Talk:Calculus/Archive 2

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DO NOT EDIT OR POST REPLIES TO THIS PAGE. THIS PAGE IS AN ARCHIVE.

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

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Lead

Resolved

 – jargon reduced, accumulation addressed later--Cronholm144 21:11, 10 May 2007 (UTC)

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

Resolved

 – Article had changed significantly since this rewrite and issue of clarity is addressed next section--Cronholm144 21:15, 10 May 2007 (UTC)

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.

Resolved

 – consensus on article improvement reached here.--Cronholm144 21:19, 10 May 2007 (UTC)

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 ${\mbox{change in }}y$ \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

Resolved

 – The I.P.'s problem was addressed.--Cronholm144 21:21, 10 May 2007 (UTC)

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

Resolved

 – not much to say, rv vandalism where you find it.--Cronholm144 21:23, 10 May 2007 (UTC)

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

Resolved

 – minor notation question--Cronholm144 21:24, 10 May 2007 (UTC)

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

Resolved

 – jargon removed from lead as per WP:LEDE--Cronholm144 21:26, 10 May 2007 (UTC)

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

Resolved

 – Proposed link, added--Cronholm144 21:27, 10 May 2007 (UTC)

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

Resolved

 – clarity issue, addressed--Cronholm144 21:29, 10 May 2007 (UTC)

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

$m={f(x+h)-f(x) \over {(x+h)-x}}$"

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:

$m={rise \over {run}}={{\mbox{change in }}y \over {\mbox{change in }}x}={\Delta y \over {\Delta x}}$.

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

Resolved

 – GA nomination results later--Cronholm144 21:29, 10 May 2007 (UTC)

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

Resolved

 – rewrite by I.P. discussed, reverted--Cronholm144 21:37, 10 May 2007 (UTC)

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

Resolved

 – notation discussion, math d's chosen for article by consensus--Cronholm144 21:44, 10 May 2007 (UTC)

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

Resolved

 – notation discussion, decided on B.C. because of the initial condition of the article, see WP:MOS--Cronholm144 21:42, 10 May 2007 (UTC)

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?

Resolved

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)

Babylon Tablets Comment

While adding the note for babylonian astronomer clay tablets, some edits were reverted (and perhaps the reversion also reverted.) Assuming good faith, it is wise to allow for 10 minutes from initial edits before removing content and asking for more citations. The citations requested were being adding during the event. I for one, appreciate the watchful eyes keeping track of article improvement. Kyle^(talk) 20:03, 29 January 2016 (UTC)

I still think that these two sources [2] and [3] suffer from wp:recentism. These are non-mathematicians reporting about a non-mathematician's recent finding. A proper wp:secondary source would be one from a scholar i.e. a mathematician in a peer reviewed article. After all, this is an math article, not an archeology one. - DVdm (talk) 21:51, 29 January 2016 (UTC)

Even though I'm the person who entered the citation to the New York Times article, I don't have strong feelings about this recent development needing to appear in Wikipedia. I will go with the flow on this one. Isambard Kingdom (talk) 22:00, 29 January 2016 (UTC)

I agree with DVdm. These references are summaries of a single article containing one person's interpretation of some apparently related clay tablets. One needs only recall the checkered history of the interpretation of Plimpton 322 to see that this interpretation may not hold up under the scrutiny of several specialists. When that vetting is done the result will be in reliable secondary sources and we may freely cite these, but until then it should be treated as a viable theory and not as an established fact. Bill Cherowitzo (talk) 05:18, 30 January 2016 (UTC)

Ok, there seems to be no consensus to keep this addition, so I have removed it again ([4]). - DVdm (talk) 09:03, 30 January 2016 (UTC)

Calculus... "is the mathematical study of change"??

That sounds cute, but it's not correct, or at best it's only correct in some instances. While dx generally represents change in x, that doesn't mean calculus is "the study of change". O-m-g. Someone please rework that intro. 76.208.70.118 (talk) 02:04, 20 August 2016 (UTC)

That someone could be you! Go for it. WP:BOLD! Ozob (talk) 02:53, 20 August 2016 (UTC)

I apologize for abusing the reverting of an edit, just to continue the discussion.
May I submit my personal thoughts on this:

• First of all, I see calculus not as the study, but rather (as already mentioned in the article!) as a methodology to exploit the results of the respective studies, which belong to, say, (functional) analysis. I would not say this about geometry and algebra in a similar way. However, if pressed, I would say that water is wet as liquid nitrogen is, but not as wet as mercury is. I also admit that I know about linguistic constructs like pars pro toto, and related ones, but prefer to be highly discriminating in an encyclopedic context.
• In extremis, Calculus reminds me more of the Ricci calculus, which is per se not a study of multilinear algebra, but a viable path to deal with tensor algebra and analysis. Certainly, calculus contains more algorithmic parts, but is similarly away from a study (at least in a sense which is is not abused like for sociological "studies") of the underlying structures. I think calculus takes its importance from its outstanding applicability, already in quite early math education.
• Calculus also does not really deeply care on which bases it is applied. It works on the reals, on the extended reals with strictly defined infinitesimals, as well as in brownie-enriched physicists' world with just very small, very useful objects, also coined infinitesimal, and even on fairly discrete domains.
• I suggest to talk about local rates of change in favour of change, since the limit of a ratio of local changes is important in differential calculus, and not the change itself. The slope of a curve is exactly such a rate (or a ratio). I admit that the notion of relative rate of change is one more of a ratio and might frighten unwary beginners.
• Integral calculus then, is concerned with summing up these local rates of change over some given domain, directly relating the sum to the measured "amount" under a curve, or, more general, pertaining in the given domain.
• I think, the introduction of the antiderivative has to stay that vague and sloppy as it ever has been in my weak efforts of recon of education in calculus.
• To me, calculus is an important item in a syllabus, and it refers to successfully hammering without knowing details about what a hammer is.

