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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. :)