2440:, 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
2030:. 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
942:. 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. —
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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 (
394:"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...
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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
Knowledge in the first place.
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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...
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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. ᛭
1969:, 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.
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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
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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
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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
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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
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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
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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.
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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
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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
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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}}
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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
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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
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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
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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
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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
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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,
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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
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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
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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
2477:. 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
2221:, 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?
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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
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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.
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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
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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
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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. —
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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).
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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... —
2281:. 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
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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
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and not that of
Knowledge. 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
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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 :
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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
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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. Knowledge
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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
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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: -->
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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.
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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.
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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?
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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
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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: -->
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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.
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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.
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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. -
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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. --
1962:, 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.
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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 "
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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.
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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: -->
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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.
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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,
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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: -->
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I find the first/second person english language usage "unencyclopadic": the various I, You, Let us, Let's, in this article is too presumptuous.
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Why in this section or in any section in
Knowledge would there be author attribution? "By:Ůmáīr Hafeez Měmõń'" Shouldn't this be deleted? --
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1903:. For solving this issue, I suggest to replace "multiplicity" by "divisibility", and, if needed, to change the order of the arguments (if
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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. -
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Right now the article is headed by four hatnotes, dated between August 2012 and
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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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. --
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at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be
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Since I am talking about style the presentation-style bulleted lists are giving me pause as well. Are they OK with
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I'm going to go with the following rationale. If we refer to a number in an equation, then I'll use <math: -->
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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By the way, a section "Elementary algebra on computers" is lacking, which should contain the information that
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This list is far to be complete, but I hope that it will help to understand what is wrong in this article.
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between algebraic expressions. Its is a topic of modern, current research. Sadly, both the articles
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one, I would possibly support {{math}} or {{math|big=1}} there too. It'll cope with fractions (e.g.
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I can't do it right now, but I'd be willing to work on this one of these days. What do you think? -
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are added together. By convention, terms with the highest power (exponent), are written on the left.
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I'm not sure what do you mean "hat describes what". For the letters, I used the term "designate".
2273:: a single example is useful. The description of the various elementary methods should be left to
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on
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before doing mass systematic removals. This message is updated dynamically through the template
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inline math. I'd definitely vote for inline-HTML and I'm prepared to do it one of these days. -
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Also, can the 3.5 example for multiplication be fixed to look more like it should (3 dot 5)?
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template for simple formulae (especially inline), (c) these shortcomings of <math: -->
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https://web.archive.org/web/20110413234352/http://web.mat.bham.ac.uk/C.J.Sangwin/euler/
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If you found an error with any archives or the URLs themselves, you can fix them with
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A significant portion of the article is devoted to working out, by hand, examples of
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axioms in place to define "objects" and "arrows" so that "squiggle blob blob" is an
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Yes, but look at the source of your spanned Pure HTML. It's pretty hard to code:
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If on the off-chance these happen to help: feel free to take or leave. Thanks.
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It can be automated: reduction is simple enough that computers can do it, e.g.
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Please refer to issue by numbers. Eg., the second issue with 1a criterion is
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Good idea, all done. Do you think that numerals should also be converted? --
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math. I think that should remain in TeX, as in most other articles (e.g.
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1. There are cleanup banners that are obviously still valid, including
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This works fine except where we have more complicated expressions. --
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I think I've fixed, showing both the
European and American forms for
2263:: It must be said that the process may be and has been automatized (
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2043:.) I repeat: this is absolutely central to the notion of algebra!
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Needs reorganization — the current organization looks fine to me.
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provide this information, because it is of encyclopedic nature.
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Similarly for the linear systems. The given details duplicates
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Well, the HTML math (as in the alternatives of my example) is
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which uses size 165% in stead of your less-standardish 150%:
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I agree with the reviewer that the article style is that of
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for additional information. I made the following changes:
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We can always make inline HTML look a bit like math PNG:
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Elementary algebra#Exponential and logarithmic equations
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I propose that we write this with inline HTML math —see
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Addition, subtraction, negation, collecting like terms.
