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- '''Algebra''' is a branch of [[mathematics]] concerning the study of [[structure (alge ...[[secondary education]] and provides an introduction to the basic ideas of algebra, including effects of [[addition|add]]ing and [[multiplication|multiply]]in18 KB (2,669 words) - 08:38, 17 April 2024
- 43 bytes (3 words) - 13:22, 8 March 2009
- ...ematics)|rings]], [[field (mathematics)|fields]], [[vector space]]s, and [[algebra over a field|algebras]].250 bytes (31 words) - 07:40, 27 July 2008
- In [[algebra]], the '''resultant''' of two polynomials is a quantity which determines wh * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-552 KB (388 words) - 17:58, 21 December 2008
- ...ap|(negation, ~)}} that reverses the truth value of any statement. Boolean algebra can be used to analyze computer chips and switching circuits, as well as lo ...mentary algebra]] as taught in secondary schools, and is only a facet of [[algebra]], the general mathematical discipline treating variables, symbols and sets13 KB (1,959 words) - 19:49, 1 September 2020
- ...range of topics, such as [[systems of linear equations]], [[matrix|matrix algebra]], and [[arrow]]s in [[Cartesian coordinates|Cartesian]] two-dimensional or ...l-world problems. Other topics in linear algebra, such as [[matrix|matrix algebra]], [[eigenvalue]]s and [[eigenvector]]s, [[linear operators]], [[matrix rep975 bytes (135 words) - 02:13, 3 September 2010
- #Redirect [[Abstract algebra]]30 bytes (3 words) - 13:29, 12 April 2008
- The '''Albert algebra''' is the set of 3×3 [[self-adjoint]] matrices over the [[octonion]]s with ...ructed using this one, it is often referred to as "the" exceptional Jordan algebra.619 bytes (88 words) - 13:53, 14 November 2008
- In [[mathematics]], a '''sigma algebra''' is a [[mathematical structure|formal mathematical structure]] intended ...is a collection of subset of <math>\scriptstyle \Omega</math>) is a sigma algebra if it satisfies all the following conditions or axioms:2 KB (314 words) - 16:35, 27 November 2008
- 117 bytes (15 words) - 19:49, 20 May 2008
- In [[mathematics]], a '''median algebra''' is a set with a [[ternary operation]] < x,y,z > satisfying a set o ...)</math> satisfies these axioms, so that every Boolean algebra is a median algebra.2 KB (316 words) - 13:38, 16 July 2011
- 12 bytes (1 word) - 10:48, 24 September 2007
- ...initesimal [[symmetry|symmetries]] or [[transformation]]s. In short a Lie algebra is a [[vector space]] together with a skew-symmetric bilinear operation den ...''Y'']] = 0 where ''X'', ''Y'', and ''Z'' run over all elements of the Lie algebra.12 KB (1,918 words) - 20:29, 22 December 2011
- In [[mathematics]], particularly in [[abstract algebra]] and [[homological algebra]], a '''resolution''' is a sequence which is used to describe the structure * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-52 KB (296 words) - 14:49, 28 October 2008
- 20 bytes (2 words) - 06:49, 1 January 2009
- In [[algebra]], the '''content''' of a [[polynomial]] is the [[highest common factor]] o ...nk=Brian Hartley | coauthors=T.O. Hawkes | title=Rings, modules and linear algebra | publisher=Chapman and Hall | year=1970 | isbn=0-412-09810-5 }}971 bytes (132 words) - 15:00, 29 October 2008
- 33 bytes (3 words) - 03:28, 2 January 2009
- * I.N. Herstein: ''Topics in Algebra''. ISBN 0-471-02371-X580 bytes (78 words) - 06:03, 7 November 2010
- Commutative algebra developed as a theory in mathematics having the aim of translating classica ...correspondence theorems, which allows us to change between the language of algebra and geometry.2 KB (338 words) - 10:01, 23 December 2008
- ...[[Diophantus]], who lived in Egypt and is often considered the "father of algebra", writes his famous ''[[Arithmetica]]'', a work featuring solutions of alge ...on reduction was included in the book and added to many methods we have in algebra now.8 KB (1,117 words) - 08:22, 5 December 2011
- 50 bytes (5 words) - 02:43, 5 January 2009
- 108 bytes (12 words) - 09:26, 4 August 2008
- In [[linear algebra]], a '''basis''' for a [[vector space]] <math>V</math> is a set of [[vector The term '''basis''' is also used in [[abstract algebra]], specifically in the theory of [[free module]]s. For more on this use of3 KB (464 words) - 19:45, 1 December 2008
- 238 bytes (31 words) - 12:17, 14 July 2011
- 12 bytes (1 word) - 13:21, 12 April 2008
- 121 bytes (17 words) - 02:25, 18 December 2008
- A fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge o195 bytes (28 words) - 14:21, 25 October 2008
- In [[abstract algebra]], an '''algebra over a field''' ''F'', or ''F''-'''algebra''' is a [[ring (mathematics)|ring]] ''A'' containing an [[field isomorphism * Any [[extension field]] ''E''/''F'' can be regarded as an ''F''-algebra.1 KB (155 words) - 15:55, 23 December 2008
- ...|year=1990 |publisher=McGraw-Hill}} An accessible introduction to Boolean algebra and its applications. ...2001}} A discussion of the wide field of sentential logic of which Boolean algebra is the tip of the iceberg.670 bytes (88 words) - 15:04, 21 July 2011
- 124 bytes (26 words) - 06:32, 20 November 2008
- 176 bytes (27 words) - 15:44, 27 October 2008
- In [[linear algebra]], a '''complement''' to a subspace of a vector space is another subspace w1 KB (195 words) - 15:17, 12 December 2008
- * [[List of basic algebra topics]] * [[Fundamental theorem of algebra]]2 KB (247 words) - 06:00, 7 November 2010
- 12 bytes (1 word) - 16:54, 14 November 2007
- A ''Lie algebra'' is a vector space together with a skew-symmetric bilinear operation (the170 bytes (23 words) - 09:27, 27 November 2011
- 106 bytes (16 words) - 14:54, 28 October 2008
- ...ilitates [[symbolic mathematics]]. The core functionality of any computer algebra systems is manipulation of mathematical expressions in symbolic form. Most Typical symbolic manipulations that can be performed by ''computer algebra systems'' include:1 KB (164 words) - 14:01, 18 January 2008
- ...''Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra'', second edition, World Scientific, 2007, ISBN 978-981-270-809-01 KB (158 words) - 10:59, 27 November 2011
- 173 bytes (23 words) - 17:40, 26 June 2008
- 124 bytes (16 words) - 10:28, 1 January 2009
- 184 bytes (23 words) - 09:31, 4 September 2009
- An exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices over the octonions.127 bytes (14 words) - 02:27, 5 December 2008
- ...he abstract [[Lie algebra]] to a simpler [[Lie algebra#Examples|matrix Lie algebra]]. ...algebra#Homomorphisms, subalgebras, and ideals|homomorphism]] from the Lie algebra to the endomorphisms (linear maps) of some vector space.4 KB (670 words) - 21:07, 22 December 2011
- 116 bytes (15 words) - 10:16, 12 July 2008
- 98 bytes (13 words) - 15:03, 29 October 2008
- * [http://www.helpalgebra.com ''Algebra Help''] Online algebra tutorials. ...://www.ucs.louisiana.edu/~sxw8045/history.htm Highlights in the history of algebra]260 bytes (36 words) - 06:03, 7 November 2010
- 12 bytes (1 word) - 11:17, 1 January 2008
- {{r|Abstract algebra}} {{r|Noncommutative algebra}}715 bytes (91 words) - 17:34, 10 December 2008
- 795 bytes (125 words) - 14:53, 10 May 2009
- The '''Fundamental Theorem of Algebra''' is a mathematical theorem stating that every nonconstant [[polynomial]] One important case of the Fundamental Theorem of Algebra is that every nonconstant polynomial with [[Real number|real]] coefficients5 KB (924 words) - 16:35, 11 December 2008
- 2 KB (371 words) - 00:36, 2 February 2009
- Auto-populated based on [[Special:WhatLinksHere/Median algebra]]. Needs checking by a human.443 bytes (56 words) - 18:24, 11 January 2010
- #REDIRECT[[Fundamental Theorem of Algebra]]43 bytes (5 words) - 21:01, 21 May 2007
- 907 bytes (145 words) - 14:06, 16 July 2011
- 879 bytes (140 words) - 17:59, 21 December 2008
- ...07-16}} An historical and introductory essay on the application of Boolean algebra to circuits.350 bytes (48 words) - 14:25, 16 July 2011
- Auto-populated based on [[Special:WhatLinksHere/Sigma algebra]]. Needs checking by a human.812 bytes (100 words) - 20:22, 11 January 2010
- 92 bytes (13 words) - 14:54, 28 November 2008
- 104 bytes (16 words) - 15:57, 23 December 2008
- Auto-populated based on [[Special:WhatLinksHere/Resolution (algebra)]]. Needs checking by a human.470 bytes (59 words) - 20:00, 11 January 2010
- 120 bytes (13 words) - 08:39, 1 June 2008
- 245 bytes (42 words) - 06:20, 4 September 2009
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55170 bytes (21 words) - 15:31, 28 November 2008
- 12 bytes (1 word) - 17:57, 23 December 2007
- {{r|Jordan algebra}}889 bytes (141 words) - 18:01, 6 December 2008
- {{r|Algebra}} ===Disciplines within abstract algebra===654 bytes (81 words) - 13:36, 29 November 2008
- 844 bytes (135 words) - 02:13, 15 December 2008
- {{r|Span (algebra)}}203 bytes (25 words) - 16:47, 6 January 2009
- 12 bytes (1 word) - 13:31, 26 September 2007
- 885 bytes (140 words) - 15:58, 23 December 2008
- {{r|Linear algebra}}885 bytes (142 words) - 15:23, 28 November 2008
- 368 bytes (47 words) - 07:54, 13 July 2008
- 144 bytes (20 words) - 02:59, 15 November 2008
- In mathematics, the '''Hasse invariant of an algebra''' is an invariant attached to a Brauer class of algebras over a field. Th ...d the [[Albert–Brauer–Hasse–Noether theorem]] we may take to be a [[cyclic algebra]] (''L'',φ,π<sup>''k''</sup>) for some ''k'' mod ''n'', where φ is the [1 KB (216 words) - 13:04, 3 January 2013
- * {{cite book | first=Falko | last=Lorenz | title=Algebra. Volume II: Fields with Structure, Algebras and Advanced Topics | year=200213 bytes (27 words) - 13:05, 3 January 2013
- 100 bytes (15 words) - 13:02, 3 January 2013
- Auto-populated based on [[Special:WhatLinksHere/Fundamental Theorem of Algebra]]. Needs checking by a human.493 bytes (64 words) - 16:43, 11 January 2010
- 827 bytes (133 words) - 13:02, 3 January 2013
Page text matches
