Talk:Calculus/Archive 2

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This archive page covers approximately the dates from 17 December 2006 until 27 January 2007.

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Contents 1 Lead 2 Rewritten 3 Here we go again. 4 Not a good explanation 5 Vandalism 6 The Calculus 7 Too advanced language 8 Proposed link 9 Differentiation 10 nomination 11 High hopes 12 mathrm d 13 BC BCE 14 Indroduction to Calculus Article? 15 Curriculum vs curricula 16 Threatened revert war

Lead

I'm not sure on the new lead it seems to have lots of fancy maths words in it. You need to get through two sentances before you get to anything substantial. I'm not sure how a layman would get it. How about

Calculus is a central branch of mathematics which deal with infinitesimal (infinitly small quantities). In Differential Calculus the ration of two infinitesimal values is considered which allow rates of change to be calculated and slopes of curves to be found. In Integral Calculus and infinite number of infinitesimal quantities are added together, giving the areas under a curves and exact summations to be found.

Just a quick attempt to simplify and reduce jargon to a minimum. --Salix alba (talk) 01:12, 19 December 006 (UTC)

Sorry to be picky, but:

'while integral calculus focuses on the accumulation of infinitely small quantities over time'

how is time essential to integration?. Salix alba is on the right track here surely? Expitheta 20:45, 7 January 2007 (UTC)

Rewritten

Accepting the flame I'm likely to receive for trashing a GA-status article, I've basically rewritten the article from scratch -- retaining what I thought I could use, of course. Why, you ask? Well, I remember a few years back, before I took years of calculus, differential equations, and all that, coming to the calculus article to see what it was all about -- and leaving with my head spinning (and I was a smart kid). Now, someone who looks up 'chain rule,' 'partial derivative,' 'Taylor expansion,' whatever, is likely to have a pretty good background to understand what's going on with symbols and concepts. Likewise, someone who looks up 'history of calculus' is looking for information about ancient Indian mathematics and the Newton vs. Lorenz issue. But... someone who just punches in calculus is probably a late high school or early university student who wants a basic explanation and a grip on the concepts. Once you learn calculus, it's beautiful how everything fits, but before then, it's a jumbled mess that seems impossible (maybe just because the ideas seem so simple but the applications are so powerful -- life is rarely like that). This basic, umbrella article should be a gentle introduction to the concepts, symbols, and methods... nothing more.

Anyway, what I'm saying is, revert if you must, but at least think about what this article should be (because I don't think it was anywhere near good enough). BryanHolland 12:27, 23 January 2007 (UTC)

Here we go again.

About a year ago a number of mathematicians, working slowing and carefully, produced a good article. But this article is a magnet, and attracts many rewrites. Slow careful work is quickly replaced by hasty, careless work. It is a flaw in Wikipedia that can only be solved by willing watchdogs, who revert any change that is not a clear improvement.

I would revert, but I would have to go back several months to find a version that wasn't terrible. The current version, which says that calculus is mostly about rates, is like saying that chemistry is mostly about acids.

I'm going to try a slow and careful rewrite. Please, if you must make changes, do not make them hastily. Rick Norwood 13:36, 23 January 2007 (UTC)

I understand your point; mine is, we have Differential, Integral, Limit; if the article is going to duplicate information, it needs to be more useful than the more comprehensive articles in some way... in this case, accessibility is the key. Calculus met 'good article' criteria, but it wasn't (and admittedly still isn't) a good article. BryanHolland 13:51, 23 January 2007 (UTC)

Ultimatly here we are writing an encylopedia article not a text book how to. This article also serves a summary style article, with brief overview of the major parts, so it needs at least some info on the history and foundations. It also needs to be broad in scope covering the extensions to multi-dimensions, esp vector calculus and differential equations which don't seem to have been mentioned before.

i'm not taken with the new lead

Calculus is a field of mathematics, concerned primarily with problems of rates. Fundamentally a means of circumventing division by zero through the use of limits, calculus consists of two broad disciplines.

Division by zero is not the motivating force for calculus.

