Analysis vs. Algebra: Choosing the Right Math Course for Next Quarter

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Discussion Overview

The discussion revolves around the decision of whether to take analysis or abstract algebra in the upcoming quarter. Participants share their experiences and preferences regarding the two courses, considering factors such as teaching quality and personal enjoyment of proof-based mathematics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Meta-discussion

Main Points Raised

  • One participant expresses uncertainty about which course to take next, noting enjoyment of proof-based linear algebra.
  • Another participant suggests that the choice may depend on the quality of the professor teaching the course.
  • Some participants argue that it does not significantly matter which course is taken first, as both subjects will complement each other.
  • A participant mentions that some professors may structure linear algebra to facilitate a smoother transition to abstract algebra.
  • One participant shares a preference for abstract algebra, indicating a positive experience with the subject.
  • Another participant emphasizes the importance of having a good professor for both courses, particularly for the challenging analysis course.
  • A suggestion is made regarding the importance of supplementary materials, with one participant recommending specific textbooks for both subjects.
  • A participant reflects on their experience with Real Analysis I, describing it as the hardest yet most rewarding class taken so far.

Areas of Agreement / Disagreement

Participants generally agree that both analysis and abstract algebra are important subjects, but there is no consensus on which course is preferable to take first. Multiple views on the significance of teaching quality and personal preference are present.

Contextual Notes

Participants express varying levels of experience with the courses, and there are references to specific textbooks and teaching methods that may influence learning outcomes. The discussion does not resolve the question of which course to prioritize.

proton
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I can't decide whether to take analysis or abstract algebra next quarter. I really enjoyed my proof-based linear algebra class, so I was wondering which class would be better to take afterwards. Or does it not matter which one you take first?
 
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The one (or two) with the better professor.
 
I don't think it matters too much. Whichever one you take will me the next one easier. Some profs teach LA so that abstract alg. follows quite nicely afterwards, in which case maybe that would be a better choice.
 
proton said:
I can't decide whether to take analysis or abstract algebra next quarter. I really enjoyed my proof-based linear algebra class, so I was wondering which class would be better to take afterwards. Or does it not matter which one you take first?

Like the other posters have said, it doesn't really matter which course you take next. I can't remember which I took first: I may have even taken them at the same time.
 
I love abstract algebra!
 
i agree with mattmns. they are both important and you want to learn both as well as possible, and learn to like them. so try to get a good prof.

they are also hard, especially analysis, so a good prof is doubly important.
 
A good book is important to: mathwonk's algebra book on his website is very good (imo better than beachy/blair or dummit/foote). Its free also. What could be better? I am trying to master it. For Analysis, although rudin is the classic, its not great for learning it the first time. I suggest Real Mathematical Analysis by Charles Chapman pugh.

Also I believe the old saying: write 3-5 pages for every page you have read (maurice auslander I think said that)? That means for a 100 page book, you would write between 300-500 pages. This is to really master it.
 
Last edited:
as stated above, both are important subjects. You may find the Algebra class a bit more of a direct extension from your Linear Algebra class, however that is not to say it would be easier. You may fancy a change form Algebra for a bit and take the Analysis. Personally I have not yet taken Abstract Algebra (scheduling conflict for next semester) but I have just finished Real Analysis I, and I can say it was the hardest class I have taken but also the most rewarding and my favorite thus far (out of Calc I,II,III, Lin Alg, Num Theory, Diff EQ and Real Analysis I).
 

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