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Complex before real analysis? How's my fall schedule look?

  1. May 20, 2015 #1

    QuantumCurt

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    Hey everyone,

    I'm transferring into UIUC this fall, and I just registered for my classes earlier today. I'm completing dual degrees in physics and math. I've completed the introductory physics sequence, and the introductory calculus sequence, plus a 200 level introductory differential equations course. I had been planning on taking both abstract linear algebra and fundamental mathematics (which is basically an introduction to upper level math and proof writing), but unfortunately both of these courses are full. A lot of the upper level math courses require linear algebra or fundamental mathematics as a prerequisite, but I was able to register for an Applied Complex Variables course, which I will need for my math degree. The only prerequisite for this course is Calculus III.

    Should I be at all concerned about taking complex analysis prior to real analysis or any other upper level math courses? Obviously the prerequisites exist to serve as an indicator of the answer to this question, but I can't help but have some lingering questions. Will the complex analysis course draw on elements from real analysis that I'll have to catch up on? I'm not opposed to this if that is the case, but I'd like to be well prepared.

    For some context, my class schedule for this fall:

    PHYS 225 - Special Relativity and Mathematical Methods in the Physical Sciences
    PHYS 325 - Classical Mechanics I
    CS 101 - Introduction to Computer Programming for Scientists and Engineers
    MATH 446 - Applied Complex Variables
    PHIL 110 - World Religions

    This seems like a well balanced mix of classes to me. It comes out to 15 credits, which is a typical course load. Anyone have any input? Any thoughts would be much appreciated. :)
     
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  3. May 20, 2015 #2

    jasonRF

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    Since you have the pre-requisites, I would not hesitate to take the complex variables course. If you are really concerned you should ask your advisor. In fact, I hope you ask your UIUC advisor all of these questions as she will know better than we do.

    I did not go to UIUC, but the "applicable" complex analysis class I took as an undergrad did not require real analysis and it was no problem for an engineering major like me that never took real analysis. Besides linear algebra, it was perhaps the most useful course I took from the math department.

    jason
     
  4. May 20, 2015 #3

    jtbell

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    There's another thread on the first page of this forum right now, about a complex analysis course. Someone there makes the point that there are basically two kinds of math courses: ones that focus on calculation techniques and applications, and ones that are proof-oriented, aimed at math majors. Judging from the title and prerequisites of your course, it appears to be the first kind, which would require only an ordinary calculus course as pre-requisite.
     
  5. May 20, 2015 #4

    QuantumCurt

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    These are very good points. My adviser worked with me to set this schedule up. She's the one that suggested the complex analysis course after we found out that the other two courses were full. I couldn't help but have some lingering questions still. As she admitted, she herself is neither a physicist or a mathematician. She's an academic adviser. It sounds like I should be fine in this class though. I'm quite looking forward to it. The course description specifies that it draws a lot on applications to physics.

    This raises some other concerns. I guess I'd say that physics is my primary major, but I'm doing a second major in math largely because of my interest in pure mathematics as well as the applicability to physics. Am I going to be doing myself a disservice as far as my pure math education is concerned by not taking complex analysis from a more theoretical approach? Clearly an applied class is still going to cover a large amount of the theory, even if it isn't in as much depth. My intuition is telling me that it shouldn't really be an issue. Might it be advisable to find a different course for this fall and take the more theoretical complex analysis course later on? Or is this basically a completely needless concern?...lol
     
  6. May 21, 2015 #5

    micromass

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    In my opinion: yes. But what other courses are still available for you? If you can find a good alternative, then you should definitely drop the complex analysis course.
    That said, you could probably try to self-study the proofs course so that you don't have to take it anymore later. That would be a good use of your time.
     
  7. May 21, 2015 #6

    QuantumCurt

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    The proofs course is a degree requirement, and I don't believe they offer a proficiency test for it. So skipping that one may not be an option.

    I think the only other option I'd have would be a statistics or probability theory course. This is also a degree requirement, so perhaps this would be a better option. Any thoughts on that?
     
  8. May 21, 2015 #7

    micromass

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    Seems like a much better idea. It's always worth knowing. Then again, you can't really do much serious stuff in probability without analysis...
     
  9. May 21, 2015 #8

    QuantumCurt

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    Well I just checked and the probability classes are all full too. So it's looking like I might not really have any other options. It's possible that some classes will open up as people adjust their schedules and such. I'll be watching them.
     
  10. Jun 8, 2015 #9

    QuantumCurt

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    I got some great news a couple days ago. There was an honors section of Fundamental Mathematics (the intro to proofs/upper level math course) that was still open, but permission to register for it had to be requested. I sent an email to the UIUC math advising requesting permission to enroll in it, and I was initially denied because they don't like to take first semester transfer students into honors courses. But, persistence pays off. I replied and assured them that I knew it would be much more rigorous, and that I could handle it. They ended up reconsidering and granting me permission to enroll.

    So, this means I won't be taking the applied complex analysis course now, and will instead later be taking a more theoretical course on complex analysis. I've got a schedule for this fall that I'm much more content with, and I think it'll be better for my math education overall. I'm happy with how things worked out. Acceptance into this honors section is basically the prerequisite to the formal honors math sequence, which includes honors sections of real analysis, advanced analysis, abstract algebra, and an honors topics course that has a new topic each semester, usually drawn from the current field of research of whatever professor teaches the class that semester. I'll hopefully be completing this sequence now, but it remains to be seen how it will work out with my physics classes.
     
    Last edited: Jun 8, 2015
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