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2707:Participate in the deletion discussion at the
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2325:I suppose that you are talking about section
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764:, because the terms containing
576:Mixed formatting of inline math
230:This article has been rated as
2755:B-Class level-4 vital articles
2601:05:37, 19 September 2017 (UTC)
37:nominee, but did not meet the
1:
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2642:17:34, 19 February 2018 (UTC)
2463:20:26, 13 February 2014 (UTC)
2431:10:59, 13 February 2014 (UTC)
2339:16:13, 17 February 2013 (UTC)
2320:13:30, 17 February 2013 (UTC)
2191:03:32, 24 November 2012 (UTC)
1797:, or similar tags. (See also
1359:+ 3''ab'' - ''x''<sup: -->
1184:First expression encoded as:
359:14:39, 4 September 2010 (UTC)
204:and see a list of open tasks.
2770:B-Class mathematics articles
2735:Former good article nominees
2664:Absolute value, inequalities
2491:21:19, 19 January 2017 (UTC)
2300:15:56, 19 January 2013 (UTC)
2231:12:25, 19 January 2013 (UTC)
1314:-- with source <span: -->
1287:-- with source <math: -->
968:with MathJax in IE8—Ouch! -
384:13:47, 13 October 2011 (UTC)
301:13:08, 4 November 2010 (UTC)
2721:11:52, 23 August 2022 (UTC)
2688:20:03, 6 October 2021 (UTC)
2271:Systems of linear equations
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2146:16:34, 18 August 2012 (UTC)
2126:17:20, 18 August 2012 (UTC)
2091:16:34, 18 August 2012 (UTC)
2076:16:16, 18 August 2012 (UTC)
2012:17:59, 11 August 2012 (UTC)
1946:17:02, 18 August 2012 (UTC)
1631:Talk:Elementary algebra/GA1
1550:18:03, 13 August 2012 (UTC)
1525:17:46, 13 August 2012 (UTC)
1502:16:44, 11 August 2012 (UTC)
2791:
2564:(last update: 5 June 2024)
2500:Hello fellow Wikipedians,
2275:system of linear equations
2041:morphism (category theory)
1986:14:32, 4 August 2012 (UTC)
1929:13:29, 4 August 2012 (UTC)
1901:multiplicity (mathematics)
1723:for the following reason:
1665:01:27, 3 August 2012 (UTC)
1480:09:21, 4 August 2012 (UTC)
1454:22:39, 3 August 2012 (UTC)
1412:17:36, 3 August 2012 (UTC)
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1366:(4) My proposed HTML with
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1027:13:37, 3 August 2012 (UTC)
1008:11:55, 3 August 2012 (UTC)
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637:19:48, 1 August 2012 (UTC)
621:18:43, 1 August 2012 (UTC)
606:15:19, 1 August 2012 (UTC)
404:20:05, 29 April 2011 (UTC)
272:I really don't think that
45:. Editors may also seek a
2151:first/second person usage
2050:. Its a special case of
1687:22:01, 25 July 2012 (UTC)
1513:re-opening the discussion
1221:(1) math PNG or MathJax:
1140:{\displaystyle x^{2}+4ab}
966:Help:Displaying a formula
757:{\displaystyle x^{2}+4ab}
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33:Mathematics good articles
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2054:. It is kind-of-like a
2037:object (category theory)
1466:). I.m.o. it's just the
499:{\displaystyle 3\cdot 5}
236:project's priority scale
2496:External links modified
2060:reduction (mathematics)
2048:computer algebra system
2024:reduction (mathematics)
473:{\displaystyle 3\ .\ 5}
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823:MOS:MATH#Using_HTML
647:Referring to point
325:wikipedia standards
2713:Community Tech bot
2672:Lights and freedom
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2505:Elementary algebra
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2312:Lincoln Josh
2309:
2270:
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2223:Lincoln Josh
2218:
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2207:
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2201:
2173:— Preceding
2168:
2154:
2134:
2115:
2107:
2099:
2079:
2045:
2031:
2021:
1971:
1964:
1952:
1916:
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1892:
1889:multiplicity
1888:
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1877:
1762:unreferenced
1717:
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1613:Instructions
1537:
1534:
1489:
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1459:
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1387:
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1321:- <i: -->
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370:— Preceding
367:
364:
322:
313:This section
311:
290:
274:this section
271:
258:
232:Top-priority
231:
191:
157:Top‑priority
135:WikiProjects
118:
83:
48:reassessment
46:
31:
30:
26:
2481:-th roots.
