Talk:Elementary algebra/GA1

GA Review
The edit link for this section can be used to add comments to the review.''

Reviewer: Ob tund  (talk · contribs) 01:27, 3 August 2012 (UTC)

Nominator: Iantresman (talk · contribs) 22:01, 25 July 2012 (UTC)

Status
''This section is supposed to be edited only by reviewer(s). Any questions and comments concerning this table should be posed in Discussion subsection below.''

This article was quickfailed for the following reason:
 * 1. There are cleanup banners that are obviously still valid, including cleanup, wikify, POV, unreferenced or large numbers of fact, citation needed, clarifyme, or similar tags. (See also QF-tags.)
 * a. cleanup-reorganize
 * b. confusing
 * c. overly detailed
 * d. technical
 * e. wikify

Discussion
''Please refer to issue by numbers. Eg., the second issue with 1a criterion is 1a2.''

This article use multiplicity for the property of being a multiple of. This seems WP:OR. Even if this can be sourced, it has to be avoided, as the mathematical meaning of "multiplicity" is different, see multiplicity (mathematics). For solving this issue, I suggest to replace "multiplicity" by "divisibility", and, if needed, to change the order of the arguments (if a is a multiple of b, then b divides a). D.Lazard (talk) 13:29, 4 August 2012 (UTC)
 * Perhaps its been fixed, looks OK now. linas (talk) 17:02, 18 August 2012 (UTC)

I agree with the reviewer that the article style is that of Wikiversity and not that of Wikipedia. In particular most sections are over detailed, in a tentative to be pedagogic. This has the consequence to make confusing the important facts. For example, details are given for how to get the quadratic formula, and the quadratic formula itself was not given before my edit. On the contrary, the quadratic formula should be given directly, leaving the details to the relevant article.

Similarly for the linear systems. The given details duplicates simultaneous equations, while the important facts are either hidden inside the details or, sometimes omitted. For example the fact that under-determined systems either are inconsistent (no solution) or have infinitely many solutions is not given, nor the fact that there are implemented algorithms that solve efficiently every linear systems.

By the way, a section "Elementary algebra on computers" is lacking, which should contain the information that computer algebra allows to do automatically every computation of elementary algebra (and many computations of higher algebra), and that this is allowed by algorithms that use many advanced results of higher algebra. D.Lazard (talk) 14:32, 4 August 2012 (UTC)


 * Many thanks to the reviewer for looking over the article. It would be helpful to have some examples on which areas the reviewer finds (a) confusing, (b) overly detailed, and (c) technical.
 * Which brings up the quandary, how do we explain a complicated subject without going into the detail necessary to explain it? I feel quite confident with secondary and some tertiary level maths. The one place I find very difficult to understand anything on the subject is Wikipedia.
 * Encyclopædia Britannica has an article on |Elementary algebra, and that also seems to include a combination of encyclopaedic and pedagogic material? --Iantresman (talk) 17:59, 11 August 2012 (UTC)

Reduction
A significant portion of the article is devoted to working out, by hand, examples of reduction (mathematics) aka term rewriting. This is fine, I guess, as it illustrates the primary operations of algebra. I find it strange, though that the lede never mentions this, and that it is not explained in the article: its kind of the whole point of algebra: to cast a problem into symbols, then take a bunch of symbols on a page, and apply certain well-defined rules, over and over, until the result has simplified to the point of providing a so-called "answer". This process of transformation from begining to end is central to algebra. The actual shapes of the squiggles on the page don't even matter! They don't even have to be 0,1,2,3, +-x/= ! You could write: "squiggle-blob-blob is equal to (reduces to) (arrow points to) boink bing bing by the law of blob blink" and this would be a perfectly valid algebraic operation (assuming we have a handful of axioms in place to define "objects" and "arrows" so that "squiggle blob blob" is an object (category theory) and "the law of blob blink" is a morphism (category theory).) I repeat: this is absolutely central to the notion of algebra!

It can be automated: reduction is simple enough that computers can do it, e.g. computer algebra system. Its a special case of theorem proving. It is kind-of-like a cobordism between algebraic expressions. Its is a topic of modern, current research. Sadly, both the articles reduction (mathematics) and term rewriting are too abstract (and incomplete) to be usable for this article, but I think terrible that the whole *point* of algebra is not even mentioned in the article. linas (talk) 16:16, 18 August 2012 (UTC)

To be precise: the section called "expressions" and the "expressions example" should be re-worked to make it clear: start with an expression, apply a rule, to get a different expression. Do it again. The end goal is to have a "simpler" expression. The route from complicated-to-simple is often not clear, and is often not possible (e.g. "solving" quintic equations for roots). The section on "solving" should make it clear that its about using reduction to find valid values for variables. ("Solving" is a special case of reduction).linas (talk) 16:34, 18 August 2012 (UTC)

operations, relations
Per talk page above, the section on "operations" was entirely removed. This is perhaps unfortunate: the very idea of "operation" is something that is generalized in higher algebra, and so by having an explicit list of the properties of operations (they're invertible, they're commutative, associative, etc), the reader is reminded that these are a part of algebra. So: I'd say -- restore a shortened version of that section, and then say "in higher algebra, these operations are generalized, e.g. to non-commutative operations, etc."

By contrast, the section on "relations" was not removed -- even though it too is "stuff a student should know by now". This is good, as, again it illustrates e.g. reflexivity, transitivity of relations: what is missing is the sentence "in higher algebra, the notion of relation is generalized, e.g. to be a preorder or whatever."

So, keeping the sections on relations and operations is good, as long as they are used to illustrate that these concepts are examples of more general concepts in higher algebra. linas (talk) 17:20, 18 August 2012 (UTC)

over-detailed
Someone above complained: "there is too much detail": and certainly, the "solving" section seems to be like that. The first half of this article is fine, but the "solving" section is ... I dunno. Perhaps it should be split into its own article, or something. Its a tedious list of techniques, a handbook of approaches. That's certainly practical, but it can make one's eyes water in tedium. Such lists of techniques and tricks are *absolutely vital*, critical, for actually solving a problem, when one needs to solve something. But, by its very nature, such lists can explode to unmanageable lengths, and its starting to do so in this article...linas (talk) 16:34, 18 August 2012 (UTC)

first/second person usage
I find the first/second person english language usage "unencyclopadic": the various I, You, Let us, Let's, in this article is too presumptuous.linas (talk) 16:45, 18 August 2012 (UTC)

Regarding 1c overly-detailed, and the other complaints as well: This article was exactly what I was hoping to find when I came here looking for an article on Elementary Algebra. Nice discussion of all of the basic elements. I do not think order of operation is out of place here. Good examples all along. I this was shortened any, important points would be left out. What would you add? A History section? A more general discussion of what kinds of problems this is used for? Its place in the current educational curriculum? I think this article is just fine. Excellent for my purposes, and why my first stop for everything is Wikipedia in the first place. — Preceding unsigned comment added by Leeeoooooo (talk • contribs) 03:32, 24 November 2012 (UTC)