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Math classes for fun

  1. Sep 4, 2012 #1
    Hello, I am a freshman EE/CompE (Hardware) major seeking a math minor. Since I have already arrived to university with Calc III and ODE's completed, I would still like to dedicate about 4-7 courses of mathematics. I would like some math classes to be applicable to my major as well as others to be entirely proof based. Note: I'm already taking Linear Algebra (Freidberg) and Complex Functions (Brown/Churchill) this semester.
    My choices are:

    -ODE 2 (Nagle, Snider)
    -PDE's (Haberman)
    -Fourier Analysis
    -Intro Analysis 1,2 (Rosenlitch)
    -Abstract Algebra (Gallian)
    -Set Theory
    -Number Theory (Niven, Zuckerman, Mont)
    -Topology 1,2 (Munkres)
    -Combinatorics 1,2
    -Mathematical Foundations (Kunen)

    For someone who wants to get a diverse feel for math, which (3-4) courses would you recommend from the ones listed? I'm likely going to take ODE 2, PDE, and/or Fourier Analysis in addition to these 3-4 classes.

    I plan on graduate studies in EE/CompE only.
     
  2. jcsd
  3. Sep 5, 2012 #2
    I would actually reject Fourier Analysis on the basis that your EE Linear Systems class is going to be 80-90 % Fourier analysis already. So if you want more breadth without seeing repeating material, I'd stay away from the Fourier Analysis class. Furthermore, if you decide to take your upper-level EE electives in signal processing, they'll keep hammering Fourier into you. Of course, if you just really love Fourier analysis and want to learn about it the mathematically rigorous way, then ignore everything I just said. :smile:

    I would suggest ODEs 2 and PDEs. These topics arise so often in all areas of engineering, but yet many EE students seem to falter when the order increase beyond two or nonlinearities arise. Since you seem to but a computers guys, combinatorics might be good too.
     
  4. Sep 5, 2012 #3
    I should also add that most Physics Departments will offer a course or two on something along the lines of "Mathematical Methods in Physics." This is their methods of condensing a wide array of math topics into one or two courses. There might already be significant overlap with what you've taken already, but it's worth inquiring about this class just to make sure. Unfortunately, it probably won't count towards a math minor, but it could free up some space for additional classes.
     
  5. Sep 5, 2012 #4
    I believe the math methods for physics course is equivalent to the intro theoretical physics class at my univ. I'll look at the fourier analysis and EE analysis syllabi to weigh the redundancy vs new. What about the proof based courses?
     
  6. Sep 5, 2012 #5
    Well I just mentioned what might be more useful for an EE. Everything's interesting, so the more "proof-based" course are up to you. I will say though, I've always wanted to study topology partly because I'm a big fan of coffee and doughnuts....
     
  7. Sep 5, 2012 #6
    I would do PDEs, abstract algebra (if you don't get to rings/fields, take abstract 2 at least, or don't take it at all), and either topology or number theory.

    I'm currently in number theory, and it's a pretty interesting course, and not too difficult... so far at least :P.

    Good luck!
     
  8. Sep 6, 2012 #7

    micromass

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    I just want to let the OP know that abstract algebra, number theory and topology will have no relevance at all to his later carreer as EE or Comp E. They are extremely interesting courses though, and it's worth taking if you're interested. But don't expect it to be useful.

    Courses which might be useful are the ODE, PDE and Fourier analysis courses. Another course which you should think of is analysis. Now, analysis is not directly useful to an engineer, but it does provide foundations for stuff like Fourier Analysis. So if you're interested in why the techniques you use in engineering work, then this might be a nice course. It is NOT an easy course though.
     
  9. Sep 6, 2012 #8
    I'm looking for 2-3 applicable/useful math and 2-4 proof based math to just get a broad understanding of mathematics regardless if these 2-4 courses are not at all useful to my major at all.

    Im just not certain which of the 2-4 such math classes would yield the most diversity of all of undergraduate mathematics. (ex: Suppose you take 2 courses from the list, does analysis 1&2 cover new material in more distinct topics of math compared to algebra and analysis 1? I don't think it is but what of 3-4 classes?)

