Talk:Elementary algebra

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Operations

I really don't think that this section belongs in this article. The order of operations is not introduced in algebra. It is a concept introduced with basic arithmetic. It needs a mention somehow and a link for completeness but beyond that it should be prior knowledge. Anyone think I am off-base on this one?Phancy Physicist (talk) 08:18, 10 June 2010 (UTC)

Why in this section or in any section in Wikipedia would there be author attribution? "By:Ůmáīr Hafeez Měmõń'" Shouldn't this be deleted? --OneAmongBillions (talk) 13:08, 4 November 2010 (UTC)

Algebraic examples

This section is longer than the rest of the article and for some reason that bothers me. Maybe because it seems that the article is written in little bit of a "teachy" way. Which I don't think is necessarily bad but is this okay with Wikipedia's style?

Since I am talking about style the presentation-style bulleted lists are giving me pause as well. Are they OK with wikipedia standards?Phancy Physicist (talk) 08:18, 10 June 2010 (UTC)

I was seeking for information about the elimination method. In a typical teachy way it is explained. I would like a link or an explanation why the method works and is allowed. I guess a link to the gaussian method would suffice... but. I think it could be explained in a more cursory way here as it is about elementary algebra. A link to the gaussian method has its problems as the readers are reading about elementary algebra and that entry would confuse most people. (English is not my first language, I hope you get what I am getting at)-- Tobbe —Preceding unsigned comment added by 83.233.238.234 (talk) 14:39, 4 September 2010 (UTC)

This section seems typical of the whole article - somewhat shoddy, and highly pedantic in tone. The object of this Wiki is to identify what elementary algebra is, not how to undertake exercises in it.

The solving of equations is an overly-laboured diatribe concerning a subset of those equations whose solutions are analytically possible. What of the others, such as x^2 + ln(x) = 5 for example? — Preceding unsigned comment added by 83.158.63.7 (talk) 13:47, 13 October 2011 (UTC)

Basic algebra

"Basic algebra" redirects here but this is also a algebraic terminology: A finite-dimensional K-algebra A is basic iff every indecomposable projective module has multiplicity one in A iff all simple modules are one-dimensional. There should be a disambiguation page (and a new article for basic algebra). I could write the new article (at least a stub) but I don't know how to change the redirecting... 92.224.233.104 (talk) 20:05, 29 April 2011 (UTC)

Operations

Per the comments above, I've removed the section on Operations. I'm going to replace it with comments that are more relevant to algebra. --Iantresman (talk) 13:01, 20 July 2012 (UTC)

Also, can the 3.5 example for multiplication be fixed to look more like it should (3 dot 5)? hydnjo (talk) 22:07, 23 July 2012 (UTC)

I think I've fixed, showing both the European and American forms for $3\ .\ 5$   or   $3\cdot 5$. --Iantresman (talk) 08:54, 24 July 2012 (UTC)

OK, thanks. Oops, I just noticed that the same problem exists with the a.b example and there is a confusing comma just above the 3 . 5 that you fixed, hydnjo (talk) 11:40, 24 July 2012 (UTC)

Thanks for that, all done, I think. --Iantresman (talk) 12:12, 24 July 2012 (UTC)

Mixed formatting of inline math

This article mixes inline HTML and <math> for math variables and expressions, with the latter aparently dominating. This should be made consistent by choosing either, but not both. They each have their problems, but consistency appears to be the one thing that is recommended. — Quondum^☏ 18:38, 31 July 2012 (UTC)

Good idea, all done. Do you think that numerals should also be converted? --Iantresman (talk) 15:19, 1 August 2012 (UTC)

Personally, I would have said yes. However, there seems to be little consensus on these matters, and I've run into resistance relating to HTML/{{math}}/<math> preferences before from others. The only argument that seems to remain relatively unchallenged is consistency of presentation within a single article, but even that not always. Different preferences seem to manifest according to individual browser/preferences settings (PNG vs. MathJax, specific font choices and associated perceived clashes, the opposing issue of font choices and the perceived benefit of differentiating math from text, available installed characters for each font, etc.). So, you're on your own on this... — Quondum^☏ 18:43, 1 August 2012 (UTC)

I'm going to go with the following rationale. If we refer to a number in an equation, then I'll use <math>, otherwise not. So if we produce an equation to represent a quantity, then no <math>. --Iantresman (talk) 19:48, 1 August 2012 (UTC)

Referring to point 1b of the GA-review, it might comply with the MOS guidelines as far as mathematics in concerned, but I find the current usage of inline <math></math> highly disturbing.