- * [http://www.helpalgebra.com ''Algebra Help''] Online algebra tutorials. ...://www.ucs.louisiana.edu/~sxw8045/history.htm Highlights in the history of algebra]260 bytes (36 words) - 06:03, 7 November 2010
- {{r|Algebra}} ===Disciplines within abstract algebra===654 bytes (81 words) - 13:36, 29 November 2008
- The '''Albert algebra''' is the set of 3×3 [[self-adjoint]] matrices over the [[octonion]]s with ...ructed using this one, it is often referred to as "the" exceptional Jordan algebra.619 bytes (88 words) - 13:53, 14 November 2008
- ...ematics)|rings]], [[field (mathematics)|fields]], [[vector space]]s, and [[algebra over a field|algebras]].250 bytes (31 words) - 07:40, 27 July 2008
- ...a sigma-algebra of subsets of the set and a measure defined on this sigma-algebra.137 bytes (20 words) - 09:52, 4 September 2009
- ...range of topics, such as [[systems of linear equations]], [[matrix|matrix algebra]], and [[arrow]]s in [[Cartesian coordinates|Cartesian]] two-dimensional or ...l-world problems. Other topics in linear algebra, such as [[matrix|matrix algebra]], [[eigenvalue]]s and [[eigenvector]]s, [[linear operators]], [[matrix rep975 bytes (135 words) - 02:13, 3 September 2010
- {{r|linear algebra}} {{r|abstract algebra}}492 bytes (60 words) - 15:09, 28 July 2009
- ...07-16}} An historical and introductory essay on the application of Boolean algebra to circuits.350 bytes (48 words) - 14:25, 16 July 2011
- * Herstein, I. N., ''Topics in Algebra'', Wiley; 2 edition (June 20, 1975), ISBN 0-471-01090-1. * Mac Lane, Saunders, and Garrett Birkhoff; ''Algebra'', American Mathematical Society; 3rd edition (April 1999). ISBN 0-8218-164242 bytes (31 words) - 08:58, 8 December 2008
- In [[algebra]], a '''division ring''' or '''skew field''' is a [[ring (mathematics)|ring ...a field, and hence ''A'' may be regarded as a ''C''-[[algebra over a field|algebra]].634 bytes (89 words) - 01:24, 18 February 2009
- In [[abstract algebra]], an '''algebra over a field''' ''F'', or ''F''-'''algebra''' is a [[ring (mathematics)|ring]] ''A'' containing an [[field isomorphism * Any [[extension field]] ''E''/''F'' can be regarded as an ''F''-algebra.1 KB (155 words) - 15:55, 23 December 2008
- ...|year=1990 |publisher=McGraw-Hill}} An accessible introduction to Boolean algebra and its applications. ...2001}} A discussion of the wide field of sentential logic of which Boolean algebra is the tip of the iceberg.670 bytes (88 words) - 15:04, 21 July 2011
- * [[List of basic algebra topics]] * [[Fundamental theorem of algebra]]2 KB (247 words) - 06:00, 7 November 2010
- {{r|Abstract algebra}} {{r|Algebra over a field}}1 KB (174 words) - 20:03, 11 January 2010
- #Redirect [[Abstract algebra]]30 bytes (3 words) - 13:29, 12 April 2008
- ...]], a '''Borel set''' is a set that belongs to the [[sigma algebra|σ-algebra]] generated by the open sets of a [[topological space]]. Thus, every open s ...>A \in \sigma(O) </math>, where <math>\sigma(O)</math> denotes the σ-algebra generated by <math>O</math>.981 bytes (168 words) - 13:28, 26 July 2008
- #REDIRECT [[Resolution (algebra)#Properties]]45 bytes (4 words) - 16:37, 1 December 2008
- #REDIRECT[[Fundamental Theorem of Algebra]]43 bytes (5 words) - 21:01, 21 May 2007
- #REDIRECT [[Resultant (algebra)#Sylvester matrix]]50 bytes (5 words) - 16:34, 17 December 2008
- #REDIRECT [[Basis (linear algebra)/Advanced]]45 bytes (5 words) - 19:42, 1 December 2008
- #REDIRECT [[Basis (linear algebra)/Related Articles]]53 bytes (6 words) - 19:43, 1 December 2008
- The structure constants of Hall algebra.77 bytes (9 words) - 08:29, 4 September 2009
- {{r|Algebra over a field}} {{r|Complement (linear algebra)}}1 KB (187 words) - 20:18, 11 January 2010
- {{r|Algebra}} {{r|Basis (linear algebra)}}2 KB (206 words) - 19:38, 11 January 2010
- In [[algebra]], an '''automorphism''' of an [[abstract algebra]]ic structure is an [[isomorphism]] of the structure with itself, that is,368 bytes (48 words) - 07:49, 5 February 2009
- ...be extended to be a [[measure]] on the [[sigma algebra]] generated by that algebra. Measure in this context specifically refers to a non-negative measure. ...a <math>\mathcal{F}=\sigma(\mathcal{F}_0)</math> (i.e., the smallest sigma algebra containing <math>\mathcal{F}_0</math>) such that <math>\mu(A)=\mu_0(A)</mat2 KB (324 words) - 16:34, 27 November 2008
- In [[algebra]], the '''Krull dimension''' of a [[ring theory|ring]] is one less than the * [[A.I. Kostrikin]] and [[Igor Shafarevich|I.R. Shafarevich]] (edd), ''Algebra II'', Encyclopaedia of Mathematical Sciences '''18''', [[Springer-Verlag]],497 bytes (67 words) - 16:20, 30 October 2008
- ==Tensor products in linear algebra==710 bytes (120 words) - 15:46, 23 December 2007
- {{r|Abstract algebra}} {{r|Algebra}}898 bytes (114 words) - 10:49, 11 January 2010
- {{rpl|Root (algebra)|In algebra}}175 bytes (23 words) - 05:09, 26 September 2013
- {{r|Shell (algebra)|In algebra}}237 bytes (34 words) - 11:31, 17 June 2009
- Commercial computer algebra system and a general purpose mathematics software.114 bytes (13 words) - 08:53, 1 June 2008
- {{r|Resolution (algebra)|In algebra}}129 bytes (16 words) - 11:36, 31 May 2009
- A computer algebra system for mathematicians interested in algebraic number theory.119 bytes (14 words) - 15:20, 28 October 2008
- An exceptional Jordan algebra, consisting of 3×3 self-adjoint matrices over the octonions.127 bytes (14 words) - 02:27, 5 December 2008
- ...tion and an identity.<ref>Fraleigh J B (2003) ''A First Course in Abstract Algebra'' ISBN 0321156080, section 8</ref> ...] is generally only concerned with groups, [[ring theory|rings]], [[field (algebra)|fields]] ''et cetera'' [[up to]] isomorphism, the generic permutation grou2 KB (244 words) - 20:34, 1 July 2009
- ....org/stream/linearassocalgeb00pierrich#page/n5/mode/2up Linear Associative Algebra] Benjamin Peirce, Van Nostrand (1882)324 bytes (40 words) - 11:22, 11 January 2010
- ...matician, specializing in the study of differential equations, series, and algebra.147 bytes (15 words) - 14:28, 26 July 2008
- Commutative algebra developed as a theory in mathematics having the aim of translating classica ...correspondence theorems, which allows us to change between the language of algebra and geometry.2 KB (338 words) - 10:01, 23 December 2008
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn= * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55500 bytes (66 words) - 12:18, 29 December 2008
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn= * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55500 bytes (66 words) - 12:27, 29 December 2008
- *{{cite book |title=An exercise book in algebra |author=Scoby McCurdy |url=http://books.google.com/books?id=0RMAAAAAYAAJ&pg *{{cite book |title=Numbers and symmetry: an introduction to algebra |author=Bernard L. Johnston, Fred Richman |url=http://books.google.com/book585 bytes (83 words) - 10:01, 6 January 2011
- {{r|Boolean algebra}} {{r|Transfinite | Transfinite algebra}}507 bytes (65 words) - 07:17, 22 July 2011
- A mathematical operator algebra used to describe magnetic states during [[Nuclear magnetic resonance|NMR]]155 bytes (18 words) - 11:48, 19 January 2009
- Commercial computer algebra system with own programming language that supports functional and procedura160 bytes (18 words) - 08:29, 1 June 2008
- ...he abstract [[Lie algebra]] to a simpler [[Lie algebra#Examples|matrix Lie algebra]]. ...algebra#Homomorphisms, subalgebras, and ideals|homomorphism]] from the Lie algebra to the endomorphisms (linear maps) of some vector space.4 KB (670 words) - 21:07, 22 December 2011
- {{r|Linear algebra}} {{r|Basis (linear algebra)}}338 bytes (42 words) - 19:08, 5 October 2009
- A countably additive non-negative function on an algebra of subsets extends to a measure.125 bytes (17 words) - 16:42, 26 July 2008
- In [[algebra]], the '''span''' of a set of elements of a [[module (algebra)|module]] or [[vector space]] is the set of all finite [[linear combination A [[Basis (linear algebra)|basis]] is a [[Linear independence|linearly independent]] spanning set.968 bytes (162 words) - 13:20, 7 February 2009
- In [[mathematics]], a '''median algebra''' is a set with a [[ternary operation]] < x,y,z > satisfying a set o ...)</math> satisfies these axioms, so that every Boolean algebra is a median algebra.2 KB (316 words) - 13:38, 16 July 2011
- In [[mathematics]], a '''sigma algebra''' is a [[mathematical structure|formal mathematical structure]] intended ...is a collection of subset of <math>\scriptstyle \Omega</math>) is a sigma algebra if it satisfies all the following conditions or axioms:2 KB (314 words) - 16:35, 27 November 2008
- A subdiscipline of abstract algebra that studies fields, which are mathematical constructs that generalize on t194 bytes (25 words) - 13:32, 7 December 2008
- {{r|algebra}} {{r|linear algebra}}579 bytes (84 words) - 14:09, 10 May 2009
- In [[algebra]], a '''Noetherian module''' is a [[module]] with a condition on the [[latt * A [[free module]] of finite [[rank (algebra)|rank]] over a Noetherian ring is a Noetherian module.1 KB (213 words) - 17:17, 7 February 2009
- In [[algebra]], '''separability''' may refer to:112 bytes (13 words) - 13:22, 8 March 2009
- Algebra concerned with the relation between solutions of a polynomial equation and158 bytes (20 words) - 08:08, 4 September 2009
- (or skew field), In algebra it is a ring in which every non-zero element is invertible.123 bytes (19 words) - 01:23, 18 February 2009
- In [[algebra]], the '''content''' of a [[polynomial]] is the [[highest common factor]] o ...nk=Brian Hartley | coauthors=T.O. Hawkes | title=Rings, modules and linear algebra | publisher=Chapman and Hall | year=1970 | isbn=0-412-09810-5 }}971 bytes (132 words) - 15:00, 29 October 2008
- A set that belongs to the σ-algebra generated by the open sets of a topological space.123 bytes (19 words) - 18:52, 24 June 2008
