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Historical Textbooks

  1. Jun 27, 2011 #1
    Just last week I relieved myself of a mathematical burden, freeing up some time for myself.
    Coincidentally I came across the following passage by Arnol'd around the same time:
    So, having a bit of free time & the ability to understand old textbooks on mathematics,
    both of which I'd previously not been fortunate enough to be in possession of, I got
    Goursat's books on calculus & differential equations on archive.org. Wow! Phenomenal
    stuff so far! This pushed me to look for a historical algebra text to go over some of the
    more elementary stuff. I found a book by G. Chrystal on Algebra that gives a proof of
    the partial fraction expansion & derives the lagrange interpolation formula from scratch!
    I haven't been able to find much on either of these topics tbh, especially not in the way
    that is done in that book. They have been very non-intuitive explanations that I have
    gotten from more modern books.

    So, with this in mind, could people recommend other similar books from the late 19th,
    early 20th century era that contain similar gold? I'm speaking particularly of the geometric
    aspect that Arnol'd is describing, further elaborated by this passage:

    Now I don't think Hardy's book is a good example of this, I have it & I don't like it that
    much. I'm just hoping people would be aware of a lot of other books that one could check
    out, contrast & compare etc... to find something akin to what Arnol'd is talking about,
    especially other books that people know about & have a good reputation that are not
    the Elements, or the Principia, or Archimedes or something :tongue2: I'm not interested
    in newer books as I'm aware of what they contain, we're talking about the seedy
    undercurrent of old mathematics textbooks :cool:
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Aug 9, 2011 #2
    sounds like theory of equations fits into that category. Most courses & books on Galois theory do the usual stuff with field extensions & automorphism groups (etc) but no mention of actually solving cubics or quartics (except for Stewart), or it's at least not emphasised. In other words no real mention of how to find out what to adjoin to a field. (btw weird how as theory of equations advanced it got taught in more advanced courses, the opposite of what usually happens) I'm not sure what the best textbooks are but I've got ones by Dickson & Uspensky, and a newer (Moore-method style) one, Polynomials by Barbeau which I like.

    zygmund's trig series is another good one. It's got lots of stuff in it that you probably wouldn't find in books on locally compact abelian groups, for example.
     
    Last edited: Aug 9, 2011
  4. Aug 11, 2011 #3
    Take a look at the http://store.doverpublications.com/by-subject-science-and-mathematics-dover-phoenix-editions.html [Broken]. They include subjects other than math and are more expensive than Dover's standard line of books, but they otherwise meet your criteria.
     
    Last edited by a moderator: May 5, 2017
  5. Aug 11, 2011 #4
    burnside's book on finite groups is another one that I thouht of which is also in that series. I don't have a copy but I've read that it all about permutation groups, which I would think is (by the Cayley-Hamlton thm) more or less good enough.
     
  6. Aug 18, 2011 #5

    mathwonk

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    i recommend reading euclid's elements and eulers elements of aLgebra and eulers analysis of the infinite[ies].
     
  7. Aug 20, 2011 #6

    mathwonk

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    as well as archimedes and newton. i.e. i suggest you reconsider them. or maybe gauss.
     
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