I am a first year graduate student in Mathematics. I am planning to take a graduate course on Homology Theory. My background is Point Set Topology (material covered in Part 1 of Munkres) and the contents of chapter 2 (Group theory) in I.N.Herstein's "Topics in Algebra". I would like to know how much more of Topology and Algebra is required as a good preparation for the course. I would especially like to know if background in Ring Theory and Modules is needed. Suggestions on books and other references which would serve for the background preparation would be very helpful. Thank you.

  • $\begingroup$ We don't know the text for your homology course, nor how advanced your professor will make the course. So you should start by asking that person. I would say you need more algebra than Herstein's chapter on groups, although the fundamental homomorphism theorem is essential. But you also need to be used to working with presentations of finitely generated abelian groups so that you can play the various exact sequence games. $\endgroup$ – Ted Shifrin Dec 13 '13 at 22:33
  • $\begingroup$ Welcome to MathSE, Shakti. $\endgroup$ – Nirakar Neo Dec 14 '13 at 1:24

Yes, some background for rings and modules will be useful. For example, to know about projective, free and flat modules etc. A good book (among many others, of course), is Charles Weibel's "An Introduction To Homological Algebra", and before perhaps a book on rings and modules (for a collection see here: http://www.math.hawaii.edu/~lee/algebra/references.html).

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