- In [[algebra]], a '''splitting field''' for a polynomial ''f'' over a field ''F'' is a [ * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=1 KB (147 words) - 09:16, 4 July 2009
- In [[algebra]], the '''discriminant of a polynomial''' is an invariant which determines The discriminant may be obtained as the [[resultant (algebra)|resultant]] of the polynomial and its [[formal derivative]].1 KB (163 words) - 18:01, 21 December 2008
- Set together with a sigma-algebra of subsets of this set.94 bytes (13 words) - 09:47, 4 September 2009
- ...ilitates [[symbolic mathematics]]. The core functionality of any computer algebra systems is manipulation of mathematical expressions in symbolic form. Most Typical symbolic manipulations that can be performed by ''computer algebra systems'' include:1 KB (164 words) - 14:01, 18 January 2008
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn= * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55733 bytes (88 words) - 02:34, 24 December 2008
- {{r|Algebra}} {{r|Commutative algebra}}770 bytes (96 words) - 19:39, 11 January 2010
- {{r|Algebra over a field}} {{r|Basis (linear algebra)}}604 bytes (80 words) - 16:01, 11 January 2010
- * {{cite book | first=Falko | last=Lorenz | title=Algebra. Volume II: Fields with Structure, Algebras and Advanced Topics | year=200213 bytes (27 words) - 13:05, 3 January 2013
- ...is the associated command line interface. They have been developed by the Algebra and Number Theory research group of the Institute of Mathematics at [[Techn * [[Comparison of computer algebra systems]]1 KB (152 words) - 08:31, 14 September 2013
- A fundamental and relatively basic form of algebra taught to students who are presumed to have little or no formal knowledge o195 bytes (28 words) - 14:21, 25 October 2008
- A ''Lie algebra'' is a vector space together with a skew-symmetric bilinear operation (the170 bytes (23 words) - 09:27, 27 November 2011
- {{r|Abstract algebra}} {{r|Noncommutative algebra}}715 bytes (91 words) - 17:34, 10 December 2008
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-5171 bytes (21 words) - 17:26, 15 November 2008
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55170 bytes (21 words) - 15:29, 28 November 2008
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-5171 bytes (21 words) - 17:11, 13 November 2008
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55170 bytes (21 words) - 15:31, 28 November 2008
- {{r|Rank (algebra)}}55 bytes (7 words) - 11:07, 31 May 2009
- * {{cite book | author=I.N. Herstein | title=Topics in Algebra | edition=2nd ed | publisher = John Wiley and Sons | year=1975 | isbn=0-471 * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-5688 bytes (93 words) - 12:57, 21 November 2008
- * {{cite book | author=I.N. Herstein | title=Topics in Algebra | edition=2nd ed | publisher = John Wiley and Sons | year=1975 | isbn=0-471 * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55687 bytes (93 words) - 12:00, 23 November 2008
- ...mber theory and for his mathematics textbooks, including the influential ''Algebra''.217 bytes (24 words) - 09:17, 4 September 2009
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55186 bytes (23 words) - 12:14, 2 January 2009
- ...[algebra]], a '''linearly independent''' system of elements of a [[module (algebra)|module]] over a [[ring (mathematics)|ring]] or of a [[vector space]], is o A [[Basis (linear algebra)|basis]] is a maximal linearly independent set: equivalently, a linearly in2 KB (307 words) - 16:08, 7 February 2009
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55190 bytes (22 words) - 12:05, 2 January 2009
- In [[mathematics]], especially in the area of [[abstract algebra|algebra]] studying the theory of [[abelian group]]s, an '''essential subgroup''' is802 bytes (112 words) - 03:33, 2 February 2009
- {{r|Algebra over a field}} {{r|Algebra}}969 bytes (124 words) - 18:42, 11 January 2010
- *[[Computer algebra system]]250 bytes (30 words) - 11:48, 8 February 2009
- In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects a * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=929 bytes (125 words) - 13:24, 18 November 2022
- ...[[Linear independence|linearly independent]] [[spanning set]] in [[linear algebra]].885 bytes (138 words) - 19:39, 31 January 2009
- {{r|Resultant (algebra)}}109 bytes (11 words) - 11:42, 31 May 2009
- * {{cite book | author=I.N. Herstein | title=Topics in Algebra | edition=2nd ed | publisher = John Wiley and Sons | year=1975 | isbn=0-471 * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55835 bytes (112 words) - 12:57, 21 November 2008
- In [[algebra]], the '''Weierstrass preparation theorem''' describes a canonical form for * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55745 bytes (116 words) - 13:35, 8 March 2009
- ...ion with [[algebra over a field|algebras over a field]], as a '''universal algebra'''.2 KB (348 words) - 16:37, 10 March 2009
- {{rpl|Median algebra}}90 bytes (10 words) - 09:36, 24 September 2013
- {{rpl|Sigma algebra}}149 bytes (17 words) - 05:19, 26 September 2013
- * Linear associative algebra, Washington (lithograph) (1870). * Linear associative algebra, Amer. J. Math., 4, 97–215 (1881)3 KB (311 words) - 10:48, 11 January 2010
- ...n a [[group (mathematics)|group]] giving the data required to construct an algebra. A factor system constitutes a realisation of the cocycles in the second [ .../sup>) gives rise to a ''crossed product algebra'' ''A'', which is a ''K''-algebra containing ''L'' as a subfield, generated by the elements λ in ''L'' and '3 KB (519 words) - 15:42, 2 January 2013
- {{r|Module (algebra)}}90 bytes (10 words) - 02:40, 16 May 2009
- {{r|Abstract algebra}} {{r|Algebra}}1 KB (146 words) - 16:32, 11 January 2010
- In [[linear algebra]] the '''characteristic polynomial''' of a [[square matrix]] is a polynomia ...morphism]] of a [[vector space]], independent of choice of [[basis (linear algebra)|basis]].911 bytes (131 words) - 22:35, 17 February 2009
- ==The algebra of the spending multiplier identity==1 KB (227 words) - 06:29, 16 November 2012
- ...ctonions, <math>\mathbb{O}</math>, are a eight-dimensional normed division algebra over the real numbers.<br/><br/> *[[Geometric Algebra]]947 bytes (123 words) - 06:31, 14 September 2013
- ...software)|Maple]] symbolic engine, allowing it to act also as a [[computer algebra system]]. The MATLAB application itself also provides an interactive mathem *[[Sage (computer algebra system)|Sage]]1 KB (141 words) - 11:14, 2 August 2010
- Hall next constructs an [[Algebra over a field|algebra]] <math>H(p)</math> with symbols <math>u_\lambda</math> a generators and mu The map from <math>H(p)</math> to the algebra of [[symmetric function]]s <math>e_n</math> given2 KB (264 words) - 22:53, 19 February 2010
- ...</noinclude>A function on a group giving the data required to construct an algebra. A factor system constitutes a realisation of the cocycles in the second c217 bytes (33 words) - 15:37, 2 January 2013
- * {{cite book | author=I.N. Herstein | title=Topics in Algebra | edition=2nd ed | publisher = John Wiley and Sons | year=1975 | isbn=0-471 * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-551 KB (137 words) - 02:15, 29 November 2008
- *[[Computer algebra system]]119 bytes (12 words) - 08:32, 1 June 2008
- {{r|Complement (linear algebra)}}296 bytes (31 words) - 11:00, 31 May 2009
- {{r|Abstract algebra}} {{r|Algebra}}1 KB (180 words) - 17:00, 11 January 2010
- ...more abstract than algebra. Why is Category Th. listed as subordinate to Algebra? Thanks, [[User:Peter Lyall Easthope|Peter Lyall Easthope]] 23:58, 24 May ...it in an algebraic way, so I think it tends to be regarded as a branch of algebra.2 KB (301 words) - 10:06, 19 November 2014
- {{r|Lattice (algebra)}}174 bytes (20 words) - 04:26, 18 January 2010
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-5297 bytes (38 words) - 07:36, 15 November 2008
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-5297 bytes (38 words) - 17:41, 20 November 2008
- In [[mathematics]], particularly in [[abstract algebra]] and [[homological algebra]], a '''resolution''' is a sequence which is used to describe the structure * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-52 KB (296 words) - 14:49, 28 October 2008
- {{r|Computer algebra system}}193 bytes (26 words) - 08:37, 1 June 2008
- .... The localisation <math>S^{-1}R</math> is an ''R''-[[algebra over a ring|algebra]] in which the elements of ''S'' become invertible, constructed as follows. ...icatively closed subset. The localisation of ''R'' at ''S'' is a [[field (algebra)|field]], the '''field of fractions''' of ''R''. A ring can be embedded in2 KB (312 words) - 09:18, 21 October 2009
- ...closure''' of a commutative unital ring ''R'' in an [[algebra over a ring|algebra]] ''S'' over ''R'' is the [[subset]] of ''S'' consisting of all elements of1 KB (172 words) - 15:42, 7 February 2009
- In [[algebra]], a '''Noetherian ring''' is a [[ring (mathematics)|ring]] with a conditio * A [[field (algebra)|field]] is Noetherian, since its only ideals are (0) and (1).2 KB (326 words) - 09:55, 23 December 2008
- {{r|algebra}}199 bytes (24 words) - 11:54, 4 December 2008
- {{r|Elementary algebra}}263 bytes (35 words) - 06:59, 15 July 2008
- {{r|Computer algebra}}164 bytes (18 words) - 08:57, 27 July 2009
- {{r|Elementary algebra}}237 bytes (29 words) - 08:06, 14 January 2009
- {{r|Span (algebra)}}203 bytes (25 words) - 16:47, 6 January 2009
- * [[Adjoint (linear algebra)]], the adjoint of a square matrix251 bytes (38 words) - 12:40, 31 May 2009
- ...e relationship between [[addition]] and [[multiplication]] in [[elementary algebra]] known as "multiplying out". For these elementary operations it is also k2 KB (226 words) - 13:15, 18 November 2022
- {{r|algebra}}317 bytes (40 words) - 00:19, 11 December 2008
- * An element of a group in a [[chain complex]] in [[homological algebra]]334 bytes (50 words) - 12:52, 31 May 2009
