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Is mathematics becoming more applied, while engineering is becoming more math-y?

I’m seeing curriculum changes at our school that has pretty good math, physics, and engineering departments, and it seems that the vision is that soon math majors will be taking courses in both the mathematics and engineering departments. And likewise, it seems that some engineering research will be done collaboratively with mathematicians. So I'm wondering if this is a general trend that is happening, at least for universities in the U.S.

Are there any references that support or oppose this trend? For example:

  • Bibliometric studies.
  • Publications of professional societies.
  • Official statements by departments, faculties, or universities.
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    In that case: edited. (CC@FedericoPoloni). – Wrzlprmft Apr 23 '18 at 8:37
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    Engineering's definitely getting more math-y, as are STEM fields in general. The kind of math that we commonly do today would've been grossly impractical before modern computers, but now we can basically do a system of coupled PDE's where someone 100 years ago would've used an estimate from a linear correlation. A lot of this stuff, e.g. CAD use, seems fairly obvious, though; dunno precisely what to comment on in an answer. – Nat Apr 23 '18 at 8:38
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    @D.Hutchinson Anecdote: I know of a university with separate math and applied math departments where the departments are having turf wars about teaching calculus and linear algebra, especially to engineering students. When the number of undergrads a department teaches improves its funding, TA support, and university-level clout, there is probably lots of pressure for (pure) math departments to cater to engineering students. Many schools may be renegotiating these questions between departments (e.g. math department teaches all calculus, applied math teaches all stats) leading to what you see. – cactus_pardner Apr 23 '18 at 18:32
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    @Nat what's CAD? ... is it like MatLab? 🤔 – D.Hutchinson Apr 23 '18 at 19:58
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    This has made the Engineering world a different place. Now, field-level engineers can just use software often without knowing all of the details behind how it works, while research-/design- level engineers have to have tons of technical knowledge to build tools. There's little call for anyone to not use advanced math; field engineers just have the software do it while researchers need to advanced math/logic to make continuously more advanced tools. – Nat Apr 25 '18 at 18:42
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I agree with all the comments, that engineering has become more mathematical because of the rise in computers and similarly applied mathematics is growing because of its well poised position to aid in many developing engineering problems.

While I could not find any studies to back this up, I made some graphs of my own from the Web of Science. The first two compare Applied Math and Pure Math. The volatility of the Pure Math graph leads to a difficult comparison. Similarly, I took screenshots of Engineering with Math and All Engineering. Which I believe more clearly shows a growth in engineering-math publication in the past five years or so, as compared to all engineering whose rise began earlier.

Similarly I looked into Arxiv, as it supplies a nice single source of data. These results are for number of uploads/publications.

------------------ 2000-2004 ---- 2014-2017 ---- Growth
App. Math --------- 577 ------------- 5456 ------- 9.45
Pure Math --------- 253 ------------- 1399 ------- 5.52
Eng. Math --------- 14 --------------- 476 ----------34
All Math ---------- 14,408 --------- 102,382 ------ 7.1

While these figures are based on publications, and therefore could be caused by changes in publishing practice I think they do give decent, data-driven evidence for the claim that math is becoming more applied and engineering is becoming more mathematical.

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