Topology Through Inquiry

What Hacker News says

1. thraxilJun 2021
   Does math count as "technical?"

   I was originally a Physics major and lately I've been on a kick of filling in the mathematics that was used in my Physics classes but that I feel like was never really gone into in much depth.

   My current reading list is:

   - "Analysis I" (and II) by Terence Tao (I finished the first volume and am now on the second, but I consider them really one book)

   - "Understanding Analysis" by Stephen Abbott

   - "Topology Through Inquiry" by Starbird and Su

   - "Introduction To Topology And Modern Analysis" by George F. Simmons

   The Terence Tao books are amazing so far. Extremely readable introduction to Real Analysis. Abbott also came highly recommended and from reading the first couple chapters I can see why as it also seems to be very readable. I don't know if it would be a better introduction than Tao, but it covers mostly the same material and I think having two different perspectives will really help solidify things for me.

   Once I finish those, I'll see whether I want to go deeper into Topology or move to Complex Analysis or Differential Geometry.

   I also have a copy of Emily Riehl's Category Theory in Context. I've read some Category Theory before and have a basic grasp, but after reading a few pages of her book, I put it aside until I feel like I'm much more well versed in Topology (the content looks amazing and I really want to read it, but it relies on Algegraic Topology more heavily than other Category Theory material I've seen). So I'll see where I'm at after getting through those Topology books.

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2. playing_coloursDec 2019
   A gem of the year for me: “A Course in Algebra”, by Vinberg https://bookstore.ams.org/gsm-56 A gentle introduction into Abstract Algebra. It is very well written, with a lot of examples. Recently, I opened for myself Soviet mathematical books, with no-nonsense terse language, without entertaining pictures, but with good examples of applications.

   Another math title that someone recommended on HN, I am digging into now: ”Foundations of Applied Mathematics” https://foundations-of-applied-mathematics.github.io/ It is going to be 4 volumes, Volume 1 is available, Volume 2 arrives soon. It is a useful book (soon books) on maths for specialists in AI and computational areas.

   Last title, not released yet: “Topology through Inquiry” https://bookstore.ams.org/text-58/ Sure, there is the famous Munkres book as a great intro into Topology, but this one may be interesting to learn maths using inquiry-based learning approach.

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