- In mathematics, the '''Hasse invariant of an algebra''' is an invariant attached to a Brauer class of algebras over a field. Th ...d the [[Albert–Brauer–Hasse–Noether theorem]] we may take to be a [[cyclic algebra]] (''L'',φ,π<sup>''k''</sup>) for some ''k'' mod ''n'', where φ is the [1 KB (216 words) - 13:04, 3 January 2013
- {{r|Fundamental Theorem of Algebra}}276 bytes (34 words) - 10:41, 21 April 2010
- {{r|Elementary algebra}}203 bytes (25 words) - 18:31, 26 October 2008
- The '''Chinese remainder theorem''' is the name of a theorem in [[abstract algebra]], which, in its most general formulation, provides information about the s394 bytes (62 words) - 13:04, 18 November 2008
- {{r|Sigma algebra}}282 bytes (38 words) - 16:42, 26 July 2008
- {{r|Elementary algebra}}259 bytes (33 words) - 08:47, 6 August 2008
- {{r|Linear algebra}}366 bytes (48 words) - 11:31, 27 July 2008
- {{r|Elementary algebra}}209 bytes (24 words) - 10:53, 6 November 2008
- .../math> is a [[set]] and <math>\scriptstyle \mathcal{F}</math> is a [[sigma algebra]] of subsets of <math>\scriptstyle \Omega</math>.346 bytes (47 words) - 15:41, 3 November 2008
- {{r|C*-algebra}}296 bytes (36 words) - 18:51, 12 July 2008
- {{r|Sigma algebra}}260 bytes (36 words) - 13:28, 26 July 2008
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=Addison-Wesley | year=1993 | isbn=0-201-55540-407 bytes (50 words) - 11:36, 12 June 2009
- ...modern mathematics for physicists and other outsiders: An introduction to algebra, topology, and functional analysis ...modern mathematics for physicists and other outsiders: An introduction to algebra, topology, and functional analysis2 KB (187 words) - 15:32, 1 August 2010
- The '''Fundamental Theorem of Algebra''' is a mathematical theorem stating that every nonconstant [[polynomial]] One important case of the Fundamental Theorem of Algebra is that every nonconstant polynomial with [[Real number|real]] coefficients5 KB (924 words) - 16:35, 11 December 2008
- {{r|Algebra}}162 bytes (19 words) - 11:42, 12 June 2009
- {{r|Algebra}}454 bytes (55 words) - 03:14, 21 October 2010
- {{r|algebra}}267 bytes (32 words) - 12:09, 19 December 2008
- {{r|Algebra}}306 bytes (40 words) - 06:01, 10 September 2009
- ...ic world, making significant discoveries in both fields but primarily in [[algebra]] and in discovering the [[solar year]]. He is most famous for his poetry a432 bytes (62 words) - 18:42, 3 March 2024
- {{r|Algebra}}542 bytes (63 words) - 14:59, 1 November 2014
- *{{cite book|last=Borceux|first=Francis|title=Handbook of Categorical Algebra Volume I: Basic Category Theory|year=2008|publisher=CUP|series=Encyclopedia611 bytes (79 words) - 20:30, 23 May 2009
- {{r|Banach algebra}}423 bytes (60 words) - 15:14, 28 July 2009
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55408 bytes (62 words) - 11:32, 13 February 2009
- *{{cite book |title=An exercise book in algebra |author=Scoby McCurdy |url=http://books.google.com/books?id=0RMAAAAAYAAJ&pg566 bytes (82 words) - 07:45, 7 January 2011
- In [[algebra]], '''algebraic independence''' is a property of a set of elements of an [[ * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-552 KB (253 words) - 17:52, 6 January 2009
- ...onstruction of a ring which formalises the [[polynomial]]s of [[elementary algebra]]. * The polynomial ring ''R''[''X''] is an [[algebra over a ring|algebra]] over ''R''.4 KB (604 words) - 23:54, 20 February 2010
- ...y algebraic geometry of algebraic sets is closely related to [[commutative algebra]]. ...and later to arbitrary [[field]]s. In the second place notions of abstract algebra have led to a natural generalization of algebraic geometry, namely to the c2 KB (287 words) - 10:43, 11 June 2009
- {{r|Abstract algebra}} {{r|Algebra}}2 KB (262 words) - 19:07, 11 January 2010
- {{r|Fundamental Theorem of Algebra}}444 bytes (57 words) - 17:15, 11 January 2010
- * {{cite book | first=Falko | last=Lorenz | title=Algebra. Volume II: Fields with Structure, Algebras and Advanced Topics | year=200611 bytes (75 words) - 15:43, 2 January 2013
- {{r|Boolean algebra}}477 bytes (65 words) - 07:22, 22 July 2011
- * I.N. Herstein: ''Topics in Algebra''. ISBN 0-471-02371-X580 bytes (78 words) - 06:03, 7 November 2010
- * In [[abstract algebra]], an equivalence relation which respects algebraic operations645 bytes (93 words) - 12:51, 31 May 2009
- In [[mathematics]], and more specifically [[algebra]], a '''polynomial equation''' is an [[equation]] involving only [[polynomi ...tion (equation)|solution]]s, a consequence of the [[fundamental theorem of algebra]]. This is not true for other types of equations. For instance,4 KB (647 words) - 16:35, 22 December 2008
- {{r|Sigma algebra}}670 bytes (76 words) - 07:31, 16 April 2010
- ...initesimal [[symmetry|symmetries]] or [[transformation]]s. In short a Lie algebra is a [[vector space]] together with a skew-symmetric bilinear operation den ...''Y'']] = 0 where ''X'', ''Y'', and ''Z'' run over all elements of the Lie algebra.12 KB (1,918 words) - 20:29, 22 December 2011
- Auto-populated based on [[Special:WhatLinksHere/Median algebra]]. Needs checking by a human.443 bytes (56 words) - 18:24, 11 January 2010
- ...f "+" ([[addition]]) and a [[topological space|topology]], for example the algebra of the real numbers with the standard Euclidean topology. Countable additiv [[Sigma algebra]]4 KB (604 words) - 05:50, 12 May 2008
- {{r|Basis (linear algebra)}}474 bytes (60 words) - 20:31, 11 January 2010
- {{r|Algebra}}509 bytes (65 words) - 19:50, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Resolution (algebra)]]. Needs checking by a human.470 bytes (59 words) - 20:00, 11 January 2010
- {{r|Algebra}}522 bytes (68 words) - 19:10, 11 January 2010
- Auto-populated based on [[Special:WhatLinksHere/Fundamental Theorem of Algebra]]. Needs checking by a human.493 bytes (64 words) - 16:43, 11 January 2010
- ...[.NET Framework]] with n-dimensional arrays, [[Complex numbers]], [[Linear algebra]], [[fast Fourier transform]] and plotting controls (2D and 3D), ILNumerics617 bytes (84 words) - 07:14, 22 October 2013
- *{{cite book |title=Linear algebra: Theory and applications |author=Ward Cheney, David Kincaid |chapter=§2.3:732 bytes (100 words) - 19:44, 10 May 2011
- {{r|Resolution (algebra)}}515 bytes (67 words) - 16:26, 11 January 2010
- {{r|Fundamental Theorem of Algebra}}544 bytes (70 words) - 18:34, 11 January 2010
- {{r|Commutative algebra}}546 bytes (70 words) - 07:47, 8 January 2010
- {{r|Computer algebra system}}626 bytes (80 words) - 18:22, 11 January 2010
- In [[algebra]], a '''normal extension''' of [[field (mathematics)|fields]] is a [[field568 bytes (88 words) - 17:21, 7 February 2009
- {{r|Algebra over a field}}580 bytes (77 words) - 19:51, 11 January 2010
- {{r|Algebra}}626 bytes (79 words) - 16:01, 11 January 2010
- ...l{F}_Y)</math> is said to be '''measurable''' (with respect to the [[sigma algebra]] <math>\scriptstyle \mathcal{F}_X</math>) if for any set <math>\scriptstyl545 bytes (92 words) - 05:55, 12 May 2008
- {{r|Commutative algebra}}565 bytes (72 words) - 19:39, 11 January 2010
- {{r|Abstract algebra}}598 bytes (78 words) - 20:14, 11 January 2010
- * {{cite book | author=C.W. Norman | title=Undergraduate Algebra: A first course | publisher=[[Oxford University Press]] | year=1986 | isbn=579 bytes (73 words) - 02:31, 13 December 2008
- ...ga</math> is a [[set]], <math>\scriptstyle \mathcal{F}</math> is a [[sigma algebra]] of subsets of <math>\scriptstyle \Omega</math> and <math>\mu</math> is a590 bytes (82 words) - 05:53, 12 May 2008
- '''Maple''' is a commercial [[computer algebra system]] and a general purpose mathematics software. It is developed by the622 bytes (100 words) - 05:16, 25 January 2009
- {{r|Basis (linear algebra)}}574 bytes (75 words) - 21:21, 11 January 2010
- {{r|Sigma algebra}}681 bytes (87 words) - 18:24, 11 January 2010
- {{r|Algebra over a field}}537 bytes (72 words) - 11:44, 11 January 2010
- {{r|Basis (linear algebra)}}679 bytes (85 words) - 18:06, 11 January 2010
- {{r|Computer algebra system}}592 bytes (77 words) - 18:05, 11 January 2010
- In [[mathematics]], especially in [[linear algebra]], Gram-Schmidt orthogonalization is a sequential procedure or [[algorithm] #H. Anton and C. Rorres, ''Elementary Linear Algebra with Applications'' (9 ed.), Wiley, 2005.2 KB (301 words) - 06:39, 21 October 2007
- {{r|Abstract algebra}}648 bytes (83 words) - 10:12, 11 May 2009
- {{r|Sigma algebra}}674 bytes (82 words) - 15:40, 11 January 2010
- {{r|Sigma algebra}}674 bytes (82 words) - 16:00, 11 January 2010
- {{r|Computer algebra system}}763 bytes (99 words) - 17:28, 11 January 2010
- {{r|Algebra}}675 bytes (89 words) - 17:28, 11 January 2010
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-5631 bytes (91 words) - 14:44, 28 October 2008
- ...>\ \mathbb{C}</math> over <math>\ \mathbb{Q};</math> and by [[algebra]] we mean a linear space which is closed under the multiplication, and whic * <math>\ z</math> belongs to an algebra of linear dimension <math>\ \le n.</math>7 KB (1,145 words) - 00:49, 20 October 2013
- Let <math>A\to B</math> be an [[Module|algebra]]. An ''A'' differential of ''B'' into an <math>A</math>-module <math>M</ma686 bytes (133 words) - 11:45, 1 January 2008
- {{r|Algebra}}856 bytes (107 words) - 18:36, 11 January 2010
- {{r|Sigma algebra}}814 bytes (102 words) - 19:54, 11 January 2010
- == Switching algebra == ...ogic gates in digital hardware. Shannon called boolean algebra "switching algebra" in the context of digital hardware design.7 KB (993 words) - 15:28, 8 January 2023
- ==Algebra==3 KB (562 words) - 00:00, 17 February 2010
- {{r|Algebra}}858 bytes (112 words) - 15:35, 11 January 2010
- {{r|Sigma algebra}}771 bytes (95 words) - 18:24, 11 January 2010
- ...rmal Dirichlet series form a ring, which is an ''R''-[[algebra over a ring|algebra]].2 KB (398 words) - 11:44, 15 June 2009
- Auto-populated based on [[Special:WhatLinksHere/Sigma algebra]]. Needs checking by a human.812 bytes (100 words) - 20:22, 11 January 2010
