Talk:Applied mathematics

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[edit] Why do mathematicians insist on the difference between applied mathematics and applicable mathematics?

Does anyone know why traditionally applied mathematics is divided into the three branches but not others? I think the answer is very important for mathematicians to insist on keeping the defference between applied mathematics and applicable mathematics. I just do not understand why mathematicians refuse to expand the scope of applied mathematics. The reason should be included in the article as it helps readers to understand the nature of applied mathematics.

Why do you think "mathematicians refuse to expand the scope of applied mathematics". I don't know any applied mathematicians like that. Billlion
It is because mathematicians try to keep the traditional definition of applied mathematics, and use the term "applicable mathematics" to name other branches of mathematics that have practical purposes. In other area of science, any study that has practical purposes would be named as "applied science" (e.g. applied physics). In mathematics, however, though applicable mathematics have some practical aims to achieve, unlike the common practice in science, it is named "applicable mathematics" instead of "applied mathematics". Why not name all of them "applied mathematics"? Salt 07:25, 3 November 2006 (UTC)
If we agree that mathematicians do use the term in the traditional sense, is there any need for further discussion? Wikipedia is for reporting things as they are, not trying to change them. That is to say, your point is well-taken, but I don't think this is the right audience to address it to. I'm reminded of the quote "When people in the humanities say something is classical they mean it has significant and enduring value. When physicists use the term, they mean that it's wrong." Applied science and applied math. use the term applied in slightly different ways. JJL 14:43, 3 November 2006 (UTC)
Yes, we agree that mathematicians do use the term in the traditional sense, and wikipedia is for reporting things as they are, not trying to change them. However, even if we are reporting things, we are not just reporting the superficial facts, but the reasons or origins for the facts as well. When we write about World War II in histroy, we don't just report the warfare, but also the origins of WWII; while we talk about "waves" in physics, we don't just mention they would interfere with each other, but also the reasons for this phenomenon to occur. In this article, I am NOT trying to "change" anything. I simply think that the reason for mathematicians' decision to use different terminology is as important as the simple fact inself. It is why I ask for the reasons behind in this talk page; the reasons behind should also be reported in this article. Salt 21:53, 3 November 2006 (UTC)
I don't agree that mathematicians, or people outside of mathematics, always, or even usually, use the term "Applied mathematics" in the traditional sense. It depends where you are. At many universities, you'll see the traditional use of the word. But then look at a program like Cornell University's and you'll find them using the term "applied math" in an unusually broad way--and also you'll find that different professors in the program will disagree (sometimes strongly) about the definition of applied math. This article should not try to gloss over the dissent but rather describe it. Other universities, like Duke University or the University of Maryland seem to have notions of applied math that are somewhat broader than the traditional. These schools are hardly insignificant--and it's also important that at any of these schools there is a great deal of variation as to how people define and use the term. Cazort 22:52, 1 February 2007 (UTC)
Well, I think that's why the section starts out with "There is no consensus view of what the various branches of applied mathematics are" and moves on from there! It gives the historical answer and then discusses the broader view some take. JJL 14:06, 2 February 2007 (UTC)
It's an historical division. Applied math. is applied analysis. Areas like Operations Research that have great applications came later and from different areas of math. and/or science. JJL 17:54, 27 October 2006 (UTC)
Applied math is NOT strictly applied analysis. Applied analysis is one of many branches of applied mathematics. People use the term "applied mathematics" to refer to "applied analysis" but this is an inaccurate and misleading use of terminology. While some people do use the term in this way, I think that this usage is inaccurate and should not be supported. If anything, we should say on the page that it is common for people to use the term in such a manner, but we should present a more accurate, balanced use of the term as its "true meaning". Cazort 03:11, 19 January 2007 (UTC)

[edit] Numerical Relativity

What the heck is that? I think I know what the author meant, that the computational relativistic mechanics might be applied, as oppose to relativity theory. I dont think it fits with the other headings. Can someone suggest an alternative, otherwise perhaps we should delete. Other than that the article is quite good, although I would argue that it is a stub. Billlion 13:18, 1 Sep 2004 (UTC)

