Talk:Applied mathematics/Archive 2

Archive 1

Archive 2

Practical application of mathematical logic

"at most a vanishingly small portion of mathematical logic could be called applied". The term "vanishingly small" is close to my heart. I was advised by a pure mathematician to refer to Hardy's Orders of infinity to complete the proof that my first Royal Society paper depended on, that led to the result that supported me for the next fifteen years. According to Wikipedia articles, the lambda calculus is part of mathematical logic. It is also at the heart of functional programming. Now the number of papers that use functional programming in scientific computing annually, divided by the total number of papers on scientific computing may be less than 10^-6, which could be considered vanishingly small. But if the functional programming work is supported by millions of dollars in research grants annually, or has led to hundreds of papers in prestigious peer reviewed journals, is "vanishingly small" an appropriate criterion for exclusion from mention of applicability to real world problems? Michael P. Barnett (talk) 00:59, 7 February 2011 (UTC)

Here, I am happy to agree with Mr. Barnett. The lambda calculus and LISP are the godparents of the statistical languages (and computing environments) S (programming language), S-PLUS, and R (programming language), which join Fortran, Matlab, and SAS/IML as the primary languages for statistical computing. The theory (and practice) of computer programming languages exemplifies the applicability of pure mathematics---category theory, lattice theory, type theory, etc.  Kiefer.Wolfowitz  (talk) 09:57, 7 February 2011 (UTC)

I beg to differ. That "vanishingly small" part of mathematical logic that has relevance to computing can hardly be called "applied". There is nothing applied about the lambda calculus - it is pure mathematics. This is the dilemma of computer science - it has no applied mathematics! It tries to take pure math and directly compute with it. That is why you can't really *calculate* anything useful in computer science, despite the profusion of so-called calculi like the lambda calculus, pi calculus, mu calculus, etc. They are all just axiomatic systems of pure math. They become useful only to the extent that computer scientists can prove useful properties, but you can't calculate a program with them. Now compare this with the situation in engineering where the differential calculus comes with a body of applied math that allows it to be used to calculate useful values for circuits, controllers, flows, etc. Houseofwealth (talk) 04:31, 21 February 2013 (UTC)

Matrix and Applied Mathematics

It's difficult to understand how does Matrix concepts are required to be in Applied Mathematics. When we talk about Matrix although it is said by Mathematical Norms. It is not by that and it is rather by discrete Mechanisms. And for Square Matrix, Determinant value is certain. But in order to arrive a Square Matrix and by Determinant, it is that hard that beyond billion times our science to advance, by that the values arrived will be certain provided there is no change in Context. Just to start with it spin-one aspects are to be understand before vulging and delve deeper into it. Lets start....

|x1 y1 1|

|x2 y2 1| . 1/2 = Δ = Area of Triangle

|x3 y3 1|

|x1 y1 z1|

|x2 y2 z2| . 1/2 = Δ = is also Area of Triangle

|x3 y3 z3|

But for the fact Z Plane is uncertain as it is said by Vector, Algebra, Modern Physics, Quantum Algorithms. Hence we have to say this value should be denoted by δ. Also we must be clear that Z Plane Analysis can't be done by Differentiation, Higher-Order Differentiation and not also by Calculus. This things fits only to Normal Physics where the results are irrational and closer to the value. This mechanics we adopt and adhere when we try to achieve results which are closer. We can say the Adoptable Physics. But to be certain, it is Vector, Algebra, Modern Physics, Quantum Algorithms.

Coming to the next level of Square Matrix.

|x1 y1 z1 1|

|x2 y2 z2 1|

|x3 y3 z3 1|

|x4 y4 z4 1| . 1/4 = δ - Area in Square Units for a Regular or Irregular Prism, i.e., Pyramid.

|x1 y1 z1 P1|

|x2 y2 z2 P2|

|x3 y3 z3 P3|

|x4 y4 z4 P4| . 1/4 = δ - Area in Square Units for a Regular or Irregular Prism, i.e., Pyramid.

So when we go higher and higher in dimension, there are Spin-One Factor, that yields out the certainty principles. That spin-one context {v1,v2,v3,v4,v5..,} may be taken in Modern Algebra, when we really want to achieve some uncertain things in a controlled way. And it is just a point that Spin-One Aspect may occur anywhere within Matrix. When we taken it for calculation Row or Column alignment to be done in accordance with this set of 1's. And we redeem certain 1's and postulate the Matrix, we can make the scenario vulged as required.

–Dev Anand Sadasivam^t@lk 11:48, 11 June 2015 (UTC)

Further reading section -please explain undo Comment

Hello user:David Eppstein or anyone, could you help me understand why the further reading section and 2 links were undone? "The MathWorld link is completely content-free, the other one (Scholarpedia) fails WP:ELNO #1."

1. From Wikipedia:Further_reading: The further reading section of an article contains a bulleted list, ...of ...works which a reader may consult for additional and more detailed coverage of the subject of the article.

2. Mathworld has content, from the menu, a person selects the subject in the menu to get to the content http://mathworld.wolfram.com/topics/AppliedMathematics.html

3. In Scholarpedia, http://www.scholarpedia.org/article/Encyclopedia:Applied_Mathematics has a menu of subjects which can be selected to get to articles like:

http://www.scholarpedia.org/article/Delay_partial_differential_equations Prof. Barbara Zubik-Kowal, Department of Mathematics, Boise State University, Idaho, USA Scholarpedia, 3(4):2851. doi:10.4249/scholarpedia.2851

A Delay partial differential equations article does not exist in Wikipedia that I can find.

4. I don't understand how WP:ELNO #1 "Any site that does not provide a unique resource beyond what the article would contain if it became a featured article" applies to Scholarpedia. The WP wording has general principles and no specifics, making it difficult/subjective to interpret.

Thank you for any explanations you could provide,CuriousMind01 (talk) 01:18, 2 November 2015 (UTC)

Mathworld has articles with actual mathematical content about some subjects. They can be somewhat unreliable but they're still sometimes useful to include in the external links of our articles. But the one you list has no actual content. It consists only of a navigation menu. It would be like linking to a Wikipedia category rather than a Wikipedia article. I don't see the point. As for Scholarpedia, that's generally of much higher quality

than Mathworld, but as it fills pretty much exactly the same role as Wikipedia (a user-edited encyclopedia) it seems to fit ELNO #1 as something that, if our article were as good as we would wish it to be, would only duplicate its content. —David Eppstein (talk) 01:25, 2 November 2015 (UTC)

Thank you for the explanation. As a side note Scholarpedia writes they try to be a complement to wikipedia, maybe the 2 will merge someday.CuriousMind01 (talk) 15:41, 2 November 2015 (UTC)