- * {{cite book | author=I.N. Herstein | title=Topics in Algebra | edition=2nd ed | publisher = John Wiley and Sons | year=1975 | isbn=0-471705 bytes (92 words) - 14:12, 23 November 2008
- {{r|Linear algebra}}879 bytes (114 words) - 03:09, 8 March 2024
- ...lean algebra]] to the design of digital circuits (and called it "Switching Algebra")''3 KB (449 words) - 13:27, 4 January 2023
- In [[algebra]], '''commutativity''' is a property of [[binary operation]]s or of [[opera695 bytes (102 words) - 19:40, 31 January 2009
- {{r|Algebra}}714 bytes (111 words) - 02:44, 9 November 2008
- ...[[Diophantus]], who lived in Egypt and is often considered the "father of algebra", writes his famous ''[[Arithmetica]]'', a work featuring solutions of alge ...on reduction was included in the book and added to many methods we have in algebra now.8 KB (1,117 words) - 08:22, 5 December 2011
- {{r|abstract algebra}}668 bytes (88 words) - 12:30, 29 November 2008
- {{r|Linear algebra}}949 bytes (118 words) - 16:12, 11 January 2010
- {{r|Algebra}}927 bytes (119 words) - 16:24, 11 January 2010
- {{r|Fundamental Theorem of Algebra}}991 bytes (124 words) - 17:15, 11 January 2010
- '''Mathematica''' is a commercial [[computer algebra system]] with own programming language that supports functional and procedu901 bytes (119 words) - 20:25, 20 September 2013
- |title = Basic Algebra I899 bytes (119 words) - 17:42, 26 September 2007
- In [[mathematics]], particularly in [[abstract algebra]] and [[homological algebra]], an '''exact sequence''' is a sequence of algebraic objects and morphisms3 KB (471 words) - 17:22, 15 November 2008
- In [[algebra]], the '''resultant''' of two polynomials is a quantity which determines wh * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-552 KB (388 words) - 17:58, 21 December 2008
- In [[algebra]], an '''absorbing element''' or a '''zero element''' for a [[binary operat726 bytes (112 words) - 15:21, 21 December 2008
- In [[algebra]], a '''polynomial''' is, roughly speaking, a formal [[expression (mathemat ...need only know how to add and multiply their coefficients. In [[abstract algebra]], an abstract collection of objects that can be added and multiplied subje10 KB (1,741 words) - 10:04, 3 January 2009
- In [[elementary algebra]], the '''binomial theorem''' or the binomial expansion is a mechanism by w ...nomial theorem''', proved by [[Isaac Newton]], that goes beyond elementary algebra into mathematical analysis, which expands the same sum (''x'' + '3 KB (507 words) - 07:34, 9 August 2010
- In [[linear algebra]], a '''basis''' for a [[vector space]] <math>V</math> is a set of [[vector The term '''basis''' is also used in [[abstract algebra]], specifically in the theory of [[free module]]s. For more on this use of3 KB (464 words) - 19:45, 1 December 2008
- ...1 for the full [[modular group]]. It is an [[eigenform]] for the [[Hecke algebra]].626 bytes (96 words) - 16:46, 3 December 2008
- ...| last=Jacobson | first=Nathan | authorlink=Nathan Jacobson | title=Basic Algebra I | edition=2nd ed | year=1985 | publisher=W. H. Freeman and Co. | place=Ne790 bytes (108 words) - 14:54, 27 October 2008
- In algebra, the term '''zero element''' is used with two meanings,853 bytes (133 words) - 19:23, 10 November 2009
- {{r|Resultant (algebra)}}870 bytes (138 words) - 17:57, 21 December 2008
- * [[Jean-Pierre Serre]], ''Local algebra'', [[Springer-Verlag]], 2000, ISBN 3-540-66641-9. Chap.IV.D.970 bytes (142 words) - 00:04, 21 February 2010
- {{r|Algebra}}890 bytes (141 words) - 02:43, 7 January 2009
- {{r|Jordan algebra}}889 bytes (141 words) - 18:01, 6 December 2008
- {{r|Linear algebra}}885 bytes (142 words) - 15:23, 28 November 2008
- {{r|Linear algebra}}896 bytes (141 words) - 14:11, 9 January 2013
- In [[mathematics]], and more specifically [[algebra]], a '''cubic equation''' is an [[equation]] involving only [[polynomial]]s ...has at most three real roots, as dictated by the [[fundamental theorem of algebra]]. [[solution (equation)|Solving]] cubic equations is more difficult than3 KB (483 words) - 23:24, 17 December 2008
- In [[algebra]], an '''idempotent element''' with respect to a [[binary operation]] is an1,007 bytes (146 words) - 16:14, 13 December 2008
- In [[matrix algebra]], the '''identity matrix''' is a [[square matrix]] which has all the entri1,020 bytes (136 words) - 10:39, 23 April 2009
- {{r|Linear algebra}}905 bytes (145 words) - 15:27, 28 November 2008
- The traditional Iverson bracket notation in algebra: [a>b] gives 1 or 0.725 bytes (109 words) - 03:08, 7 January 2009
- {{r|Boolean algebra}}910 bytes (145 words) - 14:05, 16 July 2011
- * {{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-55844 bytes (130 words) - 12:09, 2 January 2009
- ...0 per cent of the preceding deposit, and the appropriate value of r in the algebra column is therefore 0.9. The hypothetical bottom row shows the final amount !''Algebra''3 KB (418 words) - 06:43, 30 November 2008
- ==The algebra of elasticity==4 KB (675 words) - 03:20, 27 October 2013
- ==Algebra of power series==4 KB (785 words) - 14:27, 14 March 2021
- In [[algebra]], '''completing the square''' is a way of rewriting a quadratic [[polynomi The technique relies on the [[elementary algebra|elementary algebraic]] identity3 KB (517 words) - 08:49, 6 August 2008
- In [[matrix algebra]], the '''inverse''' of a [[square matrix]] '''A''' is '''X''' if1 KB (158 words) - 00:36, 18 April 2009
- ...linear associative algebra]].<ref>In 1870 B. Peirce's ''Linear associative algebra'' existed in handwritten form only. It was copied by a lady with fine handw Peirce is mainly remembered for his work on the linear associative algebra of 1870. But before that he did other important work. When he was not yet8 KB (1,209 words) - 08:09, 28 September 2013
- '''Algebra''' is a branch of [[mathematics]] concerning the study of [[structure (alge ...[[secondary education]] and provides an introduction to the basic ideas of algebra, including effects of [[addition|add]]ing and [[multiplication|multiply]]in18 KB (2,669 words) - 08:38, 17 April 2024
- ...omething about quaternions arising from pairs of reflections and Clifford algebra --> ...{H}</math>, form a four-dimensional normed division [[Algebra over a field|algebra]] over the [[real number]]s.<br/><br/>7 KB (1,160 words) - 07:41, 22 December 2008
- {{r|Algebra}}1 KB (169 words) - 08:53, 22 December 2008
- {{r|Algebra}}1 KB (169 words) - 19:54, 11 January 2010
- ...physics]]. This article deals exclusively with fields as used in abstract algebra. *[[Algebra]]3 KB (496 words) - 22:16, 7 February 2010
- In [[algebra]], an '''identity element''' or '''neutral element''' with respect to a [[b927 bytes (140 words) - 15:33, 8 December 2008
- ...ap|(negation, ~)}} that reverses the truth value of any statement. Boolean algebra can be used to analyze computer chips and switching circuits, as well as lo ...mentary algebra]] as taught in secondary schools, and is only a facet of [[algebra]], the general mathematical discipline treating variables, symbols and sets13 KB (1,959 words) - 19:49, 1 September 2020
- In [[matrix algebra]], the '''zero matrix''' is a [[matrix]] which has all entries equal to zer1 KB (172 words) - 16:40, 6 February 2009
- ...''Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra'', second edition, World Scientific, 2007, ISBN 978-981-270-809-01 KB (158 words) - 10:59, 27 November 2011
- In [[linear algebra]], a '''complement''' to a subspace of a vector space is another subspace w1 KB (195 words) - 15:17, 12 December 2008
- ..., in particular ''Algebra'', his graduate-level introduction to [[abstract algebra]]. In 1960, he won the sixth [[Cole Prize|Frank Nelson Cole Prize]] in Algebra for his paper ''Unramified class field theory over function fields in sever7 KB (1,058 words) - 07:16, 9 June 2009
- ...which is ramified over the vertices of the triangulation]]Over a [[field (algebra)|field]] in general [[Euler characteristic|characteristic]], this theorem i1 KB (166 words) - 10:43, 14 November 2007
- ...principal motivating examples include the [[arithmetic]] and [[elementary algebra]]ic operations of addition, subtraction, multiplication and division.1 KB (202 words) - 12:53, 12 December 2008
- ...used.<ref>{{cite book | author=Serge Lang | authorlink=Serge Lang | title=Algebra | edition=3rd ed. | publisher=[[Addison-Wesley]] | year=1993 | isbn=0-201-51,021 bytes (145 words) - 15:11, 30 October 2008
- In [[algebra]], the '''Frobenius map''' is the ''p''-th power map considered as acting o1 KB (166 words) - 18:17, 16 February 2009
- In [[linear algebra]] the '''minimal polynomial''' of an algebraic object is the [[monic polyno The general setting is an algebra ''A'' over a field ''F''. We give ''A'' the structure of a [[module]] over4 KB (613 words) - 02:34, 4 January 2013
- In [[abstract algebra]], '''pointwise operation''' is a way of extending an [[operation (mathemat1,002 bytes (157 words) - 13:37, 8 March 2009
- |align=right|[[propositional logic]], [[Heyting algebra]] |align=right|[[propositional logic]], [[Boolean algebra]]9 KB (1,308 words) - 13:37, 16 July 2011
- ...ly, suppose that a measure ''μ'' defined over a [[sigma-algebra|σ-algebra]] ''Σ'' of subsets of the real line satisfies4 KB (618 words) - 21:07, 15 November 2007
- In [[algebra]], a '''cyclotomic polynomial''' is a [[polynomial]] whose roots are a set1 KB (206 words) - 14:55, 11 December 2008
- * [[Jean-Pierre Serre]], ''Local algebra'', [[Springer-Verlag]], 2000, ISBN 3-540-66641-9. Chap.IV.D.1 KB (191 words) - 00:03, 21 February 2010
- T. Heath, Diophantus of Alexandria: A Study in the History of Greek Algebra, 2nd. ed, Cambridge University Press, 1910.1 KB (157 words) - 00:48, 1 January 2009
- In [[abstract algebra]], the '''group isomorphism problem''' is the [[decision problem]] of deter1 KB (164 words) - 17:17, 28 October 2008
