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Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(about 25 proofs a chapter), or I should just roughly skim through and complete, for instance, just odds. Doing all the problems takes a lot of time and I want to get started on Spivak Calculus as soon as possible. However, doing every problem also give me more practice. Any ideas?

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    $\begingroup$ My guess is just the odds would be plenty. We math teachers find fun problems, and want to include / share them. I'll bet there's more than enough in that book. $\endgroup$ – Sue VanHattum Apr 10 at 20:02
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    $\begingroup$ You could randomly pick some exercises, and if they seem too difficult, then that indicates you need more work. But if you can answer a random exercise straightforwardly, then that indicates you've mastered the techniques. $\endgroup$ – Joseph O'Rourke Apr 10 at 20:45
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    $\begingroup$ Please post answers in the answer box so that they can be upvoted, can be marked as accepted, and can host their own comment thread. $\endgroup$ – Chris Cunningham Apr 10 at 21:52
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    $\begingroup$ For what it's worth, Velleman's book seems to me a huge overkill prerequisite for Spivak's Calculus text, which doesn't really require any prerequisites outside of a fairly strong school algebra and precalculus background, such as one would get from the pre-1980's Dolciani Algebra and Trigonometry 2 and Modern Introductory Analysis texts (e.g. Chapter 1: Mathematical Statements and Proofs in the Alg./Trig. text, mathematical induction is used throughout the other book, etc.). $\endgroup$ – Dave L Renfro Apr 11 at 7:17
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I have this book. A lot of the problems are pretty similar and there are a lot in there.

Normally, I'm in favor of doing all the exercises (since you get faster as you go). But I really don't think that quantity of drill is required for a strong student, especially since this is a course that some people still eschew (not taking any proofs class). Maybe do all the Spivak problems though.

The other thing is the book only has answers for the odds. So unless you have an answer guide, you can't check the evens.

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Firstly, congratulations for taking on this task. Of course it is very important to actually complete problems, rather than just read the notes.

I would say that completing the odd numbers is a sensible compromise - you can go back and complete the even questions at a later date for more practice or revision.

Good luck!

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