Can You Succeed in Abstract Algebra Without Taking Calculus 3?

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Discussion Overview

The discussion revolves around the relationship between abstract algebra and calculus, specifically whether knowledge of calculus 3 is necessary for success in an introductory abstract algebra course. Participants explore the independence of these subjects, the perceived difficulty of abstract algebra, and its relevance to different fields such as mathematics and physics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the necessity of calculus 3 for success in abstract algebra, expressing concern about taking both courses concurrently.
  • Another participant asserts that a first course in abstract algebra should be independent of calculus, suggesting that basic knowledge of set theory is more relevant.
  • Several participants express their interest in abstract algebra, with one stating it is among their favorite subjects.
  • There is a discussion about whether abstract algebra is more suited for mathematicians or physicists, with some noting its importance in physics while others emphasize its mathematical focus.
  • A participant mentions that linear algebra is a prerequisite at their school, typically taken after calculus 3, indicating a potential curriculum structure that may influence the discussion.
  • Another participant describes abstract algebra as one of the hardest math courses at their institution, comparing it to real analysis, while questioning the connection between calculus 3 and abstract algebra.

Areas of Agreement / Disagreement

Participants generally agree that abstract algebra can be studied independently of calculus, but there are varying opinions on its difficulty and its relevance to different academic disciplines. The discussion remains unresolved regarding the necessity of calculus 3 for success in abstract algebra.

Contextual Notes

Some participants mention prerequisites and course structures that may vary by institution, indicating that experiences and expectations may differ significantly. The subjective nature of difficulty in mathematics courses is also highlighted.

tronter
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I am currently signed up for an intro abstract algebra course. I will be taking this course and calculus 3(stewart's book). I am pretty good at writing proofs. Do you have to know calculus 3 to do well in abstract algebra? Or can you take it concurrently? Is abstract algebra considered a difficult course? So to sum up, I am taking abstract algebra and calculus 3.

Thanks
 
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Abstract Algebra, at least a first course, should be completely independent of calculus, although it will likely require some basic knowledge of set theory. So taking the two classes together should not pose any problems, as far as difficulty that is a rather subjective thing, if you say you are pretty good at writing proofs, however, you should be able to handle the class well.
 
thanks a lot. It seems like a very interesting subject.
 
tronter said:
thanks a lot. It seems like a very interesting subject.

I think it is, it is one of my favorite subjects in mathematics.
 
btw, is it a course for mathmeaticians or for physicists?
 
loop quantum gravity said:
btw, is it a course for mathmeaticians or for physicists?
There are ideas in abstract algebra that are very important for physics. Of course, it's up to the professor as to what is actually taught, and with what emphasis.
 
Hurkyl said:
There are ideas in abstract algebra that are very important for physics. Of course, it's up to the professor as to what is actually taught, and with what emphasis.
yes i know, there're courses in abstract algebra also for physiciists, this is why i asked what iv'e asked.
 
this is a course for mathematicians. its an intro course.
 
at my school, linear algebra is a prereq, and that is typically taken after calculus 3. :/

(then again, the linear algebra class is treated as a weed course at my school, so ymmv.)
 
  • #10
What's the course description?
 
  • #11
At my school abstract algebra is one of the hardest math courses, besides real analysis, of course. I suppose if you are good at proofs, you should be fine. I really don't see how Calc III and Abs. Alg. have anything in common.
 

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