<p>For my senior year I was thinking about taking Real Analysis and Complex Variables at Umass. (dual enrollment) How's the difficulty of each, any advice?</p>
<p>If it's just "Complex Variables," and not a more rigorous complex analysis course, then Real Analysis will probably be more difficult. It develops the basic machinery of mathematics and calculus from the ground up - much, much more thoroughly than your calculus courses have in the past. I really like it, but it's partially a matter of individual taste. The almost universal text for this subject is Walter Rudin's Principles of Mathematical Analysis; you might want to look up a copy at a library to see what you think of it. All in all, the course's difficulty will depend almost entirely on your comfort level with proof-based mathematics.</p>
<p>"Complex Variables" could mean a wide range of things, but I assume it will cover the standard, fun complex analysis stuff - a recap of the basics of complex arithmetic and algebra, then cauchy's theorem, residues, maybe conformal mappings, etc. These are all very neat, pretty things, but if you're into the very rigorous, theoretical side of mathematics, you'd probably like Real Analysis better. That said, you're going to have to cover the material eventually if you want to study math (or physics, or engineering... probably), so if you can dual-enroll, you might as well.</p>
<p>I am doing something similar (at Umass as well). I am a senior now and have taken modern algebra and advanced calculus there. I don't know how many college courses you have taken, but I think you will like it. May I ask which Umass campus this is at? I only know about some classes at Umass Amherst where I take some classes.</p>
<p>Its at Umass Lowell, what town are you from Alex M?</p>
<p>About 20min from Umass Amherst. I would guess that most of the courses in Lowell are the same though. If I were you, I would definitely go for it. Taking university courses during high school is a great experience (especially for courses like analysis, etc.)</p>