Hmm. I wonder why these subdivisions of theoretical physics are even included. They really aren't directly related to the topic of applied mathematics (maybe in an applied physics article, or even engineering mathematics, but...). I don't think this article should become a list of "important subdivisions" of all the fields listed in the first paragraph, so I suggest we remove everything after "indistinguishable from theoretical physics.". - dcljr 20:28, 1 Sep 2004 (UTC)

There is a certain camp of applied mathematicians, perhaps mainly in certain universities in the UK, who think that Applied Mathematics consists only of mechanics and fluid dynamics, even some who think that asymptotic methods in fluid dynamics is the entirety of applied mathematics. Not sure how to treat that diplomatically. 21:12, 1 Sep 2004 (UTC)

[edit] Computer science

I would say computer science has more in common with pure mathematics than with applied mathematics, just going by the definitions given here. Axiom systems from which you can deduce results are the foundation of much of computer science. Often it is difficult to get a good intuition. As a result computer science has to find real world examples to map the problem to, for example the Dining Philosophers problem. This characterizes pure math more than applied math to me.

66.90.154.200 19:33, 5 October 2005 (UTC)s_nedunuri@yahoo.com

[edit] Bioinformatics

I would think that bioinformatics should belong into Statistics, rather than Applied Mathematics. I agree that Statistics should be considered apart from Mathematics, therefore so should be Bioinformatics. (philsf@ufrj.br)

There is not a consensus within the mathematical community about whether statistics should be considered applied mathematics. Statistics is a branch of mathematics, and it should be included in any of the broader, more general definitions of applied mathematics. Just because it is usually represented in a separate department in Univeristies does not mean that it does not fall under the umbrella of applied mathematics. Indeed, at many colleges and universities statistics is considered part of "applied math". I think NOT including statistics under applied math is POV. In fact, I would also say that not actively discussing on the main page the way people sometimes include statistics as part of applied math and sometimes don't, would also make the article POV. Cazort 03:17, 19 January 2007 (UTC)

[edit] Creative Mathematics

Creative Mathematics

Since the traditional Mathematics focus on the algorithm like that: Problem-->Find Mathematical Model-->Find Solution, the Key Algorithm for Creative Mathematics is: Problem-->Find Mathematical Model Using AI Techniques-->Find Solution.

Dr TAM Shu Ming

[edit] New Format

The new layout, with separate sections, is a definite step forward. I think more can be done though. Right now the heart of the article is just a list of topics. Is there a better way to format it so the list isn't quite so eye-striking? Or maybe having more discussion would help. JJL 15:59, 26 May 2006 (UTC)

[edit] First Sentence

Applied math is about "the mathematical techniques typically used in the application of mathematical knowledge to other domains"?

No, it is about applying math to other domains, and is not restricted to techniques that are "typical". (Cj67 10:47, 12 July 2006 (UTC))

No, applying math. is one thing; the subset of math. known as applied math. consists of certain areas of mathematical knowledge, not of certain applications of math. JJL 15:02, 12 July 2006 (UTC)

[edit] Divisions

I added the cleanup tag as the divisions of mathematics is a list where people have just added their favourite area in a nonsystematic way. This needs to be changed to a paragraph of encyclopedic prose describing the important divisions and mentioning some of the minor ones. Billlion 16:21, 24 October 2006 (UTC)