Knowing too much about small details may be adverse to your mental health - see G. Cantor. Purgy (talk) 09:27, 28 August 2016 (UTC)

I've long been concerned that the phrase "rate of change" is more of a slogan than a rigorous description of anything. I'm not sure how I would define it, even in a nonrigorous and philosophical way, without implicitly making reference to derivatives. So I would be wary of making this phrase too prominent.

Also, "summing of local rates of change" translates to $\int f'(x)\,dx$, not to $\int f(x)\,dx$. Ozob (talk) 13:48, 28 August 2016 (UTC)

See also Calculus I

After having worked on the article Calculus I, user Samantha9798 added an entry in the See also section: [5]. It was immediately removed by user Mean as custard, without an edit summary: [6]. I restored it because I think it is a valid entry per WP:SEEALSO: [7]. It was removed again without an edit summary: [8]. Samantha9798 added it again: [9].

As it would be silly to start an edit-war over this, can we, in the spirit of WP:BRD, please have a least a minimal discussion here? - DVdm (talk) 11:53, 21 November 2016 (UTC)

• It is fine in its new location under "Other related topics". I only objected to it being right at the beginning of the "See also" section with no indication as to what the article is about. . . Mean as custard (talk) 12:55, 21 November 2016 (UTC)

Ok, thx. - DVdm (talk) 15:30, 21 November 2016 (UTC)

Sorry, I removed if before seeing this thread. Self reverted pending outcome of AFD. Meters (talk) 18:51, 21 November 2016 (UTC)

No problem. Seems unlikely to survive, so... see you later . - DVdm (talk) 19:13, 21 November 2016 (UTC)

Comparison to geometry and algebra in the lead

Recently, an editor removed the phrase, " in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations," and it was replaced, evidently all in good faith. I think this should be removed. I think an article about calculus should define and explain calculus in absolute terms, without comparing it to similar concepts at the same level, except when necessary, especially in the lead. Also, since calculus, geometry, and algebra are very general, it is arguable whether the existing definitions are general enough. — Anita5192 (talk) 17:02, 18 December 2016 (UTC)

• Delete: I agree to the above intentions to delete the comparision of "study of change", "study of shape", and "study of operations ..." under their respective names "calculus", "geometry", and "algebra" in the lede of an article about calculus. As said, these maybe comparable on a very specific level and in very special hindsight, only. Imho, the article does not gain anything by referring to the names of other mathematical topics. -Purgy (talk) 17:31, 18 December 2016 (UTC)

In the light of the overwhelming votes for keep, I want to point out that a statement ('A = B' like 'C = D') .and. ('A = B' like 'E = F') would not transport much information in the math sense. In my opinion, the hope that these comparisons would induce some illustration for the notion of calculus is futile. I think that an equal value would be achieved by a statement like "calculus is the study of change in the same way as other subjects in math are the study of other topics". Putting a warning next to a statement that it is vague, by adding additional vagueness, is to me alien to math.

As an aside, "Differential Geometry" flashed through my consciousness.

In case my above argumentation is not considered convincing, I want to mention my reservation to explicitly calling the calculus-change a "continuous" one, and putting algebra in the "discrete" environment, while agreeing to the apposition being too long and too technical.

How about

Calculus encompasses the introductory settings for the mathematical study of change, mostly demonstrated along functions of one real variable. replaced!

Just to throw in some alternative. -Purgy (talk) 11:23, 19 December 2016 (UTC)

Vague is fine with me, and it shows it isn't some precise definition. Your longer form just above is long and rambly and would just confuse. The extra words make it look like something more is meant, verbosity is not a reliable defense against misinterpretation. Dmcq (talk) 14:37, 19 December 2016 (UTC)

I really tried to mean more, and I try it again, shorter, less verbose, and even including continuity:

Calculus is an introduction to the mathematical study of change, mostly along continuous functions.

This is 16 words shorter than the current version, it offers new information: (1) the introductory level of calculus within the fullblown math setting, (2) the support of the studied change, (3) refers to D. Lazard's continuity, and is not loaden with the vague comparisions, which I would call rambly, because -as shown above- they contribute nothing to make the position of calculus within math topics more graspable. I cannot imagine that this sentence of 14 words could be confusing.

BTW, omitting the empty comparisions also saves the lede from concealing curved shapes and from connecting discrete and discontinuous to algebra. -Purgy (talk) 17:22, 19 December 2016 (UTC)

It isn't an introduction. It is a full topic in itself. I can't see the point of the 'mostly along'. Personally I'm not altogether happy with 'change' though I can see its point in distinguishing from topology and others here like it. I don't think of them as changing at all, change is a physical phenomenon. I would have thought calculus differed from topology in having a measure assigned though how one phrases that easily is another question. Dmcq (talk) 01:17, 20 December 2016 (UTC)

Would it be considered inappropriate to ask for a refutation of my "emptiness"-claim, or even better, for the content of the empty comparisons?

Would you prefer something along "relative local differences", or perhaps some algebraic approach along the Leibniz rule for the derivatives, instead of the study of change?

Could you imagine to help with improving the "along"?

I certainly agree that integration without referring to a measure is outdated, but OTOH, integration in the realm of calculus is mostly based on an approach via Riemann sums, dumping the continuity aspect at some very early stage, and not involving the Lebesque picture.

For the time being I'm mostly focused on improving the status quo, containing an empty non-description, and not on the future "best lede in town". -Purgy (talk) 14:07, 20 December 2016 (UTC)

I understand you think that calculus is best defined by only saying what is included without saying what it is distinguished from. That is not what others here think. I think saying what something isn't is a good way of outlining the extent of a mathematical topic and placing it in context. Dmcq (talk) 14:31, 20 December 2016 (UTC)

Just correcting your understanding of my intentions: while I do require definitions to positively declare the definiendum, I never intended to define the notion of calculus. It is fine with me too, to rather sketch this in the lede, with, roughly, a central point and a contrasting environment.