- ...general framework. The foundations of abelian categories and [[homological algebra]] were outlined in the paper ''Sur quelques points d'algèbre homologique'2 KB (235 words) - 18:20, 21 January 2008
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=1 KB (210 words) - 01:00, 11 February 2009
- ...=PA114 |pages=pp. 114 ''ff'' |chapter= §2.2 Matrix representation of a Lie algebra |isbn=9971501473 |year=1987 |publisher=World Scientific}} ...re the basis for an irreducible two-dimensional representation of this Lie algebra.7 KB (1,096 words) - 05:49, 17 October 2013
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=1 KB (211 words) - 17:02, 7 February 2009
- In [[matrix algebra]], a '''diagonal matrix''' is a [[square matrix]] for which only the entrie2 KB (230 words) - 02:39, 7 January 2009
- In [[abstract algebra]], a linear map is a [[homomorphism]] of vector spaces.1 KB (196 words) - 17:24, 20 December 2007
- In [[linear algebra]], a '''Moore matrix''', named after [[E. H. Moore]], is a [[determinant]]1 KB (199 words) - 15:30, 7 December 2008
- ...nst one cipher he might treat the text as a vector of bits and use Boolean algebra while for another he might choose to treat it as a vector of bytes and use ...the system of equations and nonlinearity in the relations involved. In any algebra, solving a system of ''linear'' equations is more-or-less straightforward p6 KB (882 words) - 05:49, 8 April 2024
- ....ac.uk/cuter-www/ CUTEr] - testing environment for optimization and linear algebra solvers2 KB (239 words) - 06:44, 20 March 2008
- * The [[characteristic polynomial]] in [[linear algebra]].2 KB (242 words) - 02:01, 2 February 2009
- In [[algebra]], the '''Kronecker delta''' is a notation <math>\delta_{ij}</math> for a q1 KB (209 words) - 07:59, 22 December 2008
- * objects are projections in a given von Neumann algebra; ...lgebra (that is, ''E'' = ''V*V'' and ''F'' = ''VV*'' for some ''V'' in the algebra).6 KB (944 words) - 08:32, 14 October 2013
- * objects are projections in a given von Neumann algebra; ...lgebra (that is, ''E'' = ''V*V'' and ''F'' = ''VV*'' for some ''V'' in the algebra).6 KB (944 words) - 15:09, 23 September 2013
- Elasticity of Demand (an example of the algebra of elasticity)1 KB (253 words) - 11:42, 2 May 2008
- ...c concept of '''measure theory''', which studies the properties of [[sigma algebra|σ-algebras]], measures, [[measurable function]]s and [[integral]]s. ...al with such problems one developes the concept of [[sigma algebra|σ-algebra]], a family of subsets to which it is possible to assign a meaningful ''len14 KB (2,350 words) - 17:37, 10 November 2007
- In the [[mathematics|mathematical]] field of [[abstract algebra]], an '''abelian group''' is a type of [[group (mathematics)|group]] in whi2 KB (240 words) - 10:48, 21 September 2013
- {{r|Basis (linear algebra)}}2 KB (247 words) - 17:28, 11 January 2010
- ...Tholen | title=Categorical Foundations: Special Topics in Order, Topology, Algebra, and Sheaf Theory | publisher=[[Cambridge University Press]] | year=2004 |1 KB (203 words) - 13:09, 7 February 2009
- ...rcle]] ''X''<sup>2</sup> + ''Y''<sup>2</sup> = 1 defined over the [[field (algebra)|field]] of [[real number]]s. The point1 KB (240 words) - 20:00, 7 February 2009
- ...matical problem using a computer. [[Differential equation]]s and [[linear algebra]] are two of the largest fields of study within this area.1 KB (225 words) - 22:09, 3 September 2010
- ...0 per cent of the preceding deposit, and the appropriate value of r in the algebra column is therefore 0.9. The hypothetical bottom row shows the final amount !''Algebra''4 KB (634 words) - 06:19, 3 June 2022
- ...or space]]s are particular types. They have become ubiquitous in abstract algebra and other areas of mathematics that involve algebraic structures, such as a ...space]]. Although vector spaces as encountered in applications or linear algebra courses usually use real or complex number scalars, the most general type o7 KB (1,154 words) - 02:39, 16 May 2009
- ...polynomial has no roots in Q. However, from the [[fundamental theorem of algebra]] we know that it has exacly two roots in C, and can be written as the prod Using ordinary algebra and the identity <math>r_0^2 = r_1^2= 5</math>, it is quite easy to show t4 KB (683 words) - 22:17, 7 February 2010
- In [[algebra]], the '''commutator''' of two elements of an [[algebraic structure]] is a1 KB (217 words) - 15:16, 11 December 2008
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=2 KB (283 words) - 10:23, 6 January 2011
- In [[mathematics]], or more specifically [[algebra]], a '''quadratic equation''' is an [[equation]] involving only [[polynomia The [[Fundamental Theorem of Algebra]] tells us that we should expect there to be two roots for a second-degree8 KB (1,360 words) - 16:44, 17 December 2008
- ...anch of [[mathematics]] concerned with analysis of random phenomena. Like algebra, geometry and other parts of mathematics, probability theory has its origi ...concepts such as [[set|sets]], [[measure (mathematics)|measure]], [[sigma algebra|sigma algebras]] and a set of rules we expect probability to follow, known4 KB (672 words) - 14:38, 30 January 2011
- * [[George Boole|Boole, George]] (1815-1864) - inventor of [[Boolean algebra]] * [[Claude Shannon|Shannon, Claude]] (1916-2001) - association of boolean algebra with digital design; pioneering work in [[information theory]]4 KB (515 words) - 09:39, 10 November 2008
- ...mathematics, modular arithmetic is of fundamental importance in [[abstract algebra]] and [[number theory]].2 KB (267 words) - 13:18, 6 December 2008
- In [[algebra]], the '''continuant''' of a sequence of terms is an algebraic expression w2 KB (293 words) - 17:21, 13 January 2013
- ...g''. Such commutative rings are the basic object of study in [[commutative algebra]], in which rings are generally also assumed to have a unit. * [[Algebra over a commutative ring]]10 KB (1,667 words) - 13:47, 5 June 2011
- === Group theory, algebra and geometry ===7 KB (1,246 words) - 05:37, 18 October 2013
- In [[algebra]], '''associativity''' is a property of [[binary operation]]s. If <math>\s2 KB (295 words) - 14:56, 12 December 2008
- ...f 4.5 hours. The problems are in the following mathematical disciplines: [[algebra]], [[number theory]], [[combinatorics]] and [[geometry]]. On each day, the ...ems, the host country selects a ''shortlist'' with 6-10 problems each from algebra, number theory, geometry and combinatorics.7 KB (1,063 words) - 10:07, 28 February 2024
- ...>j_x</math>, <math>j_y</math>, <math>j_z</math> be generators of the [[Lie algebra]] of SU(2) and SO(3). In [[quantum mechanics]] these [[irreducible representations]] of the isomorphic [[Lie algebra|Lie algebra's]] generated by <math>\{\mathcal{J}_i\}</math> and <math>\{-\mathcal{P}_i11 KB (1,671 words) - 06:37, 1 November 2009
- ...efine it properly! In fact, at the moment, this is true. With the tools of algebra and geometry, we cannot study the rate of change of this function. The '''d ...neath one on an interval is impossible with just the tools of geometry and algebra. We don't even know how to define area! In fact, the definition of area is5 KB (912 words) - 09:26, 29 May 2009
- ...f entire functions are entire, so that the entire functions form a '''C'''-algebra. Further, [[Function composition|composition]]s of entire functions are al ...property can be used for an elegant proof of the [[fundamental theorem of algebra]]. !-->6 KB (827 words) - 14:44, 19 December 2008
- Let ''R'' be a [[ring (mathematics)|ring]] and ''A'' an ''R''-algebra (''A'' is a ring containing a copy of ''R'' in the [[centre of a ring|centr2 KB (361 words) - 16:44, 4 January 2013
- ...distributions are actually defined much more generally in terms of [[sigma algebra|sigma algebras]] and [[measure|measures]]. Using these general definitions, *[[Sigma algebra]]6 KB (870 words) - 12:20, 15 November 2007
- {{r|Computer algebra system}}3 KB (353 words) - 03:48, 24 September 2013
- ...science, and engineering. Many [[algebraic structure]]s such as [[field (algebra)|field]]s and [[vector space]]s are based on groups, and group theory provi ...cation together form the more complicated algebraic structure of a [[ring (algebra)|ring]].19 KB (3,074 words) - 11:11, 13 February 2009
- ...bb{R}),P)</math> where <math>\mathcal{B}(\mathbb{R})</math> is the [[sigma algebra]] of [[Borel set|Borel subsets]] of <math>\mathbb{R}</math> and ''P'' is a2 KB (383 words) - 17:06, 17 October 2007
- ===Some algebra=== With the same header, as in the example above, the elementary algebra can be verified. Below, the header is not copypasted (although it should ex9 KB (1,289 words) - 00:39, 24 October 2013
- ...on of a [[Lie algebra#Killing form and quadratic Lie algebra|quadratic Lie algebra]]. More precisely a Courant algebroid is a [[vector bundle]] ''E→M'' ove form a two-term [[L_infty algebra|L<sub>∞</sub>-algebra]],<ref>D. Roytenberg and A. Weistein: ''Courant algebroids and L<sub>∞</s13 KB (2,084 words) - 03:51, 7 October 2013
- * [[Submodule]]s of a [[module (algebra)]] or [[subspace]]s of a [[vector space]]. The submodule generated by a su2 KB (414 words) - 03:00, 14 February 2010
- In [[algebra]], a '''semigroup''' is a set equipped with a binary operation satisfying c3 KB (405 words) - 16:21, 13 November 2008
- ...C}^n))</math>, where <math>\mathcal{B}(\mathbb{C}^n)</math> is the [[sigma algebra]] of [[Borel set|Borel sets]] of <math>\mathbb{C}^n</math>. A formal defini2 KB (393 words) - 06:53, 14 July 2008
- The remaining Asset Classes are used in a [[linear algebra model]] to construct an Efficient Frontier. Essentially, all potential inve2 KB (362 words) - 21:49, 10 November 2007
- ...] plays for [[Lie group]]s. In the sense of abstract nonsense it is a Lie algebra with many objects. More concretely it is a [[vector bundle]] ''A→M'' who ...e [[Lie algebra#Lie algebra associated to a Lie group|association of a Lie algebra to a Lie group]]. Let 1: ''M''→''G'' be the unit elements and ''s'',''t'16 KB (2,719 words) - 04:11, 7 October 2013
