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Revision as of 19:42, 24 July 2004

<<Comment -- breaking the topics down as follows may not be such a good idea. While it might be useful for a public school teacher who has to teach the concepts to students, it might not be the best for this which is just supposed to describe what algebra is -- besides Pascal's Triangle is not specifically a topic from algebra. -- Paul Hsieh>>

Yes, it wasn't really very well thought out. I moved it to Elementary algebra just to get rid of it, since I didn't want to upset its author by deleting it. It can probably be deleted now, but I'll leave it on the talk page for the moment. --Zundark, 2001 Oct 10

Multiplication of Algebraic Expressions

Addition and Subtraction of Expressions

Coefficients

Expansion of Two Brackets

Difference of Two Squares

Squares

Important Expansions

Factorising Quadratic Expressions

Harder Factorising

Common Factorising

Harder Expansions

Pascal's Triangle

We need a section on order of operations. Order of operations was not a part of basic arithmetic.--BlackGriffen

An equation is any statement that claims that two expressions are equal. These expressions can naturally contain variables, numbers, absolute values or anything else. An identity is an equation that's claimed to be true for all possible values of the variable, such as "x+y=y+x". An inequality is not an equation; it involves ≤ or <, not =. (But algebra talks about inequalities, so they should be mentioned.) AxelBoldt 00:50 Oct 14, 2002 (UTC)

Any statement that two quantities are equal is an equation, but even then there is no "claim," merely a statement, and the statement is not that they are "the same" (which is what you put in and I took out) but that they are equal in numerical value. But an equation is a statement that "equates" two expressions, and the relationship may not be equality -- or would you have it that "x is less than or equal to 5" is not an equation? What I likened to a verb in the definition is still "is" which is what makes it an equation: (x) = (≤ 5). So equality is not the only relationship that can be expressed by an equation, before you get to the fact that a "let" statement is also an equation, as in: "Let x be a positive integer less than 5," where the expression on the right of the "=" is the set of integers (1,2,3,4), which are the solutions of that equation. So every statement of equality is an equation, but not every equation is a statement of equality: Some are statements of equivalency, and a cup of coffee may be equivalent to a dollar bill in value, but they are not "the same" or even equal. -- isis 04:00 Oct 14, 2002 (UTC)

Is there specifically a requirement that abstract algebra must be taught only to college seniors? I took trigonometry/pre-calculus in 8th grade (and got a C+, but... ya know)... yet it is impossible for me to take abstract algebra when I'm a junior in college?

Oh, and I have another question. Is there a property that would allow me (in a proof) to say that, if x = y, then x = y?

When x = a and y = -a, you will find that x = y is true, but that x = y is false. Which tends to suggest that there is no such property. -- Derek Ross

Well, no, because it can be trivially disproved. Given x = 2 and y = -2, x = y = 4, but 2 != -2 orthogonal 21:57, 19 Nov 2003 (UTC)

Of course, this is true if x and y are non-negative. Paul August 19:42, Jul 24, 2004 (UTC)