However, I see no sensible contrast of the portrayed notion to the notions listed by the "in the same way"-topics. In my perception the current wording boils down to the already mentioned "calculus is the study of change in the same way as other subjects in math are the study of other topics". The suggested epitetha do not improve this lack of manifest meaning, and my hint to "Differential Geometry", setting up even some connection, instead of a contrast, between (multi-variate) calculus and geometry has not been dealt with.

I do not perceive much cooperativeness in argueing about my objections, nor for discussing my proposals, but an overwhelming consensus, based on personal valuation and opinion, to rather insert some, imho, disconnected continuity into the current version, than pondering any change, as initiated by an IP and supported by Anita5192 and me. So for now, no additional suggestions from my side. I just hope, my use of italics does not annoy again. -Purgy (talk) 09:53, 21 December 2016 (UTC)

I thought I had discussed what was proposed directly and to the point. I don't agree with you. That is not the same as being uncooperative. I think the lead of this article should be at about the level where a young teenager who will soon start calculus would be able to read it okay - we should use what is common knowledge at that point and say what is new about this topic and distinguishes it from what they already know. Dmcq (talk) 11:01, 21 December 2016 (UTC)

It must be really embarrassing, what a blockhead I am. Having seen all this already in "numbers", and now here again: none of my 3 explicit questions answered, not even addressed, any concrete effort rejected without reasoning, just rejected on "existential non-qualification", and on "not agreeing". It won't bother you, but it does not bother me either. I'm just into constantly trying to improve Wikipedia, and be it one word for one word.

Claiming a disqualifying property, without giving a reason, is not the kind of reply I consider to show "cooperativeness". BTW, I agree with what you wrote about the level the lede should be in. -Purgy (talk) 11:00, 22 December 2016 (UTC)

• Keep I believe that one of the functions of the lead is to provide the context in which the article is to be viewed. In this case that context is, how does Calculus fit within the scope of mathematics? This can not really be addressed if you confine yourself to the intrinsic features of the subject. Also, I am uncomfortable with the bare phrase, "Calculus is the study of change", as this is too simplistic and stands a good chance of being taken too literally by the probable readers of this article. By placing the phrase in the context of similar phrases, the reader is being warned that the statement is very general and too vague to be taken as a definition. --Bill Cherowitzo (talk) 17:46, 18 December 2016 (UTC)

• Keep for necessary context in the lead, which can be as general as it is now. By the way, one of the best leads in town, i.m.o. - DVdm (talk) 19:35, 18 December 2016 (UTC)
• Keep + comment. IMO, every article, such this one, about an area of mathematics must give indications on what belongs to the area and what does not belongs to it. This cannot be done formally, as it cannot be any consensus on the exact limits of any scientific area. Instead, some indication must be given where calculus ends and where begin the other comparable areas. This is the reason of keeping the disputed sentence. (The end of this post and the resulting discussion are about another question, and have thus been moved in the next section.) D.Lazard (talk) 21:52, 18 December 2016 (UTC)
• Keep Putting it in context of simpler and better-known mathematical areas is a reasonable and useful part of the lede . Meters (talk) 22:05, 18 December 2016 (UTC)

Short description of mathematics areas in the lead

Start of the moved discussion:

However, I find the present formulation too vague for being useful for anybody. IMO, "study of change" should be replaced by "study of continuous change" (here "continuous" may be interpreted in its non-mathematical meaning, but if a reader interprets it in its mathematical meaning there is no problem). "Study of shape" is good. On the other hand, "study of operations ..." is too long and too technical. For algebra, I would prefer "study of discrete properties" or "study of discontinuous change and discrete properties". D.Lazard (talk) 21:52, 18 December 2016 (UTC)

I think of topology as the study of continuity and that discontinuity is fine in calculus though of course if something is continuous it makes life easier. And for a beginner they'd probably assume continuous anyway. And Lie groups are continuous and come under both algebra and topology but not really calculus. Dmcq (talk) 14:23, 19 December 2016 (UTC)

I have not written "calculus is the study of continuity" but "calculus is the study of continuous change". Topology is the study of continuity but not the study of change (at least at elementary level, before the study of homotopy). On the other hand, calculus is essentially the study of derivation and integration; derivation is the measure of the instantaneous rate of change of a continuously changing quantity, and (at calculus level) integration is the summation of a quantity that varies (almost always) continuously. The change of the content of a bag, in which apples are added or removed one after the other, does not belong to calculus. Therefore talking of "change" and not of "continuous change" for characterizing calculus is confusing for non-mathematicians. D.Lazard (talk) 15:04, 19 December 2016 (UTC)

That makes sense okay, yep the continuous is good. Thanks. Dmcq (talk) 01:09, 20 December 2016 (UTC)

End of the moved discussion.

It seems that there is a consensus (between only two editors) to change "study of change" into "study of continuous change" for qualifying calculus, and to keep "study of shape" for geometry. However, I am not fine with the present description of algebra nor with the alternatives that I have proposed in a previous post: many readers would not recognize algebra in such a description. Now, I suggest: Algebra is the study of generalizations of arithmetical operations. This is short, not technical (everybody should know of arithmetical operations), explains clearly that algebra is related to, but distinct from arithmetic and number theory, and, IMO, covers most aspects of algebra. Your opinion? D.Lazard (talk) 12:07, 21 December 2016 (UTC)

I was also unhappy with the short algebra description as the study of operations and think that your suggestion is a vast improvement. However, I am uncertain about the "calculus is the study of continuous change" statement. I have seen "calculus is the study of change" far too often in non-technical writing and introductory calculus texts. I fear that we are trying to change a popular misconception without adequate support in the literature. I don't have this issue with algebra since that topic does not have the same kind of track record (as a subject whose name, at least, is well known to the general public) as calculus does. --Bill Cherowitzo (talk) 19:54, 21 December 2016 (UTC)

May I, please, ask, what your specific reservations (beyond those referring to integration) to "study of change" wrt calculus are, and wherein you see the "popular misconception"? I think that "study of change" wrt differentiation is very appropriate and "better" than a more precise "local relative difference". As far as integration is concerned, I think that "summing up that change (in an interval)" equally well describes the integration, which is generally introduced either as antiderivative (perfectly corresponding to studying the "reversion of change"), or via Riemann sums, obviously summing "changes", weighted by a "duration", just rendering the continuity as contradictive. -Purgy (talk) 10:53, 22 December 2016 (UTC)

While I am fully convinced that beginners are thinking in a smooth environment, taking the "change" itself as contionuous, I do not see any gain adding a technical term, even when speculating on it being non-technically perceived. I do adhere to the thought that discrete changes are used in already in elementary natural sciences: Dirac-delta and Heavyside-step are used when their mathematical foundations are still very far away.

