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I am a communications engineering undergraduate, and I was thinking of studying pure math courses will this help me later on in graduate school, and if it will help what courses of pure math will be related to my major?

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    You may get a better range of responses to this question if you ask it on math.stackexchange.com – Ian_Fin Sep 15 '16 at 10:34
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    You mean, like the stuff that this guy did? – Willie Wong Sep 15 '16 at 13:06
  • @Willie Wong yes – h.hamid Sep 15 '16 at 13:15
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    The "pure math" label is very, very silly, ... especially as usually put in opposition to "applied math", ... when we're asking about applications to signals engineering, say. But, certainly, as in the work of C. Shannon (as @WillieWong noted), in the work of N. Wiener, and many others: yes, certainly mathematics is useful to communications engineers. Linear algebra over finite fields, Fourier transforms, and so on. So, abstract algebra, real analysis, complex analysis, functional analysis. And these have prerequisites. – paul garrett Sep 15 '16 at 22:05
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    If so, then it will be called "applied math". ;-) – David Ketcheson Oct 16 '16 at 5:37
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I'm in a similar situation to you. I'm finishing my masters in digital communications and doing my thesis right now. Math is an issue for me definitely.

In my experience, a bit more complicated math is helpful if you're going to be developing systems that do statistical signal processing (which seems to be very popular now) and anything that has "smart" in its name.

What exactly do you need depends on what you want to study in detail. It might be a good idea to first dip your toes in the fields you want to be working with first and the pick math courses you want to take. You could try looking at some books or papers about say adaptive filters or modern receivers or estimation theory. This should give you an idea what's usually needed. If you're lucky enough to have approchable professors, do ask them about what will be useful to you.

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I find Paul Garrett's recommended courses rather ambitious for a non-math major undergrad, if the context is the U.S.

You would be well served by covering most of the basic math classes needed for a physics or engineering major:

  • the calculus, including multi-variate
  • an intro to ordinary differential equations -- this is a classic course and will prepare you for the Fourier transform
  • linear algebra -- will make a lot of things easier once you've had this; also, as long as your course is rigorous and not too cookbook, you will gain mathematical maturity by doing lots of proofs
  • if you enjoy it, you could have some fun with a numerical methods class (although this is not a pure math course)
  • intro to probability or graph theory (for something totally different)
  • if you want more pure math, then take "advanced calculus" (but not without a rigorous linear algebra class under your belt)
  • If you like math, and want to take advanced math courses, it is quite likely that they will help you later in your career. Especially if you choose topics related to communications engineering. For example, the amount of probability taught in an intro to probability course is insufficient for a lot of real applications. On the other hand, if you don't like math, I wouldn't advise taking extra math courses. You'll struggle to get through them and possibly forget everything you learned before you have a chance to use it. – Peter Shor Oct 17 '16 at 20:35

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