It might be idea to work on a /draft version before going to the live article. --Salix alba (talk) 13:53, 23 January 2007 (UTC)

I have to say that

Calculus is the name given to a group of systematic methods of calculation, computation, and analysis in mathematics which use a common and specialized algebraic notation

was a big part of what motivated me in the first place... the same is true of just about every aspect of math above basic arithmetic. As for 'how to'... understood. The article just looked like a rundown of disjointed "these people and these people discovered calc" and "this physics problem uses calc" and "these senior or graduate-level math courses can rigorously demonstrate calc's validity" which would be utterly useless to someone who doesn't already know everything covered in the article. Regardless, thanks for your input... I'll work on team play. BryanHolland 14:14, 23 January 2007 (UTC)

And, Salix, Rick... from your comments, I suspect your frustrations aren't too far from mine. Certainly I didn't mean to make things worse. BryanHolland 14:16, 23 January 2007 (UTC)

The important thing, I think, is to work slowly, and consider carefully. Following that rule, I now stop for the day. I'll do a little more tomorrow, and so on. I hope that working together we can produce a worthy article. Rick Norwood 14:25, 23 January 2007 (UTC)

Still working carefully. Does anyone know how to insert spaces in "changeiny"? Rick Norwood 22:20, 24 January 2007 (UTC)

Help:Displaying a formula should have the answer to most math typsetting. Specifically change in y \mbox{change in }y. --Salix alba (talk) 22:44, 24 January 2007 (UTC)

Thanks. Rick Norwood 13:40, 25 January 2007 (UTC)

Not a good explanation

I came to the page to get a basic understanding of calculus, and it didn't help at all. I tried to find out what "b" is in mx+b under the differentiation heading, but my comments were removed without any acknowledgement or helpful explanations. i went elsewhere to find out, and put it up, acknowledging that it wasn't directly relevant to the discussion at hand, thinking that would help others with the same question, but it was removed. you can't just throw an equation in front of people unfamiliar with it and expect them to understand parts of it you don't explain. You should try to improve parts that people flag as confusing. Thanks. —The preceding unsigned comment was added by 65.78.27.85 (talk • contribs).

Questions like that are not supposed to be posted in the middle of the page. Posing those same questions here would be much better - or maybe at WP:RD/MA or WT:WPM. I'll bet someone would help you out if you can find the right place to ask. For your particular question, you might want to look at the Slope article as well. —Wknight94 (talk) 20:04, 28 January 2007 (UTC)

This is an encyclopedia, not a web-forum. You can't just stick a question right in the middle of an article. Furthermore, Wikipedia did provide an answer readily - the wiki-link to linear function would have explained that form quite clearly. The article on calculus cannot repeat things as fundamental as basic high-school algebra concepts like that - that's why there are wiki-links. You click the word linear (right before the equation y=mx+b) and it takes you right to the expaination you were looking for. There are "flags" to put into articles to denote problems, and if you have a specific question, you can come here to the article's talk page, where someone could have cleared this all up for you. However, it was not at all ambiguous, as there was a clear explaination of linear functions just a click away, as it should be. 149.43.x.x 01:28, 29 January 2007 (UTC)

The trouble with instant gratification is that it takes too long. Rick Norwood 13:39, 29 January 2007 (UTC)

Vandalism

Why do people keep replacing the history with nonsense about some jimmy bollman ? --Jackaranga 15:21, 12 February 2007 (UTC)

They are called vandals. Usually they are children who are trying to get attention. Revert and ignore. Tag the revert "rv v", short for "revert vandalism". Rick Norwood 14:04, 14 February 2007 (UTC)

The Calculus

Correct me if I am wrong.