I'm thinking of a couple of ways to go about this. It seems that one useful approach would be to separate the list of topics into several groups, such as biology (mathematical biology, bioinformatics), business (mathematical economics, actuarial science, financial mathematics), computers and computing (computer science, numerical analysis, cryptography, graph theory/network analysis), and then to write one concise paragraph about each group. (Just looking at the existing list, it seems like an awful lot to fit into one paragraph.)
Does that sound like a good plan? DavidCBryant 14:27, 23 November 2006 (UTC)
Good idea. Please give it a try. Billlion 21:37, 23 November 2006 (UTC)
OK, I dropped it in there, Bill. I hope it's OK. DavidCBryant 13:25, 26 November 2006 (UTC)
Definitely an improvement! I think the Taylor series example is helpful. The Representation theory link seems to emphasize a more theoretical approach? In this context I'm more apt to think of representations by F.S., wavelets, etc. JJL 15:30, 26 November 2006 (UTC)
Thank you for the kind words, JJL. I'm new here, so I tried not to delete any of the existing links when I restructured this section -- I don't want to ruffle any feathers. Maybe representation theory doesn't belong where I put it, but I did think about it a little bit. Approximation theory deals generally with representing objects from analysis with rapidly convergent sums of, say, Chebyshev polynomials. This always seemed like applied mathematics to me, in the strict sense, because one is applying an algebraic structure (a set of orthogonal vectors in polynomial space) to simplify a problem in another area of mathematics (analysis).
Now I'm not really an applied math guy. I did take a few courses in it, but I've mostly concentrated on analysis. Anyway, the article on representation theory talks about applying the algebra of vector spaces to group theory. That also looks like applied mathematics in the strict sense, even though abstract algebra hasn't traditionally been a big topic in the applied math curriculum. DavidCBryant 16:17, 26 November 2006 (UTC)

[edit] "Segregation within Universities" vs. "Separation within Universities"

I think the word segregation should be replaced by separation. It's not a sensitivity issue; it's just that segregation is most often associated with some type of discrimination. Indeed, the first three links for the article Segregation are about racial, ethnic, and religious segregation. Separation is the better word because it does not suggest something other than separation between pure and applied mathematics. --Db099221 22:36, 14 January 2007 (UTC)

I see your point. It's not important to me to use the word 'segregation' though I think it is appropriate; however, 'separation' doesn't have the right connotation for me, preceisley because it does not suggest something other than separation between pure and applied mathematics, as you state. These depts. often (not always) choose to remain apart, in many cases because they are at odds with one another. The Dept. of Math. and Div. of Appl. Math. at Brown U. were barely civil with one another for decades. The depts. at JHU and SCU are in separate colleges and have very limited interaction (appl. math. is in the engineering school in each case). I think it's important to indicate that these depts. aren't separate for mere convenience or taxonomoy but that there is often some degree of resentment present, and that it is often the case that each prefers to be on its own. Of course, I also don't want to overstate the case in these academic turf and financing battles. 'Segregation' captures all this nicely; mere 'separation' doesn't. What's a good synonym that covers this intentional separation? JJL 16:52, 15 January 2007 (UTC)
Sequestration? Sectarianism? I'm not sure, and my dog-eared copy of Roget's Thesaurus isn't a lot of help. I'd like to drag "schism" into it somehow (as in sch[olastic]ism), but then someone would probably object on religious grounds.  ;^> Oh – I'm not a professional academician, but I have witnessed the kind of resentment to which JJL alludes. Too often the pure math guys think of themselves as intellectually superior to (sniff) mere engineers, and the applied math guys think of themselves as diligent workers (with their shirt sleeves rolled up) who are clearly more useful than the hoity-toity pure math people. DavidCBryant 20:06, 15 January 2007 (UTC)

I renamed this section "Status in Academic Departments"...maybe someone can think of a better name, but I think it's important to try to make the heading name as value-neutral as possible. Maybe something like "Categorization" or something similar? I don't know. Maybe we should also include some active discussion about hostility between departments, like the stuff you discuss--to not mention something is to make a value judgment about it! Cazort 03:36, 19 January 2007 (UTC)

[edit] scrap the section

I really don't like the "Divisions of Applied Mathematics" section. I think parts of it are POV, and I also think it is very wordy, rambling, and poorly organized! I would love to have some other people contribute to cleaning it up but in the absence of that I think I am going to butcher it somewhat. I hope I don't offend anyone too greatly, feel free to switch stuff back or engage in active debate if you don't like the results. Cazort 03:35, 19 January 2007 (UTC)