As for the algebra topic, I disagree on the to-day algebraic view on arithmetic being a "generalization". The notion of "inverses" is imho fully alien to elementary pedagogic, and the 4 basic arithmetic opereations with subtraction/division are not really an algebraic concept. May I throw into the debate "abstract mathematical structures" (for algebra), and "trigonometry about angles" (for an alternative topic, known to the intended clientel)?

I do not expect any of my suggestions to be realized, but I'm into trying to help to improve Wikipedia. -Purgy (talk) 10:53, 22 December 2016 (UTC)

I agree that the four arithmetic operations do not belong by themselves to arithmetic. This is why I proposed "generalizations of arithmetical operations". In fact, algebra began when one (in fact Viète) wrote x + y, that is when addition (and the other operations) were applied to symbols which were not numbers. Still now, algebra is mainly devoted to the study of algebraic structures, which, generally, are sets on which are defined some kinds of generalizations of the arithmetical operations. This is clear, as the symbols used for denoting operations in algebraic structures are almost always (except maybe in some "pedagogic" introductions) those of arithmetic operations. When I have suggested my formulation, I had algebraic structures in mind, but this term is too technical to be used here (moreover, it would induce some circular definition).

May I recall you that Wp is not a textbook with a specified audience, an that the intended "clientel" is not restricted to kids at school. D.Lazard (talk) 11:39, 22 December 2016 (UTC)

Doesn't the limit of a sequence properly belong to the study of the calculus? A sequence is neither uncountable nor continuous. — Anita5192 (talk) 17:59, 22 December 2016 (UTC)

You are right, but it is impossible to summarize a whole area in a single phrase. Moreover, one has to remember that "calculus" is, originally, an abbreviation of infinitesimal calculus, and that this means "computing with infinitesimal changes". I believe that "continuous change" is better understood by the layman than "infinitesimal change". Limits of sequences belong presently to calculus, but they have been introduced (for formalizing calculus) three centuries after the "invention" of calculus (see second paragraph of Calculus#Foundations). For these reasons, I think that there is no harm in omitting limits of sequences in a single-phrase definition of calculus. D.Lazard (talk) 18:46, 22 December 2016 (UTC)

@D.Lazard, you certainly do not need to remind me of Wikipedia not being a textbook, and I do not recall having written about "kids in school". I do recall however very well, how I was reminded of the "intended clientel" for some article. Furthermore, I do not see my original claim refuted, that the current view of algebra on arithmetic, disregarding all historical roots (Al Quarizmi(?)), were not a generalisation, but a total revamp of the view as presented in pre-calculus education. -Purgy (talk) 18:32, 22 December 2016 (UTC)

I wrote above about trying to make the lead accessible to young people about to start learning calculus. That is quite different from wanting the article to be like a textbook though. Wikipedia is an encyclopaedia not a coursebook. However we should aim to make the first half worthwhile to all reasonably likely readers. I'm not quite certain what you are saying about algebra. I think you are saying we should present a view of algebra as encountered by young children rather than saying something that is a fair approximation of what the subject is actually about. If the description given would not be accessible to young children about to start calculus I would agree it would present a real problem. However the description given is in simple terms and should be easily comprehensible, if they have a problem with it they can just skip over it or go to the article. Giving a description which is not a reasonably fair approximation would bowdlerize the article. It is a hard job balancing the needs of readers and the requirement to be an encyclopaedia. Doing that well is a mark of a good editor. Dmcq (talk) 22:46, 22 December 2016 (UTC)

* As can be seen from the indentation, my comment above is a reply to D.Lazard's reply, and does not immediately refer to your comments.

* As said, I do not need any reminder of Wikipedia being no coursebook, but an encyclopedia.

* I did not say anything about presenting a view of algebra for young children, but argued against the effect of D.Lazard's suggestion of "generalization" on the targeted clientel. Perhaps you must read my whole sermon.

* To my opinion the needs of the readers are not balanced well to the requirements of an encyclopedia in the proposed texts, starting with insisting on empty contrasts, and in sequence with "continuous" and "generalization".

Rest assured, I'm just trying to contribute to improve things I consider really suboptimal, I won't edit a word against the "good editors". -Purgy (talk) 19:32, 23 December 2016 (UTC)

It is better in general to address the topic rather than specific editors. I have some difficulty in understanding what you are saying or what your points are, that is why for instance I said " I'm not quite certain what you are saying about algebra. I think you are saying". If i just said "I don't understand" you would have no idea what impression I had got from what was said. I was hoping if I was wrong then knowing that would help you address the problem in getting your points across. For instance you said "I do not see my original claim refuted, that the current view of algebra on arithmetic, disregarding all historical roots (Al Quarizmi(?)), were not a generalisation, but a total revamp of the view as presented in pre-calculus education." As far as I can make out you think I did not address that point in what I wrote, is that correct? I think it needs also to be pointed out that a talk page is for discussing improvements to an article, it is not for asserting refuting or anything else particular peoples ideas. Dmcq (talk) 22:38, 23 December 2016 (UTC)

Until further notice or legal advice I won't stop

• to suggest proposals or post criticism I consider to be advantageous for Wikipedia
• to adress changes and proposals by their authors, if this appears advantagous to me
• to repudiate any unnecessary advice or instruction about any behaviour de rigeur or any purpose and target of Wikipedia
• to hope that people at the assumed level of education can overcome petrification, mislead solidarity, and any not-invented-here syndrome, allowing for improvements not written by themselves
• to consider refuting/asserting one side of opposing opinions to be the superior methods to decide about their prevalence, especially when compared to the methods of persevering on the status quo, of promoting a personal POV, or simply of executing a silly form of backslapping (my enemy's fiend is my friend) and therefore
• to consider talk pages as the prominent and appropriate place to put those refutations/assertions in the light of transparency.

