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I have recently completed my first year of Eng. Physics taking the standard math courses: Calculus, Linear Algebra 1 and 2, Multivariable Calculus and Numerical Analysis.

Recently though I have been self studying Rudin's "Principles of Mathematical Analysis"/Abbott on my own and I enjoy this "kind" of proof based mathematics a lot more than traditional calculations. Does it ever makes sense for an engineer to actually study pure mathematics of this kind or is it,"application-wise" , a waste of time?

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closed as primarily opinion-based by Najib Idrissi, Daniel W. Farlow, Jonas Meyer, user147263, kingW3 Mar 27 '15 at 18:53

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ When you get to graduate school, most classes are mathematical in nature, so this is perfectly fine. We have Ph.D mathematicians, computer scientists, physicists, and every engineering discipline you can name. They are all called engineers and bring a unique talent to the table. So, learning how to problem solve, communicate, think on your feet, analyze things and all the rest is useful. Get as much proof work in as you can as a real world career will lead you down all type of rabbit holes. Regards $\endgroup$ – Amzoti Aug 7 '13 at 3:22
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    $\begingroup$ My first impulse is to tell you that learning new things is never a waste of time, especially if you enjoy it. I don't think that's the answer you're looking for, though... $\endgroup$ – hasnohat Aug 7 '13 at 3:24
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Of course it does, if you want to go to engineering research (PhD). Here are some engineering fields that need real analysis background:

Control theory

Dynamical systems

Communication theory

Estimation theory

Anything involving PDE: Fluid Mechanics, Structural Mechanics etc.

Pick up the latest journal of IEEE Transactions in Automatic control, and see for yourself.

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  • $\begingroup$ Signal processing can also involve real analysis. There is also the nascent field of topological signal processing, which draws heavily on pure mathematics (topology and sheaf theory). $\endgroup$ – J W Jun 28 '14 at 6:02
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It depends on what you want to do in your career. If you want to stay in academy (doing research, writing papers as your career, be the Michael Jackson Professor of Engineering), then it really is a good idea to learn pure mathematics (And there are many open problems in engineering that needs modern mathematical tools, or even perhaps needs the development of new pure math). If you will pursue an industrial career, pure math may not be as significant/useful for you.

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