I believe that Newton had arranged for this particular branch of mathematics to be called "The Calculus". Does this come up anywhere in this article?Gagueci 18:23, 27 February 2007 (UTC)

It's usually referred to as the calculus in more formal situations, and as just calculus in less formal ones. It would seem that the the would be appropriate here, but it's by far not the biggest problem in this article. 71.102.156.213 05:22, 12 April 2007 (UTC)

The term "the calculus" is antiquated,simply "Calculus" is more widely used and appropriate. "The calculus" redirects here so there should be no problem.--Cronholm144 20:50, 10 May 2007 (UTC)

Too advanced language

I suspect that the main reason this article got delisted was the use of language such as "linear operator", and "inverse linear operations". This stuff needs to made more informal, with more formal sentiments used to improve more specialized articles in this area. Geometry guy 01:15, 28 March 2007 (UTC)

The article is now a lot less formal than it was when it was delisted. But, I think you are correct that "linear operator" is too technical for the intro. I've deleted the clause, and I think the intro reads more smoothly. Rick Norwood 12:28, 28 March 2007 (UTC)

Proposed link

Shouldn't http://www.calculus.org be in the External Links? I know it's already #1 on Google, but it really is the place that students should be directed to; I think they'd appreciate it. I was actually stunned to find that that link wasn't already on here. (Sorry about my previous link add; I'm new.) Thanks! Ken Kuniyuki 18:28, 30 March 2007 (UTC)

That's an excellent suggestion, thanks. Looks like they have good stuff, maintained by a good university, includes links to other sites. I think it should be at the top, and added it there. -- Jitse Niesen (talk) 04:27, 31 March 2007 (UTC)

Differentiation

When I was reading the sub-article on differentiation I noticed it said "The slope, or rise over run, can be expressed as:

"

which seems to be slightly misleading because this expression does indeed output a slope, but it is the slope of the secant line for some points x and x+h on the function f rather than the general slope of f where f defines a line that the article had been discussing up till that point. I think mention of this might be helpful to new readers.

Also, just two minor things, there is no mention of y until

then the function can be written f(x) = m x + b, where:

.

I think that to avoid confusion perhaps it should be written f(x) = y = m x + b, where:

as is typically done in when introducing function notation in textbooks

and the article uses "linear operator" and "linear" function fairly closely together and people who do not understand the difference between a line and a linear transformation might become a touch confused.

One final thing, what do you think about archiving the older discussions? The page has become rather long and the majority of the older conflicts have been resolved.

Cronholm144 05:18, 12 April 2007 (UTC)

All of these suggestions are good. I'll try to work on the first two today. Rick Norwood 12:21, 12 April 2007 (UTC)

nomination

I added calculus to the Good Article nominee list because I believe that the issues that were the cause for its demotion have been addressed. Cronholm144 22:41, 12 April 2007 (UTC)

Well, we'll see how it goes. ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 07:51, 13 April 2007 (UTC)

High hopes

I have mixed feelings about the recent major rewrite, and have reverted it for two reasons. First, such a major rewrite probably should not be done in the middle of the consideration of this article as a good article. Second, somebody removed the illustration, without which all of the references in the rewrite make no sense.

I am not necessarily opposed to the story of the ant -- I just think it needs to be discussed here, first. To read the "ant" version, go to the history of the article and click on the rewrite by 141.211.120.199.

By the way, 141.211.120.199, "it's" is an abbreviation for "it is". "Belonging to it" is written "its".

Rick Norwood 13:32, 15 April 2007 (UTC)

Rick, i agree with your revert. No problems here :-) ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 14:47, 15 April 2007 (UTC)

I also agree with the revert, although there was some merit in the ant story: it provided a more elementary (albeit not very encyclopedic) motivation for differentiation than the current version does. Further to this, and a previous comment of mine, editors here might like to know that I have used some of the material here in recent work on Derivative. In particular I essentially copied the "differentiation as an operator on functions" discussion. Although it is well explained, and is an important idea, I find it too advanced for the front line calculus article, and suggest that it could be removed or de-emphasised now that it has another home.

Good luck with the GA nomination! Geometry guy 17:17, 15 April 2007 (UTC)

mathrm d

Natural Philosopher has gone to quite a lot of work to change all the math d's to mathrm d's in the differentials associated with integrals. I've checked several books, and all of them use math d's. Can Natural Philosopher quote a source for using mathrm d's for differentials? Rick Norwood 12:25, 20 April 2007 (UTC)

There was a discussion about this at WT:WPM recently (last month). The punchline is that both usages are acceptable, but editors should not go through articles making wholesale changes from one notation to the other, as Natural Philosopher has done here. Even though I prefer the roman d, I'm happy for you to revert these edits. Geometry guy 17:26, 20 April 2007 (UTC)