For the time being I explicitly re-state my opinion on the 30(!) words under discussion and their improvement:

• The employed comparisions to geometry, ... are vacuous, and the suggested amendments of "continuity" (conveniant preliminary, generally present in the imagination of the uninitiated, but not intrinsically important to calculus) and "generalization" (rather a conceptualisation, e.g. reducing the arity is no generalisation, ...) are no improvement, but rather deteriorating, and that my second proposal above, even when being shorter (14 words!), encompasses new, relevant, and even characterizing information (introductory level, application to functions), and could be itself easily improved -with some good will of native speakers- to be better than the status quo.

Since continued refutation of incoherent and unnecessary advice on off topic agendae leads still more off topic, I herewith, at my discretion, stop commenting in this section. -Purgy (talk) 10:07, 26 December 2016 (UTC)

Claim of "undisputed"

In the line of the complete debate and especially of the last item in my last comment in the section above I feel urged to state that I definitely tried to utter a clear objection to D.Lazards suggestions, and that in no way I consider them to be "not clearly disputed", especially when not ignoring the whole debate above. I protest against the claim in the edit comments by D.Lazard per 25 January 2017.

I do not mind any further to be disregarded in this here setting. Purgy (talk) 09:56, 26 January 2017 (UTC)

Development of calculus

We discuss the contributions to calculus of the Indian mathematician Madhava of Sangamagrama and the Kerala school of astronomy and mathematics in this article in the Medieval section. A user is adding a claim that these two should be credited with the development of modern calculus [10] and a slightly modified [11]. This seems to be overstated, and three different editors have removed the material. The material in this article at Calculus#Medieval, and in the specific articles Madhava of Sangamagrama and Kerala school of astronomy and mathematics shows work on infinite series, but the attribution is uncertain as is the possible transmission of the techniques to Europe. Claiming that this work as the development of modern calculus does not seem justified. Meters (talk) 20:33, 3 March 2017 (UTC)

I agree with this assessment. Perhaps a reliable source is needed that shows that the development of these specific ideas happened in parallel or even before Newton and Leibniz's time. I note that the citation given, Mathematics in India by Kim Plofker, on the cited page (221), says

The crest-jewel of the Kerala school is generally considered to be the infinite series for trigonometric quantities discovered by its founder, Madhava. These are preserved in about a dozen verses explicitly attributed to Madhava in various works by later members of the school, and translated in the following sections. Many of the accompanying rationales and explanations of these results are probably also originally due to Madhava, even if not directly credited to him.

The fact that only many and not all, and that these results probably are due to Madhava is what makes the inclusion a bit iffy indeed, in my opinion. Penskins (talk) 20:48, 3 March 2017 (UTC)

So it seems like there are a few separate issues here that need to be treated separately:

1. To what extent did the results of the Kerala school influence modern calculus?
2. To what extent are the results of the Kerala school attributable to Madhava as an individual?
3. How much content that we would retrospectively recognize as "calculus" is there in the results of the Kerala school?

I think Penskins's remarks seem mainly addressed to question 2, which is an interesting question in itself, but not the one that people are likely to get excited about. Most of our readers have never heard of Madhava or the Kerala school, and just the fact that some of the Newton/Leibniz content was anticipated (question 3) is already surprising and worthy of note, even taking Madhava as a pars pro toto for the Kerala school (like Pythagoras for the Pythagoreans).

But the question that's likely to be really controversial is question 1. Remember the Columbus principle: It's not who discovers it first; it's who discovers it last. If the Kerala results anticipated some of modern calculus but then were limited to some dusty old books that no one knew how to find, then they're really just an interesting historical footnote. If Newton/Leibniz somehow knew of them, that's very different. So far I have not heard of any clear evidence that the Kerala results influenced modern calculus, and the claim that they did would need to be very well-referenced. --Trovatore (talk) 21:57, 3 March 2017 (UTC)

No Dutch translated version

There is no Dutch translated wiki to Calculus. Can someone please look into this? Because the subjects under calculus are available in Dutch, but not the main topic itself. Weird enough.

Would love to read it in my language. — Preceding unsigned comment added by 2001:1C01:2104:3000:9806:9E5B:420A:EEAD (talk) 16:21, 24 March 2017 (UTC)

Mathematics of the other beings

QUOTE: In the 14th century, Indian mathematicians gave a non-rigorous method of a sort of differentiation of some trigonometric functions. Madhava of Sangamagrama and the Kerala school of astronomy and mathematics thereby stated components of calculus.END OF QUOTE.

It is only right to assume that when the animal world acquires the skill to use English, computers etc., they will also come up with similar astounding claims. — Preceding unsigned comment added by 137.97.8.238 (talk) 22:01, 2 May 2017 (UTC)

Did I address your concern in my edit? Maybe, you should be more explicit of your concerns, and try to implement this on your own. Purgy (talk) 05:59, 3 May 2017 (UTC)

I put Indian back in. There's no problem about describing people from the south of India in medieval times as Indian. Dmcq (talk) 17:47, 3 May 2017 (UTC)

Maybe, I'm definitely not sure, it's you (please, note the italics), who does not see the problem, which others try to articulate. Purgy (talk) 19:19, 3 May 2017 (UTC)

Perhaps you can articulate what you see as what they were saying and therefore you did something about? In short say why South Asian Subcontinent is better than Indian in that context. Dmcq (talk) 14:31, 4 May 2017 (UTC)

I followed the (wrong again) assumption that the intentions of the OP were well known, or even stereotyped. I'll revise my presupposition that it is sufficiently established that there are people from this region, who prefer not all of their possible ancestors being subsumed under "ancient indians", for whatever reason, and in a similar vein like others feel justified to enforce the singular they on all linguistic corpora.