1955:Wikiversity
1719:quickfailed
1703:reviewer(s)
1627:transcluded
1361:+ ''ab''}}
1315:2<i: -->
1188:2<i: -->
1179:, because..
1147:, because..
376:83.158.63.7
345:—Preceding
207:Mathematics
198:mathematics
154:Mathematics
43:renominated
2729:Categories
2596:Report bug
2442:algorithms
2179:Leeeoooooo
2004:Iantresman
1995:Knowledge.
1874:Discussion
1708:Discussion
1673:Iantresman
1670:Nominator:
1580:Authorship
1566:GA toolbox
1533:Good idea.
1517:Iantresman
1460:standalone
1395:+''ab''}}
1205:Iantresman
1000:Iantresman
629:Iantresman
598:Iantresman
556:Iantresman
508:Iantresman
419:Iantresman
415:Operations
409:Operations
267:Operations
90:Not listed
2625:location.
2579:this tool
2572:this tool
2423:LokiClock
2327:Variables
2306:Variables
2245:Variables
2056:cobordism
2018:Reduction
1851:technical
1827:confusing
1792:clarifyme
1639:Reviewer:
1603:Templates
1594:Reviewing
1559:GA Review
123:is rated
2683:contribs
2606:Hatnotes
2585:Cheers.—
2455:D.Lazard
2331:D.Lazard
2292:D.Lazard
2187:contribs
2175:unsigned
2111:preorder
2109:to be a
1978:D.Lazard
1921:D.Lazard
1915:divides
1683:contribs
1661:contribs
1608:Criteria
995:devices.
372:unsigned
347:unsigned
2509:my edit
2277:and/or
2000:algebra
1911:, then
1802:QF-tags
1732:cleanup
1448:Quondum
945:Quondum
615:Quondum
585:Quondum
254:Archive
234:on the
125:B-class
68:Process
2634:Loraof
2483:Loraof
2032:shapes
1863:wikify
1742:wikify
1692:Status
1490:Update
1468:inline
530:hydnjo
434:hydnjo
131:scale.
71:Result
29:was a
2157:linas
2138:linas
2118:linas
2083:linas
2068:linas
1938:linas
1897:WP:OR
1629:from
480:or
112:This
2717:talk
2677:talk
2654:talk
2638:talk
2487:talk
2459:talk
2451:must
2427:talk
2335:talk
2316:talk
2296:talk
2227:talk
2183:talk
2161:talk
2142:talk
2122:talk
2087:talk
2072:talk
2062:and
2026:aka
2008:talk
1982:talk
1942:talk
1925:talk
1772:fact
1699:only
1677:talk
1655:talk
1648:tund
1546:talk
1542:DVdm
1538:ages
1521:talk
1515:. --
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1494:DVdm
1476:talk
1472:DVdm
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1404:DVdm
1209:talk
1023:talk
1019:DVdm
1014:much
1004:talk
974:talk
970:DVdm
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924:DVdm
633:talk
627:. --
602:talk
560:talk
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512:talk
506:. --
438:talk
423:talk
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380:talk
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333:talk
297:talk
283:talk
277:one?
261:here
65:Date
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1344:+ 3
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226:Top
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