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jsteinhardt comments on The Best Textbooks on Every Subject - Less Wrong

167 Post author: lukeprog 16 January 2011 08:30AM

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Comment author: jsteinhardt 29 January 2011 04:31:28PM 5 points [-]

For topology, I prefer Topology by Munkres to either Topology by Amstrong or Algebraic Topology by Massey (the latter already assumes knowledge of basic topology, but the second half of Munkres covers some algebraic topology in addition to introducing point-set topology in the first half).

Both Armstrong and Massey try to make the subject more "intuitive" by leaving out formal details. I personally just found this confusing. Munkres is very careful about doing everything rigorously at the beginning, but this lets him cover much more material more quickly later, because he can safely talk about something without wondering whether the reader will correctly guess an implication, because the reader (in theory) understands the background material completely and will be able to tell what is going on.

Munkres' treatment is also far more comprehensive.

Munkres also has a lot of really good exercises, although I didn't get far enough into the other two books to really evaluate how good their exercises are.

One caveat: in topology it is easy to push definitions around without understanding what's going on. It helps to be able to draw pictures of e.g. Haussdorf condition to be able to figure out what's going on.