There probably is no exactly comparable book for algebraic topology, but I really like Algebraic Geometry - A Problem Solving Approach for beginning/elementary algebraic geometry. I have substantial problem-solving anxiety, so I tend to focus too much on definitions and concepts without ever getting a feel for them by doing problems or proofs -- but so far the exercises in the above mentioned book are all relatively straightforward and build on each other sequentially introduce the material.

Is there any similar simple-minded book for algebraic topology? Or will I have to write it myself some day in the distant future?

Since I doubt there is any analog in algebraic topology for the above book, perhaps I should ask: which introductory algebraic topology text has the easiest problems/exercises?

I would like to build confidence while overcoming problem anxiety.

Earlier in the summer I was at a conference where the speaker had us do some simple computational tasks (like compute the boundary map over $\mathbb{Z}_2$ for some simplicial complexes) which I felt were helpful in making me feel comfortable and familiar with the material. However, besides the six or so problems like that which the speaker assigned, I have not been able to find anything similar for algebraic topology, only for algebraic geometry (hence why I mentioned the above book).

In contrast, to give an idea of what I am not looking for, I hated Munkres's book for general topology. Part of the problem was that the course was taught on a compressed schedule, but Munkres's problems in Topology (at least the ones my professor assigned) all took too long and tended to rely on "tricks". I know that some people enjoy struggling over the same problem for hours or days on end until they magically re-invent the same trick as the author, but for me personally I find that this is very counter-productive when I am learning the material for the first time, because I quickly give up and then wind up unable to learn any of the rest of the book because it depends on solutions to previous problems (which I either gave up on or thought I could skip over) for results. Not to mention that, for me, inventing such tricks tends to provide very little conceptual understanding of the material, sometimes even less than what I get from carrying out basic computations which take minutes instead of hours or days and can be straightforwardly verified. Honestly I am surprised Munkres didn't leave the proof of Urysohn's Lemma as an exercise given his attitude towards exercises.

  • 2
    $\begingroup$ Hatcher's book might have the best exercises, but not all of them are easy. $\endgroup$ – Arthur Aug 22 '16 at 22:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.