- * {{cite book | author=A.G. Howson | title=A handbook of terms used in algebra and analysis | publisher=[[Cambridge University Press]] | year=1972 | isbn=3 KB (435 words) - 22:38, 22 February 2009
- In [[mathematics]], or more specifically [[algebra]], a '''linear equation''' is an [[equation]] involving only [[polynomials]3 KB (418 words) - 14:53, 4 March 2009
- ...gardless of the starting point. See {{cite book |title=An exercise book in algebra |author=Scoby McCurdy |url=http://books.google.com/books?id=0RMAAAAAYAAJ&pg3 KB (390 words) - 11:35, 12 March 2011
- ...ean algebra <math>(\{0,1\}^S, \cup, \cap, -, \emptyset, S)</math> into the algebra <math>(L^S, \cup, \cap, -, \emptyset, S)</math>.6 KB (993 words) - 08:55, 30 May 2009
- *[[Sigma algebra]]3 KB (390 words) - 07:22, 26 September 2007
- In [[algebra]], a '''polynomial''' is, roughly speaking, a formal [[expression (mathemat After [[simplify (algebra)|simplification]], a polynomial can be written as a finite sum of monomials8 KB (1,242 words) - 02:01, 10 November 2009
- * {{cite book | author=C.W. Norman | title=Undergraduate Algebra: A first course | publisher=[[Oxford University Press]] | year=1986 | isbn=3 KB (430 words) - 06:46, 23 November 2009
- In [[algebra]], a '''monoid''' is a set equipped with a binary operation satisfying cert3 KB (526 words) - 11:02, 23 December 2008
- ...s us the two expressions in square brackets are equal. Then by elementary algebra we have3 KB (480 words) - 16:53, 10 November 2007
- ...is story however is almost certainly an urban myth and Diderot knew enough algebra to answer Euler. However it is said that Euler published some not really se6 KB (1,084 words) - 03:54, 1 November 2010
- The rationals are the smallest field with [[characteristic (algebra)|characteristic]] zero: every other field of characteristic zero contains a ...th>. [[Ostrowski's theorem]] states that any non-trivial [[absolute value (algebra)|absolute value]] on the rational numbers <math>\mathbb{Q}</math> is equiva9 KB (1,446 words) - 08:52, 30 May 2009
- ...\{\mathcal{F}_t\}_{t \in T}</math> be an increasing family of sub-[[sigma algebra|<math>\scriptstyle \sigma</math>-algebras]] of <math>\scriptstyle \mathcal{3 KB (544 words) - 06:40, 6 March 2008
- ...s philosophical discoveries was published by Patrick Murdoch, and also his algebra in 1748. *‘’A Treatise of Algebra, in Three Parts. To which is Added, an Appendix ...’’by Colin MacLaurin7 KB (1,121 words) - 07:27, 10 July 2008
- ...ry]] by means of [[measure theory]], the problem is to construct a [[sigma-algebra]] of [[measurable set|measurable subsets]] of the space of all functions, a ...by means of [[expected value|expectations]] on [[C-star algebra|C-star]] [[algebra of random variables|algebras of random variables]]. In this case the method12 KB (1,781 words) - 14:50, 7 December 2008
- In [[linear algebra]] an '''eigenvalue''' of a (square) [[matrix]] <math>A</math> is a number <4 KB (731 words) - 17:16, 11 December 2008
- ...ef> to provide a concise method for performing and describing the [[linear algebra]] used throughout the [[matrix mechanics]] formulation of [[quantum mechani4 KB (690 words) - 12:51, 26 March 2011
- ...However, this question leads us outside arithmetic proper into [[abstract algebra]] and [[number theory]]. In the latter branches of mathematics it is studie4 KB (562 words) - 18:28, 5 January 2010
- ...rring for a given amount of focus shift depends inversely on the [[Square (algebra)|square]] of the lens [[focal ratio]]. Low focal ratios, such as [[focal ra3 KB (511 words) - 02:26, 18 September 2009
- In the language of [[abstract algebra]], the first five properties listed above for addition say that '''Z''' und Again, in the language of abstract algebra, the above says that '''Z''' is a [[Euclidean domain]]. This implies that '10 KB (1,566 words) - 08:34, 2 March 2024
- ...e can make them so if necessary by multiplying both by −1. A bit of algebra shows that if ''m'' and ''n'' are positive numbers and4 KB (666 words) - 11:23, 3 October 2009
- ...f{0}</math> but <math>\sim a \vee a</math> need not be '''1'''. A Heyting algebra is necessarily distributive.11 KB (1,918 words) - 18:23, 17 January 2010
- ..."The Humbug Production Function II: The Laws of Production and the Laws of Algebra", '' Review of Economics and Statistics'' February 1974]</ref>.3 KB (529 words) - 08:46, 31 January 2012
- * The [[Maxima]] computer algebra system is implemented in Common Lisp. * [[MACSYMA]] (symbolic algebra, a predecessor of Maxima.)9 KB (1,405 words) - 08:29, 2 March 2024
- ...d (such as the field of complex numbers) then the [[fundamental theorem of algebra]] states that the secular equation has exactly ''n'' roots (zeros) λ be a [[Basis (linear algebra)|basis]] for ''V''<sub>''n''</sub>, then the matrix of <font style="vertica12 KB (1,903 words) - 10:57, 2 February 2009
- *[[Sigma algebra]]4 KB (590 words) - 09:17, 26 September 2007
- '''Definition.''' A ''standard algebra'' is an algebraic structure ([0,1], ʘ, →, 0,1) where ʘ is a continuous '''Definition'''. Let ([0,1], ʘ, →, 0, 1) be a fixed standard algebra, and α be a formula. Then we say that a fuzzy interpretation (''D,I'') ''s23 KB (3,576 words) - 16:38, 29 January 2017
- ...that of the abstract [[ring (mathematics)|ring]] encountered in [[abstract algebra]].5 KB (638 words) - 14:16, 17 December 2008
- ...some facts from matrix theory must be recalled. Matrices over the [[field (algebra)|field]] of [[complex number]]s are considered. ...the same as transposing it.</ref><ref>See for a proof most books on linear algebra or matrix theory. For instance, Felix R. Gantmacher, ''Matrizentheorie'', S12 KB (1,865 words) - 02:49, 19 April 2010
- ...pers on [[differential equation]]s, [[series (mathematics)|series]], and [[algebra]].4 KB (565 words) - 11:48, 2 February 2023
- [[Abstract algebra]] studies abstract number systems such as [[group (mathematics)|group]]s, [ ...</math>) find application in many abstract mathematical fields, such as [[algebra]] and [[number theory]]. An irrational number can not be written as a fract11 KB (1,701 words) - 20:07, 1 July 2021
- ...[[processor registers]]. In addition to these rational values, [[computer algebra]] systems are able to treat many (countable) irrational numbers exactly by ...[matrix (mathematics)|matrix]]'', ''real [[polynomial]]'' and ''real [[Lie algebra]]''.19 KB (2,948 words) - 10:07, 28 February 2024
- ...s has a complex root. This result is known as the [[Fundamental Theorem of Algebra]]. There are many proofs of the Fundamental Theorem of Algebra. Many of the simplest depend crucially on [[complex analysis]]. But it is b18 KB (3,028 words) - 17:12, 25 August 2013
- In [[mathematics]], or more specifically [[algebra]], a '''linear equation''' is an [[equation]] that can be written so that e6 KB (982 words) - 03:09, 8 March 2024
- ...is the [[Levi-Civita symbol]]. These relations define a [[#Lie algebra|Lie algebra]], as discussed later in this article. In [[angular momentum (quantum)|angu ==Lie algebra==34 KB (5,282 words) - 14:21, 1 January 2011
- ...heir other applications, matrices are fundamental to the study of [[linear algebra]], since every [[linear transformation]] can be represented by a [[uniquene ...no repeated roots. The kernel and image of ''P'' are [[complement (linear algebra)|complements]]: they form an [[internal direct sum]].15 KB (2,209 words) - 02:10, 14 February 2010
- ...d sum and a product taken as a commutator of the symbols is called a [[Lie algebra]].<ref name=LieAlgebra/> In particular, one can construct sets of square ma ...=PA114 |pages=pp. 114 ''ff'' |chapter= §2.2 Matrix representation of a Lie algebra |isbn=9971501473 |year=1987 |publisher=World Scientific}}20 KB (3,045 words) - 11:21, 29 June 2011
- ...teger that is a [[multiple (mathematics)|multiple]] of each of them. In [[algebra]], one may also speak of the least common multiple of several polynomials o6 KB (743 words) - 18:42, 2 July 2009
- ...bles]] that may have only one of these two values, operations of [[Boolean algebra]] are defined: '''and''', '''or''', '''not''' for these operations, the fol6 KB (916 words) - 15:07, 16 July 2011
- ...s has a complex root. This result is known as the [[Fundamental Theorem of Algebra]]. There are many proofs of the Fundamental Theorem of Algebra. Many of the simplest depend crucially on [[complex analysis]]. But it is b20 KB (3,304 words) - 17:11, 25 August 2013
- ...[[polynomial|polynomials]], which are the object of study of [[elementary algebra]]. More generally they include all of the [[algebraic function|algebraic fu8 KB (1,289 words) - 13:46, 26 May 2009
- ...tive of any topology. Quite often, different topologies lead to the same σ-algebra (for example, the norm topology and the weak topology on a separable Hilber28 KB (4,311 words) - 08:36, 14 October 2010
- ...he extension to SU(2) is not difficult. As is usual, one goes from the Lie algebra to the group by exponentiation: ...of the fact the components of the angular momentum operator span the [[Lie algebra]] of SO(3).21 KB (3,338 words) - 10:45, 11 June 2009
- # She '''explained''' the Algebra homework to me.7 KB (1,040 words) - 11:46, 2 February 2023
- a σ-algebra (called also σ-field) <math>\textstyle \mathcal F </math> ...s <math> x_1, \dots, x_n. </math> Moreover, a helpful connection to linear algebra appears: random variables form an <math>n</math>-dimensional linear space,18 KB (2,797 words) - 14:37, 30 January 2011
- Due to a new absorbing algebra of activities which constitutes the formal base of it, the B-ADSc method ap7 KB (1,018 words) - 06:19, 29 November 2013
- * Algebra: Topics covered may include polynomials, functional equations and inequalit6 KB (1,015 words) - 16:13, 6 May 2008
