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How many problems should I do in Spivak's Calculus?

  1. Aug 31, 2012 #1
    I am currently self-studying Calculus by Spivak. I did the first few chapters a while ago, then had to stop for a while because I took a heavy course load over the summer. Now I have more free time, and currently on chapter 5 (Limits).

    Now, I have the fourth edition, so there's usually between 20 and 40 problems a chapter, and sometimes much more. I don't think it's realistic to do every single problem, considering their difficulty and the time it takes to solve them. But on the other hand, I want to make sure I'm building up a solid mathematical foundation by getting lots of practice.

    So, for those who have studied from Spivak, approximately what percentage of problems would you recommend I do? I have been making sure to do more problems when I struggled with a chapter at first - for example, I had a lot of trouble with limits and epsilon-delta proofs at first, so I've been doing almost every problem in Chapter 5. But if I want to finish working through the book in the foreseeable future, I'm not sure I can do that for every chapter.
     
  2. jcsd
  3. Jan 13, 2014 #2
  4. Jan 13, 2014 #3

    jbunniii

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    I think it's reasonable to say that you should be able to do all of the non-starred problems before you can say that you understand the material. That doesn't mean that you need to actually DO all of them, but you should be ABLE to do so. How many you should do depends on how much time you have, of course. Maybe pick 20 or so in each chapter that look the most interesting and do those. That should give you enough of a sampling to know where your weaknesses are, and then as needed you can do extra problems (in the current or previous chapters) to improve your understanding. If you're up for a challenge, then by all means do a few of the starred exercises. Most of them are pretty cool.
     
  5. Jan 13, 2014 #4

    jbunniii

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    P.S. The most important thing is to be sure you're doing the problems correctly. If you're not taking a course and no one is grading your problems, then you might be making all kinds of mistakes and be unaware of it. So try to get some feedback if you're even slightly unsure about a problem, e.g. by posting your work here at PF.
     
  6. Jan 13, 2014 #5

    PAllen

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    To second the great opportunity to use PF, I have a story I still remember from my first proof oriented college math class. On one problem set there was one problem that I couldn't get, so I talked to the 3 other people I knew from the class - 2 of thme couldn't get it either, the other thought he did. He let us look over his proof, and there was one key trick he used. So the rest of us wrote up our own proofs using the key trick. We all got it wrong - the trick did not apply. The inapplicability was subtle - 4 people who ultimately got an A in the course all missed the inapplicability.
     
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