Deciding whether to audit, take the class, or take pass/fail

[dh363]

Hey guys, I'm a sophomore thinking about adding into a complex analysis class. The thing is, I'm not sure whether the class would require concepts from Real Analysis (which I haven't taken) or not. The professor didn't list analysis as a prereq but from a conceptual standpoint speaks of the class as if it comes after analysis. I attended the first class and kept up perfectly fine, but that doesn't really say anything, since we haven't gotten into anything difficult yet.

The course description states "Complex numbers. Analytic functions including exponential, logarithmic and trigonometric functions of a complex variable. Geometric and mapping properties of analytic functions. Contour integration, Cauchy's theorem, the Cauchy integral formula. Power series representations. Residues and poles, with applications to the evaluation of integrals. Conformal mapping and applications as time permits.
"
That Conformal mapping is only "as time permits" leads me to believe that he doesn't go through stuff too quickly and this is really an introductory course. He also uses Brown/Churchill, which I've heard doesn't assume very advanced mathematical knowledge. As such, I was wondering whether y'all thought if I would be ready for this kind of intro level complex analysis course. I've had proof-heavy classes before and I aced multivariable and linalg

 

[Number Nine]

Oftentimes, introductory complex analysis courses will not strictly require tools from real analysis in the sense that the course will introduce those concepts when necessary. That said, analysis is hard enough over the reals; unless you have a good intuition for the things covered in a solid real analysis course, you're going to find a lot of complex analysis unmotivated and quite difficult.

 

[Lavabug]

If you know single-variable calculus you shouldn't have any problem. In my course, we had to resort to L'Hopital's rule at some point, Taylor series, etc. but I think the course was pretty self-contained assuming you've covered everything in one of those massive high school/1st year college Calculus texts at some point or another. Speak with your professor about your situation just in case though.

 

[Number Nine]

Question: Is this a general introductory course on complex variables (e.g. learning to do calculus with complex numbers), or a full blown course on complex analysis? Looking closer at the course description you offered, analysis would certainly offer some motivation, but you should be able to manage without that background.

 

[Matrix0]

, but not analysis.I would recommend that you gather more information before making a decision. Firstly, I would suggest reaching out to the professor and asking for their opinion on whether Real Analysis is a necessary prerequisite for the course. It's possible that the professor may have a different perspective on the level of difficulty and preparedness needed for the course.

Additionally, I would recommend talking to other students who have taken the course or similar courses in the past to get their insights and experiences. They may be able to provide valuable information on the level of difficulty and any potential gaps in knowledge needed for the course.

In terms of deciding between auditing, taking the class, or taking pass/fail, it ultimately depends on your goals and what you hope to gain from the course. If you are interested in learning the material and feel confident in your ability to keep up with the class, then taking the class may be the best option. However, if you are unsure of your preparedness or simply want to gain exposure to the material without the pressure of grades, auditing or taking the course pass/fail may be a better choice.

Overall, it's important to carefully consider your options and gather as much information as possible before making a decision. Good luck with your decision!