- ...e series. For example, some simple operations borrowed from the elementary algebra — such as a change of order of the terms — often lead to unexpe19 KB (3,369 words) - 02:33, 13 January 2010
- ...429 |year= |url=http://books.google.com/books?id=JU0DT_wXu2oC&pg=PA429&dq=algebra+%22coordinate+system%22&lr=&as_brr=0&sig=ACfU3U07j7JfzfwMigYTa2iDVygAb0WKCA ...|pages=p. 95 |url=http://books.google.com/books?id=1dZOuFo1QYMC&pg=PA95&dq=algebra+%22coordinate+system%22&lr=&as_brr=0&sig=ACfU3U1TD6WmY73w4hEYlVFcXK5NxtKSDQ29 KB (4,366 words) - 09:10, 26 March 2011
- In [[mathematics]], or more specifically [[algebra]], a '''quadratic equation''' is one involving only [[polynomial]]s of the10 KB (1,580 words) - 08:52, 4 March 2009
- ...universal infrastructure behind various specialized mathematical theories (algebra, geometry, analysis etc.) Each specialized mathematical theory deals with ...ory of linear spaces. Differential geometry investigates smooth manifolds. Algebra investigates groups, rings, fields etc.34 KB (5,174 words) - 21:32, 25 October 2013
- [[Linear algebra]]11 KB (1,589 words) - 08:58, 9 September 2020
- to use the methods of [[linear algebra]] to solve geometrical questions9 KB (1,403 words) - 02:22, 14 October 2013
- '''Switching algebra''' ...rmation theory]]. Boolean algebra subsequently became known as "switching algebra" by computer designers.26 KB (3,913 words) - 06:51, 7 April 2014
- Book II is on geometrical algebra. All quantities in Book II are handled geometrically. Numbers are represent8 KB (1,314 words) - 11:25, 13 January 2020
- ...ased on the [[subset sum]] problem (though those have been broken) and the algebra of [[braid groups]].8 KB (1,233 words) - 05:48, 8 April 2024
- Babylonian algebra (in the secondary-school sense of "algebra") was exceptionally well developed.<ref name="vanderW1">B. L. van der Waerd35 KB (5,526 words) - 11:29, 4 October 2013
- ...ssell, applied to logic mathematical techniques, such as those of abstract algebra, with a degree of sophistication never before used in the area. The result10 KB (1,529 words) - 16:45, 10 February 2024
- ''Brāhmasphuṭasiddhānta'', XVIII, 3-5 (in Colebrooke, ''Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bhá ...lois theory -- accompanied by greater rigor in analysis and abstraction in algebra.27 KB (4,383 words) - 08:05, 11 October 2011
- ...fact that rotations are generated by angular momenta [they span the [[Lie algebra]] of SO(3)] follows that the closed-shell Slater determinant is an eigenfun11 KB (1,582 words) - 07:52, 23 September 2009
- ...e study of quantity, structure, space, and change (i.e., [[arithmetic]], [[algebra]], [[geometry]], and [[mathematical analysis|analysis]]). In addition to t ...tial)|vector]]s, generalized to [[vector space]]s, and studied in [[linear algebra]]. The study of vectors combines three of the fundamental areas of mathemat30 KB (4,289 words) - 16:03, 20 January 2023
- ...ix is called [[symmetric matrix|symmetric]]). It is also known from linear algebra that the generalized eigenvalue problem with symmetric '''F''' and positive20 KB (3,082 words) - 17:39, 9 December 2008
- ...nst one cipher he might treat the text as a vector of bits and use Boolean algebra while for another he might choose to treat it as a vector of bytes and use ...unds all increase this) and nonlinearity in the relations involved. In any algebra, solving a system of ''linear'' equations is more-or-less straightforward p53 KB (8,371 words) - 05:48, 8 April 2024
- *W. H. Greub, ''Linear Algebra'', 2nd edition, Springer (Berlin) 1963.15 KB (2,366 words) - 09:09, 4 April 2010
- ...l in this regard. I think I have never read [[Mathematics]] article, nor [[Algebra]], [[Harmonic Analysis]] etc. These are surely parts of the core skeleton, : [[Fundamental Theorem of Algebra]]44 KB (7,312 words) - 03:09, 8 March 2024
- but the former procedure requires slightly less algebra.12 KB (1,893 words) - 04:51, 25 March 2010
- ...ly for a torsion angle, which involves 4 atoms, it requires tedious vector algebra to derive the corresponding values of the <math>s^t_{Ai}</math>. See for mo13 KB (1,996 words) - 10:52, 3 November 2021
- ...of the first examples of non-commutative multiplication arises in [[linear algebra]]. [[Matrix multiplication]] is not commutative (the product AB is not the15 KB (2,535 words) - 20:29, 14 February 2010
- For example, see {{cite book |title=Linear algebra: Theory and applications |author=Ward Cheney, David Kincaid |chapter=§2.3:17 KB (2,828 words) - 10:37, 24 July 2011
- ...d in the 1980's as a function in the [[Maple (software)|Maple]] [[computer algebra system]], whose interface required an explicit notation for solutions of eq14 KB (2,354 words) - 21:43, 25 September 2011
- <blockquote>These studies [on power series] stand in the same relation to algebra as the studies of decimal fractions to ordinary arithmetic. <ref name=Newto15 KB (2,342 words) - 06:26, 30 November 2011
- ...ros in the complex plane; a generalization of the [[fundamental theorem of algebra]]. ...lers. Arbitrary-precision implementations are available in most [[computer algebra system]]s, such as [[Mathematica]] and [[Maple]]. [[Pari/GP]], [[MPFR]] and32 KB (5,024 words) - 12:05, 22 December 2008
- ...0</ref>. Napier did not think of logarithms in this algebraic way - indeed algebra was not well advanced at the time - but he calculated them in a way approxi12 KB (1,843 words) - 13:57, 29 March 2009
- * In algebra, some rational expressions (a fraction with an algebraic expression in the21 KB (3,089 words) - 10:08, 28 February 2024
- *[[Basis (linear algebra)/Definition]]15 KB (1,521 words) - 09:02, 2 March 2024
- ..., schoolchildren begin to study mathematics with arithmetics, elementary [[algebra]] and 2-dimensional [[Euclidean geometry]] (plane geometry). <ref name="kis19 KB (3,106 words) - 09:53, 10 October 2013
- The [[Computer algebra system]]s such as [[Maple (sotfware)|Maple]] and [[Mathematica]] can genera22 KB (3,358 words) - 09:31, 10 October 2013
- ===The enrichment of biology by mathematical progress in geometry, topology, algebra, and analysis=== ...amazing progress in each of its three major fields: geometry and topology, algebra, and analysis. This progress has enriched all the biological sciences.46 KB (6,635 words) - 13:25, 14 April 2021
- Newton's method was first published in 1685 in ''A Treatise of Algebra both Historical and Practical'' by [[John Wallis]]. In 1690, [[Joseph Raphs17 KB (2,889 words) - 12:40, 11 June 2009
- ...community especially, added more significant number crunching (e.g. linear algebra) and other science-related algorithms to Python’s ecosystem.12 KB (1,808 words) - 22:24, 14 February 2021
- ...e the most salient words or themes represent the preferred [[basis (linear algebra)|basis]].16 KB (2,339 words) - 19:24, 29 September 2020
- ...| title = [http://www.utdallas.edu/~herve/Abdi-lann-01.pdf] (2001). Linear algebra for neural networks. In N.J. Smelser, P.B. Baltes (Eds.): International Enc16 KB (2,332 words) - 07:08, 26 September 2007
- ...n fitz Walter, 2nd High Steward of Scotland]] - [[Special:Allpages/Algebra|Algebra]]44 KB (6,041 words) - 08:06, 23 February 2024
- was being superseded by the [[algebra|algebraic]] methods of [[René Descartes|Descartes]].14 KB (2,123 words) - 13:30, 8 November 2012
- where we used Eq. (1). From vector algebra we know that (we drop temporarily the time-dependence)23 KB (3,890 words) - 10:45, 11 June 2009
- ...Mikami, 1914. pp. 4-9</ref> The most important among them concerned [[algebra]], which enabled the creation of the department of “Arithmetic Intelligen15 KB (2,247 words) - 10:12, 28 February 2024
- ...ate system]], Descartes founded [[analytic geometry]], that bridge between algebra and geometry crucial to the invention of the [[calculus]] and [[Mathematica17 KB (2,634 words) - 18:36, 19 March 2010
- ...ument is attributed to [[Thomas Kuhn]] in {{cite book |title=From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism |author=Tian Yu Ca ...on is a close paraphrase of a statement in {{cite book |title=From Current Algebra to Quantum Chromodynamics: A Case for Structural Realism |author=Tian Yu Ca44 KB (6,711 words) - 20:01, 11 October 2013
- ...s "Complex_Main", "Deriv" and "Complete_Lattice") and 48 folders (such as "Algebra", "Hahn_Banach", "Matrix" and "Probability"), about 900 theory files in the21 KB (3,291 words) - 16:07, 3 November 2013
- Pascal's triangle has applications in [[algebra]] and in [[Probability theory|probabilities]]. We can use it to compute the32 KB (4,192 words) - 18:42, 3 March 2024
- ...d through a process known as "local operation on multiple rasters" or "map algebra," through a function that combines the values of each raster's [[matrix (ma ...tistics]] is the use of [[graph theory]] and [[Matrix (mathematics)|matrix algebra]] to reduce the number of parameters in the data being analyzed. This is ne41 KB (6,343 words) - 17:02, 22 March 2024
- ...e functions are linearly independent, together they form a [[basis (linear algebra)|basis]] of ''V''. This method of defining the sine and cosine functions is33 KB (5,179 words) - 08:26, 4 June 2010
- **'''[[Jan Lukasiewicz]]''', who developed both the [[algebra of logic]] and many-valued [[propositional calculus]], which influenced Car30 KB (4,343 words) - 13:59, 18 February 2024
- Adding the times produces:<ref name=algebra group=Note/> <ref name=algebra group=Note>35 KB (5,836 words) - 17:02, 22 March 2024
- * [[Commutative algebra]]25 KB (3,396 words) - 13:29, 2 April 2024
- * [[Abstract algebra]]25 KB (3,600 words) - 14:27, 31 March 2024
- ...be better to view a [[scalar (mathematics)|scalar]] as the [[Trace (linear algebra)|trace]] of a 1×1 [[Matrix (mathematics)|matrix]] than as a mere scal46 KB (6,956 words) - 07:01, 9 June 2009
- ..., [[Computational complexity theory|computational complexity]], [[abstract algebra]], and [[number theory]]. However, cryptography is not ''just'' a branch of52 KB (8,332 words) - 05:49, 8 April 2024