Talk:Algebra

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This page on Algebra is totally inadequate.


See the example entry below from http://mathworld.wolfram.com/Algebra.html


<quotation> The word "algebra" is a distortion of the Arabic title of a treatise by al-Khwarizmi about algebraic methods. In modern usage, algebra has several meanings.

One use of the word "algebra" is the abstract study of number systems and operations within them, including such advanced topics as groups, rings, invariant theory, and cohomology. This is the meaning mathematicians associate with the word "algebra." When there is the possibility of confusion, this field of mathematics is often referred to as abstract algebra.

The word "algebra" can also refer to the "school algebra" generally taught in American middle and high schools. This includes the solution of polynomial equations in one or more variables, and basic properties of functions and graphs. Mathematicians call this subject "arithmetic," reserving the word "algebra" for the more advanced aspects of the subject.

Finally, the word is used in a third way, not as a subject area but as a particular type of algebraic structure. Formally, an algebra is a vector space V over a field F with a multiplication. The multiplication must be distributive and, for every f in F and x,y in V must satisfy f(xy)==(fx)y==x(fy).

An algebra is sometimes implicitly assumed to be associative or to possess a multiplicative identity.

Examples of algebras include the algebra of real numbers, vectors and matrices, tensors, complex numbers, and quaternions. (Note that linear algebra, which is the study of linear sets of equations and their transformation properties, is not an algebra in the formal sense of the word.) Other more exotic algebras that have been investigated and found to be of interest are usually named after one or more of their investigators. This practice unfortunately leads to entirely unenlightening names which are commonly used by algebraists without further explanation or elaboration.

SEE ALSO: Abstract Algebra, Alternative Algebra, Associative Algebra, Banach Algebra, Boolean Algebra, Borel Sigma-Algebra, C-*-Algebra, Cayley Algebra, Clifford Algebra, Commutative Algebra, Derivation Algebra, Exterior Algebra, Fundamental Theorem of Algebra, Graded Algebra, Hecke Algebra, Heyting Algebra, Homological Algebra, Hopf Algebra, Jordan Algebra, Lie Algebra, Linear Algebra, Measure Algebra, Nonassociative Algebra, Power Associative Algebra, Quaternion, Robbins Algebra, Schur Algebra, Semisimple Algebra, Sigma-Algebra, Simple Algebra, Steenrod Algebra, Umbral Algebra, von Neumann Algebra.

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As you can see by this, the entry on Algebra appears to be deficient in any number of areas, but in particular, the author of the original seems to be mistaken in assuming that algebra is merely that element which is emboldened in the text above.


--CatWatcher 13:32, 6 April 2007 (EDT)

It's not a mistake; it's the context of this encyclopedia. We meant "school algebra".
After that has been explained, then you are welcome to write about advanced kinds of algebra. --Ed Poor Talk 20:07, 3 September 2008 (EDT)

I realize that it's tacky to argue with someone who has been banned, but the "improvement" suggested by CatWatcher is so not going to happen. The educational articles here are aimed at teenagers. People who want world-class sophistication can go to the mathworld site mentioned above. Oh. And he left out Grassmann algebra, though perhaps he meant for Exterior algebra to include that. SamHB 23:47, 1 December 2010 (EST)

Can anyone help with the formatting? I don't know how to represent mixed numbers or the plus-minus sign in wiki formatting. AmyD 03:06, 25 February 2014 (EST)

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