As an example, take for instance this statement:

...for example, $2x^{2}+3ab-x^{2}+ab$ is written as $x^{2}+4ab$, because the terms containing $x^{2}$ are added together, and, the terms containing $ab$ are added together. By convention, terms with the highest power (exponent), are written on the left.

I propose that we write this with inline HTML math —see MOS:MATH#Using_HTML—, like for instance

...for example, 2x²+3ab-x²+ab is written as x²+4ab, because the terms containing x² are added together, and, the terms containing ab are added together. By convention, terms with the highest power (exponent), are written on the left.

or even better:

...for example, 2x²+3ab-x²+ab is written as x²+4ab, because the terms containing x² are added together, and, the terms containing ab are added together. By convention, terms with the highest power (exponent), are written on the left.

I can't do it right now, but I'd be willing to work on this one of these days. What do you think? - DVdm (talk) 07:10, 3 August 2012 (UTC)

Some might take the view that since MathJax is largely working and the font, size and baseline offset problem is (or should be) largely solved by it, we should be moving towards the inline <math> form. Try switching your preferences to MathJax to see whether you think this'll have any merit; at least it may argue against actually reformatting an article that uses inline <math>. But I would not be surprised at strong objections, such as yours. I seem to remember similar objections to use of {{math}}, so I have stopped using this template in place of HTML (and I would also like to see a tie-up between its font and that of MathJax). Straightforward HTML does seem most common in most articles, though I prefer a distinct font to distinguish math. In summary, I think that there is a general consensus not yet reached on this matter, but I am wary of kicking this debate into life again. — Quondum^☏ 09:17, 3 August 2012 (UTC)

Up to now I had my prefs set to "Always PNG", which makes the inline math quite ugly indeed. I tried the (still experimental) MathJax on this article and I must say it looks much better. Drawback is that it takes an eternity to load in IE8. Firefox is faster. Also note that there's no caching. By the way, try opening Help:Displaying a formula with MathJax in IE8—Ouch! - DVdm (talk) 10:04, 3 August 2012 (UTC)

I didn't know there was a MathJax option. For now, I would stick with inline PNG math on the grounds that it is faster, and works. While it is ugly, it help differentiate the maths from the text. It will also probably be faster on mobile devices.

There is indeed the odd inline equation where the terms are not grouped and in order, but it might be deliberate, to demonstate grouping. If so, the text will make it clear. --Iantresman (talk) 11:55, 3 August 2012 (UTC)

Well, the HTML math (as in the alternatives of my example) is much faster and takes much less browser cache space and network bandwidth, than PNG, which is even more important on mobdevs. The main problems with PNG are that it presents itself differently on different browsers, and that the text falls below the lines, which is what makes it so terribly ugly for inline math. I'd definitely vote for inline-HTML and I'm prepared to do it one of these days. - DVdm (talk) 13:37, 3 August 2012 (UTC)

We can always make inline HTML look a bit like math PNG:

• [math png] ..for example, $2x^{2}+3ab-x^{2}+ab$ is written as $x^{2}+4ab$, because..
• [Pure HTML]..for example, 2x² + 3ab - x² + ab is written as x² + 4ab, because..
  

First expression encoded as:

<span style="font-family:times new roman;font-size:150%">2<i>x</i><sup>2</sup> + 3<i>ab</i> - <i>x</i><sup>2</sup> + <i>ab</i></span>

This works fine except where we have more complicated expressions. --Iantresman (talk) 16:27, 3 August 2012 (UTC)

Yes, but look at the source of your spanned Pure HTML. It's pretty hard to code:

(1) math PNG or MathJax:

$2x^{2}+3ab-x^{2}+ab$ -- with source <math>2x^2 + 3ab - x^2 + ab</math>

(2) Your pure HTML (with the i.m.o. awkward to maintain span tags):

2x² + 3ab - x² + ab -- with source <span style="font-family:times new roman;font-size:150%">2<i>x</i>² + 3<i>ab</i> - <i>x</i>² + <i>ab</i></span>

(3) Almost like your pure HTML with template:Math which uses size 165% in stead of your less-standardish 150%:

2x² + 3ab - x² + ab -- with source {{math||big=1|2''x''² + 3''ab'' - ''x''² + ''ab''}}