I have no strong feelings one way or the other, but I do favor consistency. Rick Norwood 12:35, 21 April 2007 (UTC)

BC BCE

There are people who spend a great deal of their spare time going through Wikipedia and changing all the BC's to BCE's and there are others who spend a great deal of their spare time going through Wikipedia and changing all the BCE's to BC's. It keeps them off the street. Best to ignore them. Rick Norwood 22:01, 6 May 2007 (UTC)

Well, maybe they are on the street editing this before they have their next drug-related bowel movement. I kid; every contribution no matter what it's intentions, so long as good, is okay by me :-) ♥♥ ΜÏΠЄSΓRΘΠ€ ♥♥ ^{slurp me!} 22:05, 6 May 2007 (UTC)

Indroduction to Calculus Article?

Given the extremely technical nature of calculus (to non mathematicians) and the importance and interest of it, might it be a good idea to follow the example of the Entropy article which has a separate Introduction to entropy article? Tomgreeny 18:11, 1 June 2007

Did you read the article? What in particular about the article is overly technical? We have attempted to craft an article that builds slowly and is intelligible to the layman. The reason that entropy has a separate article for introduction is because the math (calculus in fact!) is very difficult to understand if you are just trying to understand what entropy is in a general sense. This article is already aimed at general audiences, so having a separate introduction would be redundant. --Cronholm144 01:51, 2 June 2007 (UTC)

OK I've read the article now. It doesn't seem overly technical (although since I'm a mathematics student who already understands calculus I may not be fit to judge). People who want more detail can look in the derivative and integral articles. I just thought I'd put the idea out there as something to think about. Tomgreeny 11:48, 2 June 2007 (UTC)

Ok understood.--Cronholm144 11:57, 2 June 2007 (UTC)

Curriculum vs curricula

Certain rather inflammatory comments were made in the edit summaries, followed by multiple reverts between the university curriculum and university curricula. For the benefit of those who might care, I have copied my earlier comments left at User:Cheeser1's talk page. Arcfrk 07:13, 21 June 2007 (UTC)

Idiom. 3. a. A form of expression, grammatical construction, phrase, etc., peculiar to a language; a peculiarity of phraseology approved by the usage of a language, and often having a signification other than its grammatical or logical one. (Oxford English Dictionary)

The issue here is not single university (sing) versus a variety of universities (pl), but the fact that there is a commonly adapted scheme of mathematical instruction at present time, that is referred to as 'modern university curriculum', just like in Middle Ages there was a common such scheme, referred to as 'quadrivium'. Arcfrk 02:34, 21 June 2007 (UTC)

On the other hand, at least in the United States, many universities choose their own curriculum, similar but not identical to their colleagues; resulting in many curricula. It occurs to me as I type that this may be an Anglo-American difference; insofar as there is governmental oversight of university teaching in the United States, it is done by the several states, and the role of the Federal Government is advisory (with a big stick of funding, of course).

More to the point, this entire debate is over a point irrelevant to calculus, and which will be lost on our readers — I hope no–one will advocate a paragraph explaining the matter. ;-> Substituting education; if someone has a better idea, fine. Septentrionalis PMAnderson 13:31, 21 June 2007 (UTC)

I believe you mean educations. (I kid, I kid...) Yes, I see merits to such a proposal on the grounds that curriculum/a may sound elitist (see the most recent contribution by yet another player in this ongoing battle.) I'm curious to see what tweaks are in store.  ;-) Silly rabbit 13:40, 21 June 2007 (UTC)

The use of a single "university curriculum" to describe university education presumes, without question, that there is (and ought to be) a standard university curriculum, across the board. It is a simple, minor fix to make the word plural and avoid that presumption. And please, the use of the word is not elitist (this is an encyclopedia, we can say "university curricula" without having to dumb it down or use smaller words). "Education" and "curricula" are not equivalent, and the latter is far more precise and more appropriate in this context.

For the record, I will point out, yet again, that "the university curriculum" is not an idiom, it is a common phrase. Just because it is a common phrase, used to represent a tacitly assumed (and arguably nonexistent) "standard curriculum," does not make it an idiom. An idiom is a phrase whose meaning is different that the sum of the literal meanings of its parts. University curriculum means "a curriculum of a university." Not an idiom. It can be easily pluralized (as could an idiom, by the way).

