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.

In mathematics, the ADE classification ( originally A-D-E classifications ) is the complete list of simply laced Dynkin diagrams or other mathematical objects satisfying analogous axioms ; " simply laced " means that there are no multiple edges, which corresponds to all simple roots in the root system forming angles of ( no edge between the vertices ) or ( single edge between the vertices ).

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.

* ADE classification, a mathematics classification

On the Infinite was Hilbert ’ s most important paper on the foundations of mathematics, serving as the heart of Hilbert's program to secure the foundation of transfinite numbers by basing them on finite methods.

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

In mathematics, particularly theoretical computer science and mathematical logic, the computable numbers, also known as the recursive numbers or the computable reals, are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

# all of mathematics follows from a correctly chosen finite system of axioms ; and

The set of objects studied in discrete mathematics can be finite or infinite.

The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business accounts.

In mathematics, an elementary function is a function of one variable built from a finite number of exponentials, logarithms, constants, and nth roots through composition and combinations using the four elementary operations (+ – × ÷).

# REDIRECT finite mathematics

# REDIRECT finite mathematics

An example of such a finite field is the ring Z / pZ, which is essentially the set of integers from 0 to p − 1 with integer addition and multiplication modulo p. It is also sometimes denoted Z < sub > p </ sub >, but within some areas of mathematics, particularly number theory, this may cause confusion because the same notation Z < sub > p </ sub > is used for the ring of p-adic integers.

In mathematics, a finite set is a set that has a finite number of elements.

Linear algebra is the branch of mathematics concerning vector spaces, often finite or countably infinite dimensional, as well as linear mappings between such spaces.

In this sense, propositions restricted to the finite are still regarded as being either true or false, as they are in classical mathematics, but this bivalence does not extend to propositions which refer to infinite collections.

In mathematics, a polynomial is an expression of finite length constructed from variables ( also called indeterminates ) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups ; they share many properties with their finite quotients.

In mathematics, the symmetric group S < sub > n </ sub > on a finite set of n symbols is the group whose elements are all the permutations of the n symbols, and whose group operation is the composition of such permutations, which are treated as bijective functions from the set of symbols to itself.

They involve only simple mathematics that are taught in grammar school arithmetic classes.

Arithmetic or arithmetics ( from the Greek word ἀριθμός, arithmos " number ") is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations.

From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics.

There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory ; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.

simple: Lemma ( mathematics )

A 2008 draft mathematics standard proposed that Kindergartners multiply to 30 by skip counting ( also known as counting by twos: 2, 4, 6, 8 ...), and that second graders solve simple algebra story problems.

simple: Product ( mathematics )

Feynman avoids exposing the reader to the mathematics of complex numbers by using a simple but accurate representation of them as arrows on a piece of paper or screen.

* Reflections and Refractions in Ray Tracing, a simple but thorough discussion of the mathematics behind refraction and reflection.

In mathematics, specifically in ring theory, the simple modules over a ring R are the ( left or right ) modules over R which have no non-zero proper submodules.

The true period of an ideal simple gravity pendulum can be written in several different forms ( see Pendulum ( mathematics ) ), one example being the infinite series:

A simple and ubiquitous concept throughout physics and applied mathematics is the flow of a physical property in space, frequently also with time variation.

This may seem like a simple idea, and it is, but many deep results in mathematics concern when you can prove distinctness by particular methods.

In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.

In mathematics, more specifically graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one simple path.

simple: Projection ( mathematics )

# REDIRECT Fraction ( mathematics )# Common, vulgar, or simple fractions

In mathematics, more specifically ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is an ideal which consists of those elements in R which annihilate all simple right R-modules.

In mathematics, a Fourier series decomposes periodic functions or periodic signals into the sum of a ( possibly infinite ) set of simple oscillating functions, namely sines and cosines ( or complex exponentials ).

In physics and mathematics, in the area of dynamical systems, a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with a strong sensitivity to initial conditions.

In mathematics, the sieve of Eratosthenes (), one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit.

Ziggurat designs ranged from simple bases upon which a temple sat, to marvels of mathematics and construction which spanned several terraced stories and were topped with a temple.