I hope this is articulate enough. In no way I oppose to having been reverted, I just tried to make WP a safer space. ;] Purgy (talk) 06:35, 5 May 2017 (UTC)

Most of that subcontinent has been referred to as India from long before then. People looking up this article on the English Wikipedia cannot be assumed to be familiar with the constituent parts of India, it is not a Hindi or Indian encyclopaedia. The article does immediately afterwards refer to Kerala so they would know from that vaguely where Kerala is. Those are the reasons I think saying Indian is best. It is all very well trying to cater for people but Wikipedia's main purpose is not to be a social forum but to be an encyclopaedia. They haven't answered your query about what their concern actually is. What did you think the intentions of the OP were or what type of stereotype did you think I had? There just is not enough there to get any handle on anything that I can see. Dmcq (talk) 10:10, 5 May 2017 (UTC)

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Thank you, wikipedia, for this opening line

Thank you, wikipedia, for this opening line:

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, like on an abacus) is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

— wp editors, Calculus, Isaac Newton

It clarifies so much for me. Actually, it says: "This is what math is". - DePiep (talk) 21:07, 1 February 2018 (UTC)

Well, this is the best "consensus" in WP could generate. You may want to look at the intense discussion about the lead here, here and here, too (scroll up ~20 lines, in case), to see the intense effort, just recently spent, to improve the lead, and you can also learn where to place your thanks more precisely. Purgy (talk) 08:22, 2 February 2018 (UTC)

Allow me to skip those readings. I'm so happy with the result as it is now. I didn't read "compromise", I read clarity. (I'm trying to understand QM these days. For example, this is the one, pre-wikipedia). -DePiep (talk) 00:18, 3 February 2018 (UTC)

The history section

Shouldn't the history section have at least some content? I mean, more than the link? --31.45.79.44 (talk) 22:46, 27 February 2012 (UTC)

In the main text we read: "Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term. (André Weil: Number theory. An approach through history. From Hammurapi to Legendre. Birkhauser Boston, Inc., Boston, MA, 1984, ISBN 0-8176-4565-9, p. 28.) " I think that this is misleading. Fermat borrowed from Bachet de Meziriac's Latin translation of Diophantus’ Arithmetika the noun adaequalitas and the verb adaequare where they have a meaning in a completely different context, namely solving a special class of arithmetical problems by the method of false position. Fermat, however, uses those words (and the word adaequabitur) in his method of determining maxima and minima of algebraic terms and of computing tangents of conic sections and other algebraic curves. Fermat’s method is purely algebraic. There is no "infinitesimal error term". Fermat uses two different Latin words for "equals": aequabitur and adaequabitur. He uses aequabitur when the equation describes the identity of two constants or is used to determine a solution or represents a universally valid formula. Example:

$x^{3}+y^{3}=(x+y)(x^{2}-xy+y^{2})$.

And he uses the word adaequabitur ($\doteq$) when the equation describes a relation which is no valid formula. Example (Descartes' folium):

$x^{3}+y^{3}\doteq 3xy$.

Typical examples are:

$(x+e)(b-x-e)=bx-x^{2}-2ex+be-e^{2}$

and

$be\doteq 2ex+e^{2}$.

Equations which describe relations between two variables (x and y, x and e) were unknown to Vieta. So the 21-year-old Fermat felt compelled to introduce a new concept of equality and called it adaequalitas. Later, when he created his analytic geometry he abandoned this special terminology of his younger days. See my paper Barner, Klaus: Fermats <<adaequare>> - und kein Ende? Math. Semesterber. (2011) 58, 13-45, unfortunately written in German. 91.4.83.79 (talk) 17:28, 7 February 2013 (UTC) Klaus Barner (talk) 14:40, 5 February 2013 (UTC)

Very interesting. Is there perhaps a translation of your article online somewhere? Tkuvho (talk) 16:13, 6 February 2013 (UTC)

Unfortunately there is none. The reason is: my German is sophisticated and requires reading between the lines whereas my English ist rather weak. It is no artical about mathematics but about history of mathematics which requires a better command of English than I have. However I feel that I should produce a raw translation and ask a native speaker to improve it. Klaus Barner (talk) 19:09, 10 February 2013 (UTC)

https://www.google.com/imgres?imgurl=http://academic.pgcc.edu/~sjohnson/ancientcurvetext.jpg&imgrefurl=http://academic.pgcc.edu/~sjohnson/casestudy2.html&h=1012&w=1331&sz=324&tbnid=Wx15eqipFgydwM:&tbnh=90&tbnw=118&zoom=1&usg=__rwdu-Js_exE4O78S94CeAopgX1Q=&docid=H8UYTm3StwLcWM&sa=X&ei=yS5CUp0HrrbgA6TwgYAG&ved=0CDwQ9QEwAw

A text found at Saquara has a picture of a curve and under the curve the dimensions given in fingers to the right of the circle as reconstructed to the right. It was presumed the horizontal spacing was based on a royal cubit but the results if based on an ordinary cubit are different. It appears the value for PI being used is 3 '8 '64 '1024. which at 3.141601563 is slightly better than the Rhind value. The circumference of the circle is 1200 fingers and the diameter of the circle is 191 x 2 = 382 3 '8 '64 '1024 x 382 ~= 1200.0 The side of the square is 12 royal cubits and its area is 434 square feet. The area of the circle is 191^2 x 3.141601563. The algorithm suggests working with coordinates and numerical analysis to define a curve.

