Algebra

What Hacker News says

1. ssequeiraNov 2022
   Understanding Analysis by Stephen Abbott and Algebra by Michael Artin.
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2. mrkgnaoJun 2016
   This is usually part of an introductory undergrad course in algebra. What you're looking for is called "ring theory".

   Michael Artin's Algebra is a good, concrete book with tons of motivation and zero prerequisites. Wanna try it? ;)

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3. karamazovApr 2014
   I'm a big fan of SICP. I'd describe it as "hard-core": requiring hard work, but extremely rewarding for the people who take the time and effort to go through it.

   I'd recommend the following three books to similarly cover the three main areas of higher mathematics (analysis, algebra, and topology):

   1. Principles of Mathematical Analysis by Rudin (http://www.amazon.com/Principles-Mathematical-Analysis-Inter...)

   2. Algebra by Artin (http://www.amazon.com/Algebra-2nd-Featured-Titles-Abstract/d...)

   3. Topology by Munkres (http://www.amazon.com/Topology-2nd-James-Munkres/dp/01318162...)

   Working through all three (including the exercises!) will give you a solid understanding of the basis of modern mathematics. If you don't have experience with proofwriting, you might find them difficult at first - the activity is very different from performing calculations or solving equations. It's also best to have someone trained in mathematics talk to you about the proofs, until you develop a feel for the needed level of logical rigor.

   Rudin, in particular, leaves a lot of work to the reader; going through that book is the most intellectually difficult work I've ever done. If you find it hard-going (which is completely natural), you might want to try Artin first, especially since you have some background in algebra.

   (Incidentally, these are the three books used to teach analysis, algebra, and topology to MIT mathematics majors. You can look up the assignments and exams for the three courses - 18.100B, 18.701, and 18.901 - for a good list of exercises to work through.)

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4. SlyShyFeb 2011
   I also recommend Algebra by Michael Artin--but it isn't free, unfortunately.
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5. vector_spacesDec 2019
   Thank you for your perspective here. I've felt that way in the past and I have certainly purchased international editions intentionally.

   For me, as someone who's learning primarily independently, the North American editions tend to have features that make self-study a lot easier, and do sometimes have different chapters. For example, I have both the international/Indian version and the North American version of Michael Artin's Algebra second edition in front of me.

   The international edition is missing a preface (I like those because they give you some insight into the author's point of view and approach), doesn't have solutions in the back (useful for validating your work if you're self-studying), the table of contents isn't broken down by section only by chapter (not too big a deal for me), and is missing chapter 16 on galois theory, a bibliography (sometimes I like to use these to pursue topics in more detail), as well as an appendix altogether (the NA version's appendix has a section of proof strategy, construction of the integers, Zorn's lemma, the implicit function theorem -- for me these are 'nice-to-have's but not required).

   Much of this I can probably live without -- and if I were a student on a very tight budget, I would probably! But I hope you can see how paying for what I thought was a used copy of the North American edition and receiving the International edition would be a bit disappointing (this particular case happened to me on hpb.com, not Amazon)

   In particular I think my point is that sellers of international editions sometimes conceal the fact that what they are selling is the international edition. The example I gave with Casella & Berger in my first post is clearly doing this with how the cover is blotted out and nowhere on the listing does it mention it's an international edition.

   So for me it's about transparency and meeting expectations -- I'm fine with international editions being sold at all on Amazon, I think it's great that they can be an accessible option for some people who don't need/care about the features I mentioned.

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6. sunnypsMay 2016
   Thanks for both references. It's been a while since I studied algebra in college and I'm hoping to get back into it and solidify my understanding. What do you think of Artin's Algebra? http://www.amazon.com/Algebra-2nd-Michael-Artin/dp/013241377...
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