Courses Can't Decide What Math Course To Take Next

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A bioengineering major expresses a growing interest in pure mathematics, particularly Real Analysis and Abstract Algebra, while nearing the completion of their degree. They are currently taking advanced courses in ODE, PDEs, and Complex Analysis but face challenges in selecting classes for the next semester. Real Analysis is preferred, but the presence of an undesirable classmate is a concern. Alternative options include Topology, Non-Euclidean Geometry, PDEs, or Dynamical Systems, but there are questions about their suitability without having taken Real Analysis first. It is suggested that Real Analysis should be prioritized due to its importance in pure mathematics, despite social discomfort, as other classes may also have challenging dynamics. Checking with professors about course prerequisites is recommended.
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Currently, I am a bioengineering major, but I have been taking math electives the past year and a half, and now I am finding myself liking pure mathematics much more than engineering and only two classes away from a degree. The two courses I need are Real Analysis and Abstract Algebra. Currently, I am finishing up an upper level course in ODE and PDE's and one in Complex Analysis. However, I am running into problems finding something to take next semester. I can't take algebra because it overlaps with Cell Biology. I want to take Real Analysis but unfortunately this super obnoxious kid is taking it, and it's only a 7 or so person class, so I don't think I could bare it. My other options are Topology, Non-Euclidean Geometry, PDE's, or Dynamical Systems. Are any of these courses suited to take without Real Analysis, or should I just suck it up and take analysis?
 
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Depending on how the courses are taught, you might be able to take PDE's or Dynamical Systems without a class in analysis, but it sure wouldn't hurt to have first. You could check with the professors of these classes, and see what they think. However, any good topology class without any course in Real Analysis is out of the question.

I'd think that if you are more interested in pure mathematics, you should take real analysis as soon as possible. It sounds like you already sort of know this, but are avoiding it for social reasons. There are annoying people everywhere, and there could just as easily be someone else just as annoying in whichever other class you decide to take.
 
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