• 1
• 1 1
• 1 2 1
• 1 3 3 1
• 1 4 6 4 1
• 1 5 10 10 5 1
• 3
• 3 + 1/2y^3 is 3 '8, = 3.125
• 3 + 1/2y^3 + 1/2y^6 is 3 '8 '64,= 3.140625
• 3 + 1/2y^3 + 1/2y^6 + 1/2y^10 is 3 '8 '64 '1024 = 3.141601563

For purposes of comparison(3 '7 = 3.142857143)

From a published reference "Ancient Egyptian Construction and Architecture" Here it is as a Google Book. "Ancient Egyptian Construction and Architecture" See The referenced graphic Architects Curve What you see there was already referenced on the page as an artifact from Saqarra, but without the graphic. Its Fig. 53 p. 52. Figure 54 p. 53 is a scale drawing of it. The Graphic is in Wikipedia commons used in two other articles which have the text I copied to the talk page. "The algorithm suggests working with coordinates and numerical analysis to define a curve". Its similar to adequabiture and an exampl≤e of how Pascals triangle may be used to generate PI with a series formed by the third diagonal; 1,3,6,10.≤″24.93.139.28 (talk) 21:43, 2 June 2018 (UTC) https://upload.wikimedia.org/wikipedia/en/f/f3/Egyptian_circle.png 24.93.139.28 (talk) 21:53, 2 June 2018 (UTC)

Just for the records:

adequabitur is the verb form 3rd sg fut ind pass of the verb adequare. The construction of a noun the adequabiture is a mystification.

Purgy (talk) 07:01, 3 June 2018 (UTC)

In the intro to this section "Fermat uses two different Latin words for equals". I'm expecting he means not "equals" necessarily, but adequately equal or something to that effect. I couldn't find an etymology that goes back before "adequate" from early 17th century Latin where the noun means "equal" and the "verb made equal to". 24.93.139.28 (talk) 08:16, 6 June 2018 (UTC)

Separate Section

The lead sentence does not include the alternate term infinitesimal calculus, which would help clarify. I'd change it myself, but Wikipedia... — Preceding unsigned comment added by 96.40.48.159 (talk) 23:43, 8 June 2019 (UTC)

Also this article is the target of the redirect infinitesimal calculus. I have thus exchanged the places of this term and the etymology. By the way, I have done some other modifications. D.Lazard (talk) 08:19, 9 June 2019 (UTC)

Unaware of Lazard’s edit, I also made changes! Dolphin (t) 08:21, 9 June 2019 (UTC)

I have removed the second mention of "infinitesimal calculus", as, placed there, it is unclear whether it denotes integral calculus, differential calculus, or both. By the way, it is astonishing that there was no edit conflict: I have edited all paragraphs of the lead but one, and Dolphin51 has edited the only paragraph that I have left unchanged! D.Lazard (talk) 08:45, 9 June 2019 (UTC)

D.Lazard’s changes are sound. I have no intention to meddle any further. I agree it is puzzling that I saw no alert to an Edit conflict. It seems that Edit conflicts occur when I would prefer they didn’t, and an Edit conflict doesn’t occur when it would actually be beneficial! Dolphin (t) 09:33, 9 June 2019 (UTC)

Semi-protected edit request on 12 January 2020

"developed independently in the late 17th"? How can it be? Both Leibniz and Newton died in 18th century. Datdinhquoc (talk) 23:24, 12 January 2020 (UTC)

 Not done Newton died in 1726, which is during the 18th century. His work on the calculus was done in the late 1600's, which is the 17th century. This offset of the century number is due to the fact that there is no "zero" century. --Bill Cherowitzo (talk) 23:35, 12 January 2020 (UTC)

Oh yes, 16xx is 17th century. — Preceding unsigned comment added by Datdinhquoc (talk • contribs) 22:29, 13 January 2020 (UTC)

Contested April 2020 additions

@Prototypehumanoid: WP:BRD is a very good idea to follow. The short version: there already is some material in the history section about precursors to the Calculus in South Asia. Overloading the lead with that, though, would probably lend WP:UNDUE weight to the overall importance of that with respect to the rest of the article. We also don't discuss the precursors in ancient Greece in the lead. Moreover, changing to a statement like "Modern calculus was developed in AD 1530 by Jyesthadeva of the Kerala school of mathematics ..." is simply not reflective of the mainstream view and violates WP:FRINGE. –Deacon Vorbis (carbon • videos) 14:18, 25 April 2020 (UTC)

Sorry, but you seem to be missing the point. Your edit incorrectly ascribes development of modern calculus to 17th century, which contemporary scholarship disproves. You keep stating that this is not mainstream view while providing no evidence. I have backed up my edits with reputable references including Royal Asiatic Society of Great Britain & University of St Andrews, Scotland. I wouldn't refer to them as 'fringe' views. This is the mainstream contemporary consensus. If you are reading material from the 1950s, I suggest kindly refer to the latest scholarship. Please note, I have not taken anything away from the article, simply adding the latest material. You seem to be doing the opposite. European contributions are amply provided in the page including precursors. But the chronology needs to be correct. In the absence of you providing evidence to disprove my references, I will be reincorporating the latest scholarship onto this article. May I suggest, please explain how you are arriving at the conclusion where you are dismissing the latest global scholarship on the subject. Please provide reference for such. Prototypehumanoid (talk) 14:50, 25 April 2020 (UTC)

Please, take your nationalist POV nonsense elsewhere. --JBL (talk) 15:05, 25 April 2020 (UTC)

(edit conflict) The mainstream view is that while there were pieces of the Calculus worked out, a full-fledged picture with the general tookit of it that resembles its modern form wasn't put together until Newton & Leibniz. One single paper (the Raju one, which has some problems, which we can discuss if needed) does not allow you to make this kind of claim in the article. Your other sources are either junk (some slides, some weird poster with a nationalist POV, etc), or are just backing up secondary stuff, like the basics of the work itself. –Deacon Vorbis (carbon • videos) 15:16, 25 April 2020 (UTC)

