- 1 Created a decision sciences subgroup
- 2 Mathematical Physics expanded
- 3 Remove Chaos
- 4 Principles
- 5 See Pure Mathematics footer
- 6 Theoretical Computer Science
- 7 Purpose: Modern applicable mathematics not just British "applied maths"
- 8 Proposed rename: Industrial and Applied Mathematics
- 9 Computational mathematics does not correspond to what the other links claim
- 10 Place for information theory
Created a decision sciences subgroup
Mathematical Physics expanded
The International Mathematical Union sponsored Mathematics Unlimited for the millenium. Following Mathematics Unlimited, I added some topics that should bring the template closer to contemporary applicable mathematics, especially by adding ideas that have led to breakthroughs in science and re-conceptualized mathematics. See recent popular articles by Atiyah, Manin, etc.
Notice that algebra has an expanded role, reflecting the change in research articles in the last 40 years. (In the USA, The AMS Notices have tracked an expanding proportion of algebraic theses, for example.) Kiefer.Wolfowitz (talk) 21:09, 17 January 2010 (UTC)
It would be good to cover the principles of applied mathematics besides the fields of applied mathematics.
I would suggest topics under Mathematical modeling like:
- Model formulation: dimensional analysis and Scale analysis (mathematics), linearization, parameterization, functional form or functional equation
- Design of experiments and Planning of observational studies
- Hypothesis testing or Model validation
- Expansion of models: Scalar to vector, Static to Dynamic, from Deterministic to Stochastic, etc.
Applied-Mathematics editors may be interested in my proposal of a similar footer for pure mathematics. I also suggest that a footer for Basic mathematics be created. Thanks Kiefer.Wolfowitz (talk) 17:18, 18 March 2010 (UTC)
Theoretical Computer Science
There has been a discussion on the talk page for the "P versus NP problem" article. There appears to be a consensus there that Theoretical Computer Science is not in Applied Mathematics. With this in mind, I propose that the template be modified. Jwesley78 17:23, 18 March 2010 (UTC)
- Your portrayal of consensus should be qualified. There was a lot of support for the truth that theoretical CS overlapps with applied mathematics (in the modern sense). What people object to is a suggestion that CS theory is a subset of (British traditional) "applied mathematics". Don't you agree?Kiefer.Wolfowitz (talk) 19:48, 18 March 2010 (UTC)
- Certainly, there is no such consensus. As the voice that opposes your visison of things perhaps the most, I would like to point out that there is agreement that there is overlap between these disciplines. While it may be agreed that statement that TCS is branch of applied mathematics does not reflect the situation, it has also been pointed out that on this very template was listed as branch of applied mathematics (apparently by a previous consensus opposite to one which is claimed), and it has also been pointed out that many theoretical computer scientists work at applied mathematics departments at places like MIT rather than in CS departments. To disregard all this and say that there is a "concensus" while there is ongoing controversy is awful misrepresentation of facts. Dlakavi (talk) 12:54, 19 March 2010 (UTC)
- I started this discussion on Wikipedia talk:WikiProject Mathematics#Theoretical Computer Science. That page would likely be the best venue for this discussion. Jwesley78 18:13, 18 March 2010 (UTC)
- Thanks for your comments: I shall look at the discussion referenced. Indeed, Theoretical CS is not a subivision of applied mathematics: however, there is a lot of overlap, and "theoretical CS" provides some coherence to research in the sub-listings. Will you suggest a better name for this grouping of activities, please, recognizing that no name is perfect? Thanks, Kiefer.Wolfowitz (talk) 18:53, 18 March 2010 (UTC)
- Also, has the Computer Science WikiProject been notified of this discussion? Verbal chat 20:48, 18 March 2010 (UTC)
- Good point. I'll add a section for it. Jwesley78 20:50, 18 March 2010 (UTC)
Purpose: Modern applicable mathematics not just British "applied maths"
As stated previously, this footer covers more than so-called "Applied Mathematics" in the British tradition. This footer attempts to represent the living areas of applied (applicable) mathematics, especially those that are vitally connected with (empirical) science, industrial applications, and computing. The old usage of "Applied Mathematics" was long ago dropped by SIAM and the mathematics community --- as represented by the International Mathematics Union's Mathematics Unlimited project
- Engquist, Björn (ed.); Wilfried Schmid (ed.) (2001). Mathematics Unlimited: 2001 and Beyond. Berlin: Springer. p. 1225. ISBN 9783540669135.