(4) My proposed HTML with template:Math:

2x²+3ab-x²+ab -- with source {{math|2''x''²+3''ab''-''x''²+''ab''}}

When you take any standard math book, I think the obvious way to go is the fourth, and i.m.o. it's not that hard to code and maintain. - DVdm (talk) 17:36, 3 August 2012 (UTC)

This is risking starting a debate when others pitch in. However, considering that (a) I (and evidently others) find MathJax and PNG are rather slow and download size is greater, and (b) presentation seems to be best IMO (I've seen contention on this, due to browser font choices) with the {{math}} template for simple formulae (especially inline), (c) these shortcomings of <math> have not yet been and might not be corrected for some time despite some progress, and (d) the template approach should still allow centralised font choices to match MathJax if need be, my personal support is for option 4. In fact, for the simple stand-alone formulae such as in an article like this one, I would possibly support {{math}} or {{math|big=1}} there too. It'll cope with fractions (e.g. ^{a + b}
₃) and surds (e.g. ⁿ√x^m) a bit clumsily, but that is the worst I see. But we don't have a really good solution. — Quondum^☏ 22:39, 3 August 2012 (UTC)

I would not touch the standalone math. I think that should remain in TeX, as in most other articles (e.g. Escape velocity). I.m.o. it's just the inline math that really would benefit from getting htmled. That way the standalone math stands out and can be chosen by the reader (i.e. PNG or Jax) and the text becomes homogeneous. - DVdm (talk) 09:21, 4 August 2012 (UTC)

Update. It looks like the article failed the GA-review, so I will not touch the inline math for now. - DVdm (talk) 16:44, 11 August 2012 (UTC)

It seems that there is no recommended style guide for inline equations, which seems like a surprising omission considering its importance. I note one earlier discussion on "Inline math notation", but it is inconclusive. I've suggested re-opening the discussion. --Iantresman (talk) 17:46, 13 August 2012 (UTC)

Good idea.

By the way, I have now activated MathJax (again). I admit that it makes all math —that is, inline and standalone— look significantly better. Major drawback is that some articles take even more significant ages to load :-( - DVdm (talk) 18:03, 13 August 2012 (UTC)

GA Review

This review is transcluded from Talk:Elementary algebra/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Obtund (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 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)

The introduction

"US algebra"?

The pushing of algebra from high school, where it has traditionally been taught, to elementary school has met with some controversy. Whereas students 30 years ago memorized multiplication tables in math class, students today, driven by the new Common Core Standards, are being introduced to variables as early as 6th grade.

So, look at that: if we're introducing elementary algebra, we should rely on overall accounts, or, when we refer to a national account, we'd better treat it as an example, an instance, not leaving such a passage without any allocation as if the subject of the article is certainly national by default. M? Lincoln Josh (talk) 12:25, 19 January 2013 (UTC)

The first question is what is "elementary algebra"? I do not know any generally accepted definition, and reading this article, I agree that the only definition that one may extract from it is "the part of algebra that is taught in elementary school". Thus a better title would be "Algebra in elementary school". But, IMO, the main question is not if it is "US-only" or not (although this question is relevant). The problem, shared with most mathematics articles of elementary level, is that it fails the main objectives of an encyclopedia: an encyclopedia is aimed to provide information that the reader does not has at hand. In other word, in case of students, an encyclopedia should provide insights that are not in textbooks (WP:NOTTEXTBOOK). Here are some examples of points where the article is wrong:

• Variables: They represent not only numbers, but they may represent any mathematical object. They "describe" (3 times in the article) nothing, but "allow or help to describe"
• Quadratic equation: Only the formula is needed here, the various ways to derive it appear or should appear in quadratic equation. It must be mentioned with links that formulas exist for degree 3 and 4 but not for higher degrees
• Evaluating (and simplifying) expressions: It must be said that the process may be and has been automatized (computer algebra).
• Systems of linear equations: a single example is useful. The description of the various elementary methods should be left to system of linear equations and/or simultaneous equations. On the other hand it is fundamental to mention that the methods extend to any number of equations and unknowns, and that there are computer programs that solve them efficiently. Even for small kids, it may be interesting that weather forecasting needs to solve huge such systems.

