Taking a graduate course in Algebraic Topology or not?

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Discussion Overview

The discussion revolves around the decision to enroll in a graduate course in Algebraic Topology within a Master's program in pure mathematics. Participants explore the relevance of the course to other areas of mathematics, the quality of the instruction, and the necessary prerequisites for success in the course.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses interest in Algebraic Topology due to its relevance to analysis, geometry, and analytic number theory, but is concerned about the quality of the lecturer.
  • Another participant suggests that Algebraic Topology is useful for understanding cohomology and may aid in studying differential geometry, recommending the course if no better alternatives exist.
  • A participant mentions they have seven courses left to take and plans to assess the course during the first two weeks before making a final decision.
  • There is a suggestion that the lecturer might perform well in their area of specialization, potentially alleviating concerns about their teaching ability.
  • Questions arise regarding the essential prerequisites for Algebraic Topology, with some participants asserting that a solid understanding of point-set topology is necessary, while knowledge of abstract algebra is deemed less critical for an introductory course.
  • Clarifications are provided about the level of understanding required in point-set topology and abstract algebra, indicating that basic knowledge of groups and category theory may suffice for beginners.

Areas of Agreement / Disagreement

Participants express differing opinions on the quality of the lecturer and the decision to take the course. While some highlight the importance of Algebraic Topology, others emphasize the need to consider alternative courses. There is no consensus on whether the course is advisable given the lecturer's reputation.

Contextual Notes

Participants note the importance of prerequisites, particularly in point-set topology, and the varying necessity of abstract algebra knowledge, indicating that these factors may influence the decision to enroll in the course.

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Hi, I am enrolled in an Msc programme in pure maths, I wanted to ask for your recommendations on taking a basic graduate course in Algebraic Topology.


Basically my interest spans on stuff that is somehow related to analysis, geometry or analytic number theory.

The pros for choosing this course is that nowadays most pure mathematicians know at least basic algebraic topology, and taking a course is better than learning by my own pace which is much slower than through a course.

The cons for choosing this course, is only one really, the lecturer is quite awful, I took two UG courses with him, in one of them he was reasonably OK (but this maybe becasue it was really basic course of first year), in the other course he was quite horrible.

Any advice?
 
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It depends. What are some of the other courses that you might be taking instead of this one??

Algebraic topology is certainly useful if only because you get an easy introduction to cohomology and stuff. Looking at cohomology from an algebraic topology point-of-view eases the subject a bit. Furthermore, if you're interested in differential geometry, then some concepts of algebraic topology might be useful in that study too.

So, if there are no other courses that you're really interested in taking instead of this one, then I'd say to take the course...
 
Well I have to take 8 courses and 2 seminars, Iv'e taken 1 course already, so I have left with 7 courses to take, I have three other courses that I pretty much settled on taking this comins semester, and this course in AT is a fourth course which I am contemplating.

I guess I'll try the first two weeks and see if I can continue taking this course.

I know that it's quite essentail topic in geometry and topology this is why it's a hard decision for me.
 
that sounds good to me. there is also a chance this lecturer is a specialist in algebraic topology and he might do a good job in his specialty.
 
micromass said:
It depends. What are some of the other courses that you might be taking instead of this one??

Algebraic topology is certainly useful if only because you get an easy introduction to cohomology and stuff. Looking at cohomology from an algebraic topology point-of-view eases the subject a bit. Furthermore, if you're interested in differential geometry, then some concepts of algebraic topology might be useful in that study too.

So, if there are no other courses that you're really interested in taking instead of this one, then I'd say to take the course...

What are the essential prerequisites for Algebraic Topology? Does one need to have mastered undergraduate point-set Topology and Abstract Algebra?
 
ahsanxr said:
What are essential prerequisites for Algebraic Topology? Does one need to have mastered undergraduate point-set Topology and Abstract Algebra?

Point-set topology: yes. You'll have to know it very well. Especially things like "connected" and "path-connected".

As for abstract algebra, it is much less necessary for an introductory course. Basically, you'll have to know a bit about groups (groups, subgroups, homomorphisms,free groups,...), but a first course on groups would usually suffice. Knowledge of category theory is also helpful (but again: the basics suffice).

This is only for an introductory course though.
 

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