If we are writing this properly, we would use the word curricula - it is the appropriate word, and the one generally used to describe the courses of study at a university. We would use the plural because it is not necessary to presume that there is a common or standard curriculum; we ought to avoid doing so if we're interested in writing a good encyclopedia. As for whether or not this is "irrelevant" - it may not concern the subject matter of calculus, but when someone reverted it to "curriculum," citing a nonexistent English idiom, I felt as though it was important to fix and to explain that it is not an idiom. This lead to some arguments due to a lack of assumptions of good-faith, arguments that I am not reviving here, just explaining, because the facts of the matter are plain and simple. Curricula is the appropriate word, and because there are a multitude of curricula (a plurality, if you will), presuming a standard single curriculum is unnecessary (and based on some of the justification, US-centric). We don't need to pick an imprecise "compromise" word, and we don't need to argue about this. It was a minor, well-justified edit that's been reverted several times now for reasons that have not been correct, and I'm not really wondering why I ever had to explain it any further. --Cheeser1 15:21, 21 June 2007 (UTC)

The issue of idiom vs non-idiom is a red herring. Changing 'curriculum' to 'education' dilutes the meaning somewhat. I submit that, de facto, there is a core university curriculum (how is that for a better idea?) that includes Calculus. I am quite familiar with the US higher education system, and it is certainly true within that system, notwithstanding the valid observation that universities, and to some (rather small) extent, the states, have lattitude into what to include into their programs of study. I know that that instruction of Calculus is a fixed component of the higher education in a few other countries, including Canada, France, Germany, UK, Australia, Turkey, and Russia. I presume that it is also the case in Mexico, India and China, and given the influence of English-language textbooks, it may well be the case in the rest of the developed world. This existence of a standard (in the past 40-50 years) university mathematics curriculum represented by Calculus is independent of whether or not there ought to be one. We are reporting things based on the facts, not our idealized view. And I wholeheartedly agree with PMAnderson that the issue itself is rather tangential to most of the article. Arcfrk 16:57, 21 June 2007 (UTC)

And your de facto assertion would be a welcome point to discuss in an article like Higher education, but in an article about mathematics, we need not make unjustified de facto assertions about the state of education in the particular countries we consider to be the model for higher learning. The fact that it's irrelevant to a discussion of calculus is more reason to not make such unjustified a priori assumptions. --Cheeser1 17:07, 21 June 2007 (UTC)

Substituting education changes the meaning. I agree on that; I was willing to say something different. (I took out most because all too many college educations fail to educe calculus.) However, the lead looks to me, in either version, as a way of saying "Calculus is notable". I urge people not to worry about details as long as they are accurate. This entire argument might be worth having at Talk:Curriculum, but why here? Septentrionalis PMAnderson 18:18, 21 June 2007 (UTC)

To me, saying "education" when you should say "curriculum" is like saying "animal" when you should say "cat." It's an analogy, but I think there's a clear idea that a curriculum is a part of an education, but not the other way 'round. One is far more precise. --Cheeser1 18:39, 21 June 2007 (UTC)

A curriculum is not a kind of education; so I fail to see the analogy. Septentrionalis PMAnderson 20:38, 21 June 2007 (UTC)

I didn't say it was a kind of education, I said it was more specific than the term education, it is a part of an education, not the education entirely. A currilum is a specific course of study. An education is the sum total of the educational experiences of the time spent at a school (including extracurricular educational opportunities). It is clearly the appropriate word, the way I read it. --Cheeser1 20:44, 21 June 2007 (UTC)

Because no one seems to have justified using the word "education" except as a "compromise," I am removing it. "Education" is far too vague, whereas "curriculum/a" denotes exactly what we want - it means "the grand sum of academic coursework" at a university (roughly), which that is the sense we wish to convey. When one speaks of the kinds of courses offered at a university, one speaks of the curriculum, not of the "education." I also have yet to see a single valid point explaining why or how there exists some sort of universal university curriculum (furthermore, such an issue is debatable, and if we can avoid assuming something debatable or questionable, we should). There are, in fact, many curricula, as far as I'm concerned, and the way I see it, it would be presumptuous to state something contrary to that effect. Unless someone justifies this point, I would expect it to be left plural. This is a minor point that I (and a neutral third-party administrator) believe I have justified fully. --Cheeser1 02:38, 22 June 2007 (UTC)

