I am a computer science student who, by nature of my major, am disallowed from taking all the of the math needed to get to algebraic topology for credit as an undergrad(there are a limited amount of credits I can take, and those credits will be eaten up by computer science classes at my university). Despite this I would like to build a path to understanding algebraic topology in my free time. There have been a lot of insights and inspirations from algebraic topology in my field in recent years and I see it as a good branch of mathematics to know generally for solving problems in computer science(proof writing, abstract thinking, etc).

I am finishing multivariate calculus, which covers some areas of elementary analysis, this fall alongside linear algebra. I have been doing linear algebra for a while now as I tutor it already and use a lot of it in my personal work/self study. I've also already done differential equations and numerical methods.

What will I need to ramp up to algebraic topology and is computational algebraic topology just an application of the theory? I noticed that Michael Robinson at American University posted his class online and I plan to watch that lecture or Norman Wildbergers once I get to the point to be able to do problems in algebraic topology.

I noticed that Michael just requires Calculus and Linear Algebra for his course but others on here seem to think an understanding of Groups is also necessary. How necessary are groups?

  • $\begingroup$ Unless the course you plan on reading has an introduction to group theory embedded, you will need to have at least a basic understanding of group theory before taking a course in algebraic topology. The whole point of algebraic topology is to assign algebraic objects (groups/rings/vector spaces/etc.) to topological spaces. It also would be helpful (some may say necessary) to have a grounding in point-set topology before starting algebraic topology. $\endgroup$ – Dan Rust Sep 1 '16 at 12:33
  • $\begingroup$ The book groupoids.org.uk/topgpds.html starts with the beginnings of point set topology and develops that in a geometric way for continuing in algebraic topology. There is no homology theory. $\endgroup$ – Ronnie Brown Sep 1 '16 at 14:37
  • $\begingroup$ So I looked into it and most of the applications covered in the Michael Robinson course are from homology. Does this still require you to assign algebraic objects to topological spaces? $\endgroup$ – jake mckenzie Sep 2 '16 at 1:47

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