- Regardless of whether it means applicable mathematics or applied mathematics, I don't see what discrete mathematics is doing on the list. Yes, there are applications to e.g. cryptography, but the existence of applications doesn't make number theory qua number theory any less impure. Similarly discrete geometry, combinatorics, and graph theory are all commonly studied as pure mathematics subjects, divorced from applications, despite having some. I don't think they should be included in the footer, unless we want to include all of mathematics in the footer. —David Eppstein (talk) 20:39, 18 March 2010 (UTC)
- The content of "discrete mathematics" in the header was my attempt to survey the articles in the related SIAM journals and the usual courses in mathematics for CS.
- David, you raise 2 issues.
- First, I separated the topics of "discrete mathematics" from the Theoretical Computer Science/Computational mathematics group because they are pursued for their own sake and because they are significant in applications & computations.
- Second, are you objecting to an implication that "discrete mathematics is studied exclusively or even mostly for applications". Regardless of its truth, that implication would be unwarranted from this header. Would you suggest improvements?
- Kiefer.Wolfowitz (talk) 21:11, 18 March 2010 (UTC)
- I strongly object to giving British tradition separate weight. Applied mathematicians were not all British, far from it, and British applied math should not have more weight than say German tradition in applied mathematics, or Russian or Chineese. This sort of nationalism is leading nowhere. Mathematics (pure or applied) CS or science of any sort is essentially cosmopolitan and particular national traditions, while clearly distinct, should not be singled out to give impression that other contributions to the field are less worthy.
Also, discrete mathematics is certainly part of mathematics (with applied flavor), and in particular Hungarian school is one of the more important there (Erdos, Laslo Lovasz); graph theory is as much applied mathematics as say functional analysis with its application to quantum mechanics (fon Neuman, who also has contributions to theoretical computer science).Dlakavi (talk)
Proposed rename: Industrial and Applied Mathematics
"Applied mathematics" is often associated with the grand British tradition of "applied mathematics", which prized scientifically insightful results derived with analytic expansions (often used without safety belts!). (C.f. Hammersley "The Enfeeblement of Mathematical Skills by so-called Modern Mathematics and other soft intellectual trash taught in the schools and universities"). Does anybody object to our renaming the template? Kiefer.Wolfowitz (talk) 20:49, 18 March 2010 (UTC)
("Applicable" mathematics would be wrong on many grounds --- like category theory in programming language or number theory in cryptography.)
- I implemented the name-change. Kiefer.Wolfowitz (talk) 20:53, 18 March 2010 (UTC) Alas, Industrial mathematics is linked to Applied mathematics. Kiefer.Wolfowitz (talk) 20:57, 18 March 2010 (UTC)
- This was reverted. Please look at the long discussions and you will find that the people in theoretical computer science objected to being included on the "applied mathematics" footer (definitely in the narrow sense of British "applied mathematics"). I will redo the name-change and respectfully ask the editor kindly to respond to the theoretical CS comments before reverting again. Thanks Kiefer.Wolfowitz (talk) 21:17, 18 March 2010 (UTC)
The change from "theoretical computer science" to "computational mathematics" is inconstent to the rest of the template. The two things are not the same, and the articles listed were for TCS, not computational mathematics. We need to keep consistency there. Computational mathematics is more part of TCS, than an appropriate umbrella title for what is listed. Also, as examples of people such as Daniel Spielman show, TCS can be listed under the template (interdisciplinary fields can belong to more than one area, there is no contradiction there).Dlakavi (talk) 13:11, 19 March 2010 (UTC)
Place for information theory
As an illustration of arbitrarines of any such division, information theory was listed under TCS (even worse, computational mathematics). But it can as easily be listed under probablity or some other field. Dlakavi (talk) 13:14, 19 March 2010 (UTC)
- Would you agree that Kolmogorov wanted to re-found probability theory on combinatorial complexity theory? And that much of information theory deals with processes of symbols, so it has great ties to e.g. coding theory. There is no doubt that measure-theoretic probability also has a lot of overlap with probability, but there is a great overlap with computing. Kiefer.Wolfowitz (talk) 16:51, 20 March 2010 (UTC)