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 $I$, Abstract Algebra?


closed as not a real question by user4594, Did, Thomas, rschwieb, martini Dec 6 '12 at 14:38

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ I like to recommend people take abstract algebra early since it gets you familiar with the language of higher math, in addition to its own content. Then again, I am an algebraist. $\endgroup$ – Alexander Gruber Dec 6 '12 at 9:38
  • $\begingroup$ What do you mean by "further understand all the concepts discussed in linear algebra"? Unless you're asking about seeing linear algebra over other fields (or rings), or in infinite dimensions, I'd say the best course to learn about linear algebra is linear algebra, preferably an "honors" course with lots of proofs. $\endgroup$ – Jesse Madnick Dec 6 '12 at 9:46
  • $\begingroup$ @JasperLoy I will edit my question to minimize the vagueness but it is closed. Why is it closed for? $\endgroup$ – diimension Dec 6 '12 at 21:52
  • $\begingroup$ @JasperLoy Did not know that. Sry for that then. $\endgroup$ – diimension Dec 6 '12 at 21:59
  • $\begingroup$ @AlexanderGruber Thank you very much for informing me on that because after taking a year and half of computational heavy math courses, I jumped right into a proof related class, in linear algebra, that I struggled in because I have never seen that type of math before. I hope that abstract algebra will help clarify all the issues I had in linear algebra. $\endgroup$ – diimension Dec 7 '12 at 9:45

As Jasper says in the comments, it really does depend on what the exact content of the courses are. It would help if you could edit your question to include a rough syllabus for each course. But here's my two cents:

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.

  • $\begingroup$ Thank you very much! I will take your advice and take Analysis and Abstract Algebra. Should I take these classes before signing up for Algebraic Topology? $\endgroup$ – diimension Dec 6 '12 at 21:55
  • $\begingroup$ That's usually how it's done, but you should ask the professors (and other students) at your university. Again, it really depends on how the algebraic topology course is taught. $\endgroup$ – Jesse Madnick Dec 7 '12 at 1:06

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