I agree that 'curriculum' is a more precise term, however, I would like to highlight that compromises have their merits. At any rate, I rewrote the lead and restored the reference to the university curriculum (singular form) as the more proper form in this context. Compare with 'Liberal Arts curriculum'. US universities have a fairly standardized approach to mathematics curriculum, requiring most of their students to take a 3 or 4 semester calculus sequence (occasionally, a shorter sequence for business students, known colloquially as 'Business calculus'). Modulo the recent split between 'traditional' vs 'reform' calculus, which affects the pedagogical side more than it affects the content, these courses use a very limited number of common textbooks. In this respect, Calculus arguably occupies a fairly unique position of a course that nearly all students have to suffer through complete. This, I believe, is a notable societal fact about calculus that deserves a mention in its 'definition'. Arcfrk 03:33, 22 June 2007 (UTC)

P.S. We have all agreed that the curriculum wording is a minor point. However, if anyone is craving for a peer review, I propose taking the discussion to Wikipedia talk:WikiProject Mathematics, where many highly qualified mathematics editors will have a chance to comment. Arcfrk 03:33, 22 June 2007 (UTC)

You have got to be kidding me. You are still suggesting that there is evidence of a universal university curriculum across the entire world, at every single institution? I'm glad you want to assert that calculus is a part of many curricula, but using the plural of the word will not stop you from doing so. Using the singular, on the other hand, will tacitly assume that there is a standard or universal curriculum that all universities share. This is highly inappropriate and has not been justified. I have explained myself clearly several times, and you have not justified the underlying assumption that you are making by using this word. Until you do so, I will continue to fix your error (it is an error, after all, to put something into Wikipedia if you cannot justify or source it - even if it is a result of a minor grammatical nuance). --Cheeser1 04:10, 22 June 2007 (UTC)

What is going on here??? This is supposed to be the page for improving the calculus article, not the Latin vs. idiom grammar discussion. I am going to archive this as soon as you are done arguing.--Cronholm¹⁴⁴ 04:54, 22 June 2007 (UTC)

I wish I could have been done arguing the first time I explained myself. *sigh*! I'm under the impression that we're done arguing, since no one else has cited policy yet and editing seems to have cooled off. Then again, I didn't think fixing it would have attracted an argument to begin with. --Cheeser1 05:03, 22 June 2007 (UTC)

Threatened revert war

Cheeser1 has, cheesily, threatened to revert war if he does not get his way on curricula. Does anybody else support his crusade, or should we simply recast the first sentence as well, to get rid of the bone of contention? I honestly thought education was far enough; guess not. Septentrionalis PMAnderson 00:28, 23 June 2007 (UTC)

Thank you for blatantly violating WP:GF. All I meant was that I will revert it because the issue was resolved and my version was determined to be appropriate, [1] not because I intended to start a revert war. You know, if you trump it up in your imagination as if I'm crusading to destroy your article by reverting the change from "curricula" to "curriculum" (and subsequently, to "education"), it's going to start to seem that way. Works the same way as WP:CABAL. You people want to dumb down the article with imprecise language, feel free. I'm done with this worthless argument. Don't expect a response, regardless of what you say here. --Cheeser1 00:45, 23 June 2007 (UTC)

For the record, then: One editor preferred curricula to curriculum. So what? Both are off topic. Septentrionalis PMAnderson 00:55, 23 June 2007 (UTC)

For the record, I intentionally archived the entire discussion to get that kind of silliness of this talk page. I think that we are all on the same page on 1. avoiding the word or 2. reaching a consensus without an editwar, so I plan on archiving this rather soon as well. Any further discussion of commonly used idioms vs. latin plural should take place on the talk pages of the concerned editor. --Cronholm¹⁴⁴ 04:36, 23 June 2007 (UTC)