    I will likely take ODE2, PDE, and Fourier analysis for my first group of courses.
     
  10. Sep 6, 2012 #9

    Dembadon

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    From your list, I'd suggest abstract algebra, analysis 1 & 2, and topology. This will give you exposure to three major fields of mathematics.

    While you can take algebra and analysis concurrently, I'd suggest completing analysis 1 before taking topology.
     
  11. Sep 7, 2012 #10
    I think "no relevance at all" might be too strong of a statement, since there are many different kinds of electrical engineers, including some guys in academia who are basically just like mathematicians.

    There are certain very small areas in engineering that use heavy topology (motion-planning, sensor networks, data analysis). Also, when studying analysis and algebra, you usually get really good at linear algebra, and you get to revisit calculus, so that you understand the subtleties better.

    Sometimes, things that seem as if they are not useful are actually useful, just because they help to hold your knowledge together and reinforce things that you already know.
     
  12. Sep 8, 2012 #11
    It might be helpful to take Fourier Analysis before you start your EE classes. I dunno what they teach in such a class but you'll be doing Fourier in so many classes. So far 4 of my EE classes have been heavy on Fourier and I'm doing alot of Fourier Series in my PDE class right now.

    Perhaps a more proof-based apporach would be helpful but I can't imagine much else
     
  13. Sep 8, 2012 #12
    I would do the ODE 2 and PDE's class, Fourier's also good along with a complex variables class if they offer it, Real Analysis I think would be useful, that's the one math class I wish I could take.
     
  14. Sep 8, 2012 #13
    Im still debating on fourier analysis. The EE signal methods course basically teaches applied fourier analysis for EE. I prefer to avoid redundancy but for now, i still have plently of time to figure this out.

    So far, everyone has recommended analysis, algebra and topology. I'm still considering topology, but analysis 1 and topology 1 is offered fall only. Taking one after the other is a year apart. What other course would you recommend in place of topology if it doesn't work out?

    Edit: There is a computer science class*required for the major and covers a bit of combinatorics 1&2. To avoid redundancy, i'll probably exclude these courses 2 courses.
     
    Last edited: Sep 8, 2012
  15. Sep 8, 2012 #14
    Also foundations (if its like mine and teaches proof techniques) is also a good class to take. Not directly applicable but teaches you a different mind set as well as some set theory and other tidbits of math. Helps in general.

    Also a really helpful one that you didnt mention is a good course in Prob/Stat. I had to take one for engineers but the math/stat major version was alot more helpful. Good for control/communication courses. Also surprised to see no Vector Analysis course which would be helpful in EM type work. Maybe your calc 3 went far enough into it (mind didnt)
     
  16. Sep 8, 2012 #15
    If you are going to take 7 math classes on top of ODE, you might as well double major in math not minor. In my university, you need only 8 more 300-400 level classes after ODE.
     
  17. Sep 8, 2012 #16
    If you are going to take any abstract mathematics classes it is essential that you take the foundations course first. It is probably the least interesting but.... lays the foundation... for proofs and abstract mathematical thinking.
     
  18. Sep 8, 2012 #17
    @Aero I took an intro abstr math course which was half logic. Topics included the axioms, de morgan's laws, quantifiers, and proving equivalencies (ex proving a method for proving uniqueness). The other half was trivial proofs using sets, classes, operations, classes, power sets, and some relations.

    Is this what you mean by foundations or do you refer to: undecidability, independence, turing machines, etc.?
    (these are topics in the foundations course).

    @nano Perhaps. If I do end up taking more math I probably will. These are just potential electives ill take if i can accommodate room for them/ no conflict with required courses.

    Edit: well, by electives, this includes substitutes for gen ed classes spaces (ive finished most of them)
     
    Last edited: Sep 8, 2012
  19. Sep 9, 2012 #18
    By foundations, I am referring to a first course in proofs. That's what this type of class was called at my old school.
     
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