Of the four courses you listed, I'd say that algebraic topology will be the best at developing geometric intuition. Depending on how it's taught, there may be lots of proofs, or there may be very few. However, I think that the other three courses you listed are generally considered somewhat more fundamental to an undergraduate math education.
Your complex analysis class will probably involve lots of computation, but hopefully there will be quite a few proofs as well. In the sense that calculus can be considered geometric, I would say that complex analysis also contains many beautiful geometric ideas.
Both Analysis I and Abstract Algebra should involve lots of proofs, and not much rote calculation. Analysis I will help you understand the functions on euclidean space, and abstract algebra will study groups (which could be regarded as generalizations of vector spaces). Both of these courses are really important for any math major.
However, all of this is just my opinion. Perhaps other people will think differently. Before accepting any answers, I would suggest waiting at least a day or two so that others will be encouraged to provide alternative viewpoints.
manpreet![Tuteehub forum best answer]()
Best Answer
2 years ago
I want a class that will help me improve my intuition on geometric spaces. All the math classes I have taken this far has been computational heavy and didn't help me understand the concepts other than knowing how to compute. I took linear algebra this semester, which I enjoyed -- it was the first math class that I actually had a small, intuition understanding of the concepts. It was heavy on proofs, even though I never did proofs before, I struggled at it, but it did help me understand the topics a lot better.
Which classes will help me further understand all the concepts discussed in linear algebra like Euclidean space and so on. Which class are best for me: Algebraic Topology, Complex Analysis, Analysis