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How long can I expect to work on Spivak?

  1. Mar 1, 2012 #1
    Hey guys, I'm an electrical engineering student on my first year. I'm from Canada and I think our first year of University is the equivalent of 2nd year in the USA. I've taken calc I, II and III (multi-variable calculus, PDE's...), statistics and linear algebra. I've also learned some discrete mathematics in my EE courses, but nothing rigorous (it was mostly logic algebra).

    I'm in a co-op program and I'll spend the whole summer in northern Quebec working in a zinc mine, and I'd like to use that opportunity to work on Spivak. I've learned that it's a great book to learn work through before tacking real analysis, which is something that seems daunting and fascinating to me.

    Assuming I can put 3 hours a day in the book during the week and about 10 hours total during the weekends, can I expect to finish Spivak in 16 weeks? (that's about 25 hours working on the book a week, for the lazy :P)

    Also, do I have the required mathematical baggage to tackle Spivak? If not, what book(s) do you guys recommend? I've never learned much about mathematical proofs at school so that might be a problem (I've never even seen stuff like induction).
  2. jcsd
  3. Mar 1, 2012 #2
    First, I'd like to ask why you want to study Spivak. If you think it will help you as an electrical engineer, then I can assure you that it will probably not so much. The calculus courses you take are likely enough.
    On the other hand, if you're interested in rigorous math, then Spivak is a wonderful interesting book. It won't help you much, but it's very enjoyable.

    How long you will do on Spivak depends. If you intend to cover the theory and not the exercises, then you can cover it quite swiftly. If you intend to make the exercises, then expect that they will cost some time. The exercises in Spivak are very daunting and quite difficult. You should also expect that you'll probably need some help and hints along the way. Don't be afraid to ask questions here.

    Generally, your schedule seems a good one. But it depends on you whether you need more or less time.
  4. Mar 1, 2012 #3


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    the goal with a math book is not to finish it, but to learn something from it. that can occur on just one page.
  5. Mar 1, 2012 #4
    Thanks for the answer. I'm aware that rigorous mathematics probably won't help me in electrical engineering, I want to study some mathematics and physics on my own out of pure interest. Unfortunately the electrical engineering program at my university uses PBL (problem-based learning), which means my schedule changes every week and we're not allowed to take other courses because we sometime have to work for 80+ hours in a week to complete our 2 week's module lab work.

    Thanks for the reminder mathwonk, that was very inspiring.
  6. Mar 1, 2012 #5
    I switched from EE to math. I'm actually considering trying to get an EE job after finishing my PhD. The math may or may not help me, but for me, it's a necessity to keep my sanity to completely understand the underlying math behind anything that I am doing, even if I don't actually "use" it. For example, there's a very ugly argument that is used to deduce a wave equation from Maxwell's equations. However, it seems to be trivial if you use differential forms. So, while it's not strictly necessary, at least for me, my math background would help me from going crazy because I am the type of person who has to know why everything works (though the PhD in topology is almost certainly overkill).
  7. Mar 2, 2012 #6


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    if memory serves me, Spivak was written to cover a full year course. trying to cover it "all" in 16 weeks might be asking a bit much.

    the first 4 chapters will probably be fairly easy going, although some of the exercises may make you stop and think for a bit.

    chapters 7 & 8 are "must-read". sup's and inf's are what typically give people the most trouble, especially later on, if they haven't gotten familiar with how they work (and are really the reason why we want real numbers at all, or else rational numbers would pretty much do).

    i disagree that Spivak won't be "that helpful" with course-work on electrical engineering. fourier analysis is used, for example, in signal processing, and the material in section IV is a good beginning towards that.

    part V (the epilogue) is my personal favorite. although it's not strictly necessary, it is enlightening.

    i see it like this: you can learn how to follow a recipe (learn problem-solving algorithms), or you can learn how to cook (learn problem-solving). if you learn how to cook, you don't need any recipe books, you can write your own, if you wish to. the first makes you competent, the second makes you capable. understanding "why" sometimes makes understanding "how" obvious.
  8. Mar 2, 2012 #7
    If you start working through the text and find you won't be able to finish everything, I recommend proving all of the theorems presented in the chapter and worrying about the problems when you have more time. The problems are great and challenging but the most important results are usually proven for you. There really are a lot of problems included in this text so don't feel like you have to complete every single one. Some chapters have over fifty problems, many with multiple parts.
  9. Mar 2, 2012 #8
    I've searched around and a lot of people suggest reading about real analysis before attacking Spivak. I was recommended Charles Chapman Pugh's Real mathematical analysis for someone in my position. It's shorter than Spivak, but it's (supposedly) a great introduction to real analys. Would working through this before starting Spivak be overkill? If the contents of both books are very similar, I'd rather work on something else.
  10. Mar 3, 2012 #9
    Calculus is typically taught before Real Analysis.

    Spivak is a great calculus textbook and precursor to standard real analysis textbooks. I prefer Apostol's Calculus Volumes 1 and 2 though because they include linear algebra and multivariable calculus.
  11. Mar 3, 2012 #10
    As I said in my first post however I already took Calc I, II and III, linear algebra and statistics. Calc I and II were shown using the infinitesimal approach, and our calc III teacher showed us the definition of epsilon but the course wasn't proof based. Unless you consider these approaches to be so bad that they don't count as calculus, then I've already taken calc I, II and III.
  12. Mar 3, 2012 #11
    Then why did you ask if you should read a real analysis book before a calculus book?

    Spivak is an advanced introductory textbook on single variable calculus. If you have not experienced calculus in a rigorous context or dealt with proofs in any other class, then I highly recommend reading a book like Spivak or Apostol before you handle real analysis.
  13. Mar 3, 2012 #12
    Indeed! Most real analysis books are much harder than Spivak. Books like Rudin are deadly for people who are having troubles with Spivak.

    Do Spivak first. If you find it too easy (I doubt it), then you can do real analysis.
  14. Mar 3, 2012 #13
    You have it the wrong way round. You need to read Spivak's calculus book before Pugh's book. It's shorter than Spivak, but covers more and at a higher level. A book like Spivak is a prerequisite for Pugh. I hope I've drummed that into your head, lol.
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