I think I agree with @Prototypehumanoid. Further references could be added. Including Divakarans papers. Also the original paper 'Yuktibasha'. Madhava is increasingly seen as the true inventor. Marcus du sautoy for instance has done previous studies that showcase - lack of due credit to eastern mathematicians (during 17th to 21st century Europe). Imagetoimageless (talk) 12:16, 23 August 2020 (UTC)

Evidence based change should be made welcome. There has been an increasing consensus for many elements- See Madhava series, formula for pi etc... Imagetoimageless (talk) 13:50, 23 August 2020 (UTC)

However for a point by point consensus in mathematics for the invention of calculus, please see Divakarans work. Imagetoimageless (talk) 13:53, 23 August 2020 (UTC)

Prototypehumanoid made obviously terrible edits for dumb nationalist reasons. Their edits were correctly reverted, and nothing that closely resembles them is going to come back into the article. --JBL (talk) 16:18, 23 August 2020 (UTC)

Request that this article be semi-protected to prevent vandalism. — Preceding unsigned comment added by TheMaxinumMaker (talk • contribs) 00:52, 13 November 2020 (UTC)

"continuous" versus "contiguous" in the lead

Considering the hidden comment explicitly states that the terms in the lead are not being used in mathematical senses, it would be incorrect to use "continuous" over "contiguous" to describe change. Sikonmina (talk) 16:56, 23 October 2021 (UTC)

Even for the common meanings, "continuous" and "contiguous" are not synonyms. D.Lazard (talk) 19:34, 23 October 2021 (UTC)

Agreed. "Contiguous" is simply incorrect. And the note appears to be saying that the normal links for "change" and "continuous" will not have the correct mathematical meaning, not that the terms as used in the lead do not have the mathematical meaning. We correctly link to Continuous function elsewhere in the article. Meters (talk) 00:24, 24 October 2021 (UTC)

Rigorizing the lead section

User:D.Lazard Apparently my last edit wasn't consensual, so I will explain my motivations:

• I'm against the use of "rates of changes" or even worse "instantaneous rates of change" as synonyms for "derivatives". Not only are these expressions more of a talking term for non-mathematicians than a real mathematical vocabulary (and there is no reason to invent new words for "derivative", an established expression already exists, namely "derivative"), but there is also a risk of ambiguity because "rate of change" can also refer to the rate of increase of a function between two values (ie ${\frac {f(a)-f(b)}{a-b}}$) (as shown on the distinction page), which is not a derivative.
• I'm also against the use of "accumulation of quantities" as synonyms for "integrals" for the same reasons : this is misleading non-mathematical gibberish. As the page Integral correctly reminds us, an integral is not defined as an "area between curve", but more abstractly as a number assigned to a function and expressing an idea of mass or volume. --L'âne onyme (talk) 16:55, 27 October 2021 (UTC)

I think it's important to recognize that this article is about calculus, not mathematical analysis. Calculus is not a branch of research mathematics; hasn't been for well over a century. It's a mathematical toolkit for science and engineering.

With that in mind, I think it's important to reference the intuitive meaning of the terms early and often, rather than shoving the formalism down the readers' throats. The formalism should certainly be available for the interested reader, but the motivations are of utmost importance. --Trovatore (talk) 17:51, 27 October 2021 (UTC)

I don't understand why anyone would have a problem with the phrase "rate of change." A derivative is an instantaneous rate of change in that it is the infinitesimal limit of how one variable changes with respect to another. This is how "derivative" is defined in every calculus textbook I have ever seen.—Anita5192 (talk) 18:55, 27 October 2021 (UTC)

User:Anita5192 I explained why I have a problem with this phrase: firstly because there is no need for another synonym since the word "derivative" already exists (which pertains to the principle of least astonishment), and secondly because it is an ambiguous phrase that can also mean other things than derivatives. L'âne onyme (talk) 19:38, 27 October 2021 (UTC)

Your personal moral qualms about a phrase that is used in essentially every textbook on the subject are interesting but certainly cannot be used to determine article content. Wikipedia is guided by reliable sources, not by the most idiosyncratic views of its editors. (Though I must say that I think the substance of your edit is surprisingly good given the total absurdity of your defense for it -- I would not personally have reverted it.) (I don't watch this page, if you want my attention here please ping me.) --JBL (talk) 20:21, 27 October 2021 (UTC)

Semi-protected edit request on 6 December 2021

The last sentence under History > Ancient, and second sentence under Principles > Fundamental Theorem use the word "Formulas" as opposed to the preferred "Formulae" in academic writing, used in History > Medieval. I suggest only one to be used throughout the article (preferably "Formulae") to avoid confusion.

Change from "Calculations of volume and area, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (13th dynasty, c. 1820 BC); but the formulas are simple instructions, with no indication as to method, and some of them lack major components." to "Calculations of volume and area, one goal of integral calculus, can be found in the Egyptian Moscow papyrus (13th dynasty, c. 1820 BC); but the formulae are simple instructions, with no indication as to method, and some of them lack major components."

Change from "The fundamental theorem provides an algebraic method of computing many definite integrals—without performing limit processes—by finding formulas for antiderivatives." to "The fundamental theorem provides an algebraic method of computing many definite integrals—without performing limit processes—by finding formulae for antiderivatives." Atrochez42 (talk) 22:30, 6 December 2021 (UTC)

 Done. See [12], per

Google	Scholar
formulas	3.640.000
formulae	2.170.000
"mathematical formulas"	65.800
"mathematical formulae"	101.000

and since this is a mathematics article. But as far as I'm concerned, we could do it just as well the other way around . - DVdm (talk) 00:34, 7 December 2021 (UTC)