symbol for Big O notation, representing the asymptotic rate of growth of a function.

The Pythagorean school of mathematics originally insisted that only natural and rational numbers exist.

Wigner begins his paper with the belief, common to all those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed.

Metamathematical metatheorems about mathematics itself were originally differentiated from ordinary mathematical theorems in the 19th century, to focus on what was then called the foundational crisis of mathematics.

Born at Edinburgh in 1710 and originally educated for the church at the Royal High School, Short attracted the attention of Maclaurin, professor of mathematics at the university, who around 1732 gave him permission to use his rooms in the college buildings for experiments in the construction of telescopes.

The mathematics of population genetics were originally developed as the beginning of the modern evolutionary synthesis.

Banks originally planned to study mathematics in higher education.

JumpStart Math for First Graders ( originally JumpStart 1st Grade Math-teaches mathematics to children of the first grade )

JumpStart Math for Second Graders ( originally JumpStart 2nd Grade Math-teaches mathematics to children of the second grade level )

In mathematics, the pentagonal number theorem, originally due to Euler, relates the product and series representations of the Euler function.

It was originally developed to support the SETI @ home project before it became useful as a platform for other distributed applications in areas as diverse as mathematics, medicine, molecular biology, climatology, and astrophysics.

Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalising it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

The Speak & Math was sold in both the United States and in Europe ; it was originally advertised as a tool for helping young children to become better at mathematics.

Hardy himself did not originally find a passion for mathematics only seeing it as a way to beat the other students, which he did decisively, and gain scholarships.

He originally applied for a degree in physics, but was instead given one in mathematics, and was first required to significantly rewrite his thesis, de-emphasizing the physics content.

He claimed that “ tonalité ” is the primary organizing agent of all melodic and harmonic successions and that the efforts of other theorists to find the fundamental principle of music in “ acoustics, mathematics, aggregations of intervals, or classifications of chords have been futile .”

Many research journals in mathematics ask authors to classify their papers according to this scheme ; the classifications appear in the published work.