Category talk:Algebra

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What is to the be the distinction between what we put here and what we put in "Category:Abstract algebra"?

I suppose if the topic deals with something abstractly enough, you'd put it in Abstract algebra. If you read Abstract algebra, it may give you a guideline too. Dysprosia 22:30, 3 Jun 2004 (UTC)

Abstract algebra isn't just different algebra, it's something that resembles algebra but it isn't really. It resembles algebra because both use strictly enforced rules to transform one expression into another, and the expressions have symbols representing variables, perhaps constants, and operations on their values. But the variables and operations in an abstract algebra aren't necessarily numeric, and therefor the rules for manipulating expressions are accordingly different. Examples: A Boolean algebra has variables having either the value "true" or "false", the operations include "and", "or" and "not", and the rules include De Morgan's laws. Permutation groups are an abstract algebra that isn't commutative. Applications: Scientists and engineers depend on algebra, but abstract algebra is used mainly to employ professors and justify research grants. Exceptions: Rubik's cube (but that's a game), quarks (but only to describe the symmetry), and computer programmers (who really can use De Morgan's laws). Art LaPella 17:07, 1 October 2005 (UTC)

Abstract algebra is not high school algebra instead it is analysis of abstract systems. I can use it in a lot of ways. I could it in geometry. There are all of kinds of ways.http://mathworld.wolfram.com/Algebra.htmlTimothy Clemans 20:25, 21 December 2005 (UTC)

My concern is that the person below making the statement starts with "um". The writer's assertion that "Al" is a traditional prefix meaning "of" or "from" is incorrect. "Al" is the definitive article "the".

[edit] Origin of word 'algebra'

Um, in Arabic, 'Al' is a traditional prefix meaning 'of' or 'from', so having the entire thing mean 'reunion' or something of the like seems incorrect. A little searching reveals this gem of a web-page-nugget: algebraquoted here as follows:

Origin of the Word Algebra The word algebra is a Latin variant of the Arabic word al-jabr. This came from the title of a book, Hidab al-jabr wal-muqubala, written in Baghdad about 825 A.D. by the Arab mathematician Mohammed ibn-Musa al-Khowarizmi.

The words jabr (JAH-ber) and muqubalah (moo-KAH-ba-lah) were used by al-Khowarizmi to designate two basic operations in solving equations. Jabr was to transpose subtracted terms to the other side of the equation. Muqubalah was to cancel like terms on opposite sides of the equation. In fact, the title has been translated to mean "science of restoration (or reunion) and opposition" or "science of transposition and cancellation" and "The Book of Completion and Cancellation" or "The Book of Restoration and Balancing."

Jabr is used in the step where x - 2 = 12 becomes x = 14. The left-side of the first equation, where x is lessened by 2, is "restored" or "completed" back to x in the second equation.

Muqabalah takes us from x + y = y + 7 to x = 7 by "cancelling" or "balancing" the two sides of the equation.

Eventually the muqabalah was left behind, and this type of math became known as algebra in many languages.

It is interesting to note that the word al-jabr used non-mathematically made its way into Europe through the Moors of Spain. There an algebrista is a bonesetter, or "restorer" of bones. A barber of medieval times called himself an algebrista since barbers often did bone-setting and bloodletting on the side. Hence the red and white striped barber poles of today.

I think it would be nice if the word origin was robusted up a bit, and actually made reference back to the document that was the source of the name: Hidab al-jabr wal-muqubala ":) --Fish-man 00:01, 12 October 2005 (UTC)