Number theory doesn't belong here, in my mind. Applied math. is, like topology, a reasonably well defined body of knowledge. It doesn't mean all math. that can potentially have applications--that would be essentially all math. It no longer distinguishes. JJL 14:27, 19 January 2007 (UTC)
I like the way it is worded now after your edits! Thanks. Cazort 18:58, 19 January 2007 (UTC)
I just went through part of the article and corrected grammatical and punctuation errors. I agree that it was a bit of a jumble before – I had tried to string a simple list of subjects that was already here into a connected narrative, and the result was not outstanding. I am curious about one thing, Cazort. What's your opinion of verbs? I think the article leans on the verb "to be" a bit too heavily, as it stands. DavidCBryant 19:53, 19 January 2007 (UTC)

[edit] Computational mathematics

I have split off all that NSF stuff that User:JJL edited out into a separate article, and added some explanations there. Computational mathematics deserves a separate article anyway, I just did not think it would be so soon. Jmath666 05:04, 3 April 2007 (UTC)

I recall that was some kind of NSF panel report in early 80s that justified the existence of computational mathematics and I think gave it the name. Much like DDDAS and I think high performance computing. If I track it down I'll add it to references. Jmath666 05:10, 3 April 2007 (UTC)

I would think that a redirect to computational science or scientific computation would suffice. It's just another example of the profusion of terms now used to describe scientific computing. What's the difference between a computational mathematician and an applied mathematician specialising in computing (or numerical analysis)? Or a computational scientist? Looking at the SIAM CS&E conference, I think computational science is becoming the accepted term. JJL 13:21, 3 April 2007 (UTC)

(indent above added) Perhaps computational mathematics should not be a simple redirect also for historical reasons. The profusion of buzzwords is unfortunate. The way it works, a group creates a new buzzword and pushes for funding for it, hence, the role of NSF and other research funding agencies in making buzzwords stick. I have taken the description of computational mathematics right out of the cited NSF website.

There is indeed no difference between someone in computational mathematics and an applied mathematician specializing in computing or numerical analysis - that's what computational mathematics means. But computational mathematics does proofs and they are essential (look at an issue of Mathematics of Computation) while computational science usually does not and just computes away (most papers at said SIAM CS&E conference), projects are often interdisciplinary and involve collaboration with an actual scientist, and correct science not the math is what's important. There is a big difference between mathematics and science. By the way, I am on different sides of that fence myself at times depending on the project. Jmath666 16:46, 3 April 2007 (UTC)

Proofs? So, is computational mathematics the same as numerical analysis? JJL 00:07, 4 April 2007 (UTC)

Numerical analysis is a subset of computational mathematics. Please look in the references in the current version of computational mathematics what the accepted descriptions of computational mathematics are. You will find references to numerical analysis in the Rheinbolt report. Jmath666 01:50, 4 April 2007 (UTC)

I am suggesting that what you and/or the NSF call computational math. isn't the final say on the matter. I think you're multiplying terms needlessly. The distinctions you're drawing are very minor. JJL 03:03, 4 April 2007 (UTC)

People keep inventing names and shifting meanings, and that's what DAB is for. What do you think about the computational mathematics page now? Jmath666 01:38, 8 April 2007 (UTC)

[edit] Pure and applied mathematics - that's just not how it happened

JJL, regarding the edit about pure mathematicians resisting applied hires, I have, sadly, seen it happen more than once. I do not want to return to it in the article, also because of WP:OR, and I do not want to cite specific examples here. But I am curious, how did it happen then, in your experience? Jmath666 01:30, 8 April 2007 (UTC)

That kind of thing happens now. But 100+ years ago, the depts. started as depts. of (pure) math. on the one hand, and depts. of appl. math./theoretical mechanics on the other. In many cases they were separate from the beginning. What you wrote indicated they split from dislike--rather, they merged from financial necessity, and occasionally now some split off again. In any event, going too deep into this isn't important here--the goal is to describe appl. math., not to compare and contrast the pure and the applied. JJL 03:01, 8 April 2007 (UTC)

It has been happening at least for several decades as far as I know. They do split and chase applied people away from dislike even if there was no merger in the past. An opposite trend exists also: theoretically inclined engineers end up in math departments these days... Thanks for the longer perspective. Perhaps a separate history article, but that would be hard to document without original research. Jmath666 03:33, 8 April 2007 (UTC)