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Lists Of Mathematics Topics
Lists of mathematics topics cover a variety of topics related to mathematics. Some of these lists link to hundreds of articles; some link only to a few. The template to the right includes links to alphabetical lists of all mathematical articles. This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables. They also cover equations named after people, societies, mathematicians, journals, and meta-lists. The purpose of this list is ''not'' similar to that of the Mathematics Subject Classification formulated by the American Mathematical Society. Many mathematics journals ask authors of research papers and expository articles to list subject codes from the Mathematics Subject Classification in their papers. The subject codes so listed are used by the two major reviewing databases, ''Mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Set Identities And Relations
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. The binary operations of set union (\cup) and intersection (\cap) satisfy many identities. Several of these identities or "laws" have well established names. Notation Throughout this article, capital letters such as A, B, C, L, M, R, S, and X will denote sets and \wp(X) will denote the power set of X. If it is needed then unless indicated otherwise, it should be assumed that X denotes the universe set, which means that all sets that are used in the formula are subsets of X. In particular, the complement of a set L will be denoted by L^C where unless indicated otherwise, it should be assumed that L^C denotes the complement of L in (the univers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Commutative Algebra Topics
Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers \mathbb, and p-adic integers. Research fields * Combinatorial commutative algebra * Invariant theory Active research areas * Serre's multiplicity conjectures * Homological conjectures Basic notions * Commutative ring * Module (mathematics) * Ring ideal, maximal ideal, prime ideal * Ring homomorphism **Ring monomorphism **Ring epimorphism **Ring isomorphism * Zero divisor * Chinese remainder theorem Classes of rings * Field (mathematics) * Algebraic number field * Polynomial ring * Integral domain * Boolean algebra (structure) * Principal ideal domain * Euclidean domain * Unique factorization domain * Dedekind domain * Nilpotent element ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Cohomology Theories
This is a list of some of the ordinary and generalized (or extraordinary) homology and cohomology theories in algebraic topology that are defined on the categories of CW complexes or spectra. For other sorts of homology theories see the links at the end of this article. Notation *''S'' = π = ''S''''0'' is the sphere spectrum. *''S''''n'' is the spectrum of the ''n''-dimensional sphere *''S''''n''''Y'' = ''S''''n''∧''Y'' is the ''n''th suspension of a spectrum ''Y''. * 'X'',''Y''is the abelian group of morphisms from the spectrum ''X'' to the spectrum ''Y'', given (roughly) as homotopy classes of maps. * 'X'',''Y''sub>''n'' = 'S''''n''''X'',''Y''* 'X'',''Y''sub>''*'' is the graded abelian group given as the sum of the groups 'X'',''Y''sub>''n''. *π''n''(''X'') = 'S''''n'', ''X''= 'S'', ''X''sub>''n'' is the ''n''th stable homotopy group of ''X''. *π''*''(''X'') is the sum of the groups π''n''(''X''), and is called the coefficient ring of ''X'' when ''X'' is a rin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Category Theory Topics
The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of ''objects'' and ''arrows'' (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories. Essence of category theory * Category – * Functor – * Natural transformation – Branches of category theory * Homological algebra – * Diagram chasing – * Topos theory – * Enriched category theory – * Higher category theory – * Categorical logic – Specific categories *Category of sets – * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Boolean Algebra Topics
This is a list of topics around Boolean algebra and propositional logic. Articles with a wide scope and introductions * Algebra of sets * Boolean algebra (structure) * Boolean algebra * Field of sets * Logical connective * Propositional calculus Boolean functions and connectives * Ampheck * Analysis of Boolean functions * Balanced boolean function * Bent function * Boolean algebras canonically defined * Boolean function * Boolean matrix * Boolean-valued function * Conditioned disjunction * Evasive Boolean function * Exclusive or * Functional completeness * Logical biconditional * Logical conjunction * Logical disjunction * Logical equality * Logical implication * Logical negation * Logical NOR * Lupanov representation * Majority function * Material conditional * Minimal axioms for Boolean algebra * Peirce arrow * Read-once function * Sheffer stroke * Sole sufficient operator ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Algebraic Structures
In mathematics, there are many types of algebraic structures which are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates one or more sets with one or more binary operations or unary operations satisfying a collection of axioms. Another branch of mathematics known as universal algebra studies algebraic structures in general. From the universal algebra viewpoint, most structures can be divided into varieties and quasivarieties depending on the axioms used. Some axiomatic formal systems that are neither varieties nor quasivarieties, called ''nonvarieties'', are sometimes included among the algebraic structures by tradition. Concrete examples of each structure will be found in the articles listed. Algebraic structures are so numerous today that this article will inevitably be incompl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Abstract Algebra Topics
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this area from what was normally referred to as algebra, the study of the rules for manipulating formulae and algebraic expressions involving unknowns and real or complex numbers, often now called ''elementary algebra''. The distinction is rarely made in more recent writings. Basic language Algebraic structures are defined primarily as sets with ''operations''. *Algebraic structure **Subobjects: subgroup, subring, subalgebra, submodule etc. *Binary operation ** Closure of an operation **Associative property **Distributive property **Commutative property *Unary operator **Additive inverse, multiplicative inverse, inverse element ***Identity element ***Cancellation property * Finitary operation **Arity Structure preserving maps called ''homomo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Ring Theory
Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. For the items in commutative algebra (the theory of commutative rings), see glossary of commutative algebra. For ring-theoretic concepts in the language of modules, see also Glossary of module theory. For specific types of algebras, see also: Glossary of field theory and Glossary of Lie groups and Lie algebras. Since, currently, there is no glossary on not-necessarily-associative algebra-structures in general, this glossary includes some concepts that do not need associativity; e.g., a derivation. A B C D E F G H I J K L M N O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Linear Algebra
This is a glossary of linear algebra. See also: glossary of module theory. A B C D E I L M N R S U V Z Notes References * * * {{Linear algebra Linear algebra Algebra Algebra () is one of the 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 mathematics. Elementary a ... Wikipedia glossaries using description lists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Group Theory
A group is a set together with an associative operation which admits an identity element and such that every element has an inverse. Throughout the article, we use e to denote the identity element of a group. A C D F G H I L N O P Q R S T Basic definitions Subgroup. A subset H of a group (G, *) which remains a group when the operation * is restricted to H is called a ''subgroup'' of G. Given a subset S of G. We denote by the smallest subgroup of G containing S. is called the subgroup of G generated by S. Normal subgroup. H is a ''normal subgroup'' of G if for all g in G and h in H, g * h * g^also belongs to H. Both subgroups and normal subgroups of a given group form a complete lattice under inclusion of subsets; this property and some related results are described ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Field Theory
Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring (''F'',+,*) in which 0≠1 and every nonzero element has a multiplicative inverse. In a field we thus can perform the operations addition, subtraction, multiplication, and division. The non-zero elements of a field ''F'' form an abelian group under multiplication; this group is typically denoted by ''F''×; The ring of polynomials in the variable ''x'' with coefficients in ''F'' is denoted by ''F'' 'x'' Basic definitions ; Characteristic : The ''characteristic'' of the field ''F'' is the smallest positive integer ''n'' such that ''n''·1 = 0; here ''n''·1 stands for ''n'' summands 1 + 1 + 1 + ... + 1. If no such ''n'' exists, we say the characteristic is zero. Every non-zero characteristic is a prime number. For example, the rationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
