Talk:Algebra

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This subject is featured in the Outline of algebra, which is incomplete and needs further development. That page, along with the other outlines on Wikipedia, comprise Wikipedia's Outline of Knowledge, which also serves as the table of contents or site map of Wikipedia.
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Algebra was a good article nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these are addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Reviewed version: November 6, 2007
edit · history · watch · refresh Stock post message.svg To-do list for Algebra: 
It has been said by "The Gavatron" that it is impossible to live a single day without using algebra

Fix the part about Brahmagupta in history.
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[edit] old comment

Cut from article pending reorganization:

An algebra is based on a 2→1 morphism having 2 inputs (multiplicator and multiplicand) and one output (product). It can be dualized using categorial duality by reversing all arrows in the commutative diagrams which describe the algebra axioms; this defines the structure of a coalgebra named sometimes also cogebra.

I moved this paragraph to associative algebra. AxelBoldt 04:09 26 May 2003 (UTC)

[edit] Reason why Algebra formed

Khwarizmi contributions on top of the Indian mathematics was based on a determination to predict the future. In Islam, there are two consepts of "Algaber" and "Alghader". Algaber means everything has a destination and God almighty is aware of all destinations. Alghader means all beings have the power to change their own faith and destiney. As a Muslim, he was interested to know if a change in "controlling" variables can determine destination of "unknown" variable(s). In his book, Algabre val moghabelah, he devised techniques to resovle and predict destination of unknown varibles. During crusades between Christians and Muslims, Jacobson broders tried to tranlsate his book in english and since they were not able to find a good word to do the name justice, they settled on the name "Algebra".—Preceding unsigned comment added by Msalehisedeh (talk • contribs) 21:02, 31 May 2009 (UTC)

[edit] Algebra Comes From Arabic

I changed the unsourced opening sentence, with a more factual, sourced one. To my knowledge, the word Algebra comes from the Arabic Al Jabr. It might have found it's way into Farsi/Persian after the Islamic conquest of that region, along with many other words. I'm sure it can be found somewhere in the Quran/Early Arab/Islamic texts, which is proof it was originally an Arabic word before contact with the Persians. I am currently researching that with people who actually do read religious texts, unlike myself.

Despite being of Persian heritage, Mohammad ibn-Musa al-Khwarizmi spent most his life, and implimented most his studies in Baghdad and Cairo - Arabic countries where he undoubtably had to adopt the Arabic language in order to communicate, maybe even becoming Arabised later on. Thus his book's title, where Algebra came from, was Arabic not Persian.

Either way, I have replaced the unsourced material with a sourced info. Appologies I don't know how to put sources in with those little numbers, I'm learning how to do it now. The sources are:

- http://www.und.nodak.edu/instruct/lgeller/algebra.html

- http://mathworld.wolfram.com/Algebra.html

- http://wiki.answers.com/Q/From_where_did_the_Word_algebra_come_from

- http://83.223.102.16/index.cfm?fuseaction=main.viewBlogEntry&intMTEntryID=2740

- also, further down the article it says: "The word "algebra" is named after the Arabic word "al-jabr , الجبر" from the title of the book al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala , الكتاب المختصر في حساب الجبر والمقابلة, meaning The book of Summary Concerning Calculating by Transposition and Reduction, a book written by the Islamic mathematician Muhammad ibn Mūsā al-khwārizmī in 820." The first sentence is contradictory to that - as well as virtually every reliable internet source.

Also, I'm researching claims that Algebra might have been developed further back in time than al-Khwarizmi by someone whose name is Al-Jabr - which to this day is a common Arabic name.

Please feel free to contact me of you are doing similar research, or willing to help. Take care. Pink Princess (talk) 17:52, 28 August 2008 (UTC)

[edit] Algebraic combinatorics

Yes check.svg Resolved.

{{editsemiprotected}} I found an error. Algebraic_combinatorics points to http://en.wikipedia.org/wiki/Combinatorics instead of pointing directly to http://en.wikipedia.org/wiki/Algebraic_combinatorics. Good day.—Preceding unsigned comment added by 84.108.53.132 (talk • contribs)

OK done. --Salix (talk): 11:00, 26 May 2009 (UTC)

[edit] Elementary... algebra?

The problem to me seems to be that elementary algebra and abstract algebra are two completely different things with no special connection. They just happen to have the same surname, like Dave Smith and Harry Smith or something. Classifying mathematical subjects according to their names seems to me to be no more informative than classifying people according to their names, when two subjects/people can have the same name by coincidence.

When students do elementary algebra they are doing integer arithmetic or (naive) real number arithmetic, except with variables as well as specific numbers. It starts being called algebra when one moves from specific integers, to arbitrary/variable integers. The same goes for real numbers. It is the move from just having constants, to having constants and variables. But this has nothing to do with any particular branch of mathematics. All branches of mathematics do this. What on earth does it have to do with abstract algebra that it doesn't have to do with combinatorics or analysis, say?

A better name for elementary algebra would be "elementary arithmetic/number theory" or "elementary (naive) real analysis".

We can all think of better names for things, but what we cannot do is change what things are called. Elementary algebra is much more like abstract algebra than it is like advanced arithmetic or number theory, so I don't understand your objection. In any case, many more people understand "algebra" to mean "using letters to represent numbers" than any other sense of the word. Dbfirs 12:22, 17 June 2009 (UTC)
Elementary algebra has something in common with advanced algebra. Both are the study of the rules of operations. In elementary algebra, these rules are taken from real numbers, or some subset thereof. We think about what rules hold if we know that x is a number and use those rules, for example to solve an equation. Advanced algebra is just the study of what happens when those rules change.
Actually, warming to my theme, I would say that something along the above lines should be stated in the article. Yaris678 (talk) 12:08, 5 August 2009 (UTC)

[edit] should we mention

That this is one of the more toughest part in maths cause a lot of people seem to find it to be a very tough subject. user--Stephendwan (talk) 19:54, 14 December 2009 (UTC)

No. Besides not being relevant, it is also quite untrue. David spector (talk) 00:59, 16 December 2009 (UTC)
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