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Calculus Mike Spivak Math Textbooks

  1. Apr 1, 2015 #1
    Hi, everyone

    I was directed here by a poster in another thread and thought I'd post my question to you guys in this area of the forums.

    I had some questions about Mike Spivak's math textbooks. It was alluded to in another thread that his books are quite difficult. Yet, from what I can gather, they seem to also be popular.

    I'm curious what makes his books difficult and how they may differ from other math textbooks used in college. And, secondly, if I'm just starting Calculus, which of his books (if any) would fit my level of math (beginning Calculus I next Fall 2015 semester).

    Thank you all much!
  2. jcsd
  3. Apr 1, 2015 #2
    They are more proof based then your average calculus book and its more of a real analysis textbook then a calculus textbook. If you are familiar with writing proofs then you may be fine but I would recommend reading it after your first calculus course and possibly a proof writing class. I feel it would be a better textbook to read before taking real analysis or to compliment that class rather then before calculus or to compliment it.

    Its popular because spivak is great mathematical expositor.
  4. Apr 2, 2015 #3
    In my opinion, only his calculus book is good, I don't like the rest. But I can see why some people like them.

    That said, if you never studied calculus before, then you probably shouldn't be doing Spivak. Once you're a bit comfortable with the intuitive concepts of limits, derivatives and integrals, and once you can calculate them pretty adequately, you can try Spivak (and it'll still be difficult). For your situation, I recommend "A first course in calculus" by Lang. It's a terrific book and very well written.
  5. Apr 2, 2015 #4


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    I like all of mike's books, but they are very different. to give a goldilocks justification for micromass' view, the multivariable book is in a sense too short, and the diff geom book too long, while the Calculus book is just right. In my opinion also, the Calculus book benefits greatly by being, in some sense, a more entertaining rewrite of Courant's great calculus book. You also need to be careful what you mean by "difficult". Spivak presents difficult material, but does it so clearly, that if your goal is actually to learn what is in his Calculus book, he makes learning it about as easy as it can be made. However if you want to understand Stokes' theorem, I feel that the version in Lang's Analysis 1 (for simplices), is clearer and easier to read than the one in Mike's Calculus on Manifolds. I like that latter book though for a clear and precise presentation of differentiation and integration in several variables and of forms over chains.
    Last edited: Apr 2, 2015
  6. Apr 3, 2015 #5
    Some helpful responses guys. Thanks very much. I'll check out the Lang book, but was curious what the name of the good Spivak Calculus book was? I'll look it up when I get the chance.
  7. Apr 3, 2015 #6
    Last edited by a moderator: May 7, 2017
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