This list is far to be complete, but I hope that it will help to understand what is wrong in this article. D.Lazard (talk) 15:56, 19 January 2013 (UTC)

Variables

I'm not sure what do you mean "hat describes what". For the letters, I used the term "designate". Lincoln Josh (talk) 13:30, 17 February 2013 (UTC)

I suppose that you are talking about section Variables. I have edited it and hope that this solves your problem. D.Lazard (talk) 16:13, 17 February 2013 (UTC)

Equation balance analogy animations?

Multiplication, division, collecting like terms.

Addition, subtraction, negation, collecting like terms.

Animations of the equation balance analogy.

If on the off-chance these happen to help: feel free to take or leave. Thanks. M∧Ŝc²ħεИ_τlk 22:34, 18 May 2013 (UTC)

Conflict with process-oriented nature of subject

Although introduction to the foundations for the techniques in axiom is important, making that the article does not reflect how elementary algebra is taught. Rather, what is being taught is a system of techniques - substitution, descriptions in terms of variables or indeterminates, and solution of an equation or isolation of a quantity. So the treatment should seek first to explain the processes, what's possible because they work, and how they integrate with one another (to constitute elementary algebra), and then to axiomatize them in order to explain why they work, or that they work in other situations where those axioms hold. ᛭ LokiClock (talk) 10:59, 13 February 2014 (UTC)

As Wikipedia is not text book, and this article is not about pedagogy, but about mathematics, this does not matter if it does not reflect how elementary algebra is taught. On the other hand, it is important for an encyclopedia to provide to the reader a wider view on the subject than that he can find in his/her textbook. I cannot find any axiomatization in this article, and axiomatization is not relevant here: elementary algebra was widely used by mathematicians and students a long time before the introduction of axiomatization in mathematics (at the end of 19th century). I do not understand why you are talking about axiomatization. I agree that the description of the elementary methods is much too detailed here: we can describe them briefly and refer to the corresponding articles for details. On the other hand the described problems should be put in their context, and they are not. For example it should be said (and this is not said) that the linear equations are always solvable, as well that quadratic ones, and that the other equations in one variables can be solved only in very specific case (in practice, only in examples that are devised for being solvable by students). Similarly, for linear systems it should be said that the presented methods may be generalized to any number of equations and variables, and that these methods can be automatized into algorithms and computer programs. Another information of encyclopedic nature, which is lacking, is the fact that the rules for transforming and simplify expressions may be and have been automatized in computer algebra systems. All kinds know about computers. It is very strange that the mathematic teachers are reluctant to explain what is used in computer and what the computers can do in the area of their courses. Wikipedia must provide this information, because it is of encyclopedic nature. D.Lazard (talk) 20:26, 13 February 2014 (UTC)

Exponential and logarithmic equations?

The article contains a section Elementary algebra#Exponential and logarithmic equations. While this may well be something that is taught in high school algebra courses, is it really part of what is called algebra? I think algebra in the elementary sense only includes the operations addition, subtraction, multiplication, division, and taking n-th roots. Loraof (talk) 21:19, 19 January 2017 (UTC)

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Hatnotes

Right now the article is headed by four hatnotes, dated between August 2012 and January 2013. I propose that I remove three of them:

• Needs reorganization — the current organization looks fine to me.

• May be confusing or unclear — I don’t think that’s a general problem with the article; if there are any specific confusing passages, someone could put confusing tags there.

• Doesn’t give a worldwide view — while it’s probably true that elementary algebra is taught differently in different countries, this article is not about what is taught and how; it’s about the topic of elementary algebra itself, which is a topic that is independent of location.

I think these three hatnotes should be removed. I think it’s legitimate to retain the other hatnote, saying the article contains excessive intricate detail. I don’t have an opinion about that, but I can see that someone might reasonably think so.

Loraof (talk) 17:34, 19 February 2018 (UTC)

I think you can get rid of all of them. Besides the worldwide view tag, the others were all placed at the same time by a now banned user (probable sockpuppet). While there are a couple of places where there is too much detail, I don't think that it is an overall problem. The worldwide tag comes from Hong Kong by a still active user. If he wishes to expand on this point he still can, but I agree with your statement about this. --Bill Cherowitzo (talk) 19:47, 19 February 2018 (UTC)

Absolute value, inequalities

Absolute value is not mentioned here; is there any reason for that? It seems like an important topic to me. Also it might be useful to have an example of solving an inequality, and mention that the sign (< or >) has to flip when multiplying by a negative number. —Lights and freedom (talk ~ contribs) 20:03, 6 October 2021 (UTC)

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