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I have finished theory for single variable calculus taught at high school level, and want a book to practice problem solving in the same. The problem level should be difficult. Also mention some math competitions that include calculus in syllabus (at high school level).

EDIT 01 : The book should not be a tome of thousands of questions, a possible example can be "101 algebra problems by Titu Andresscu". The questions should be math contests style.

Thanks a lot.

  • Some references here: http://math.stackexchange.com/questions/295790/best-practice-book-for-calculus (though that question was closed for asking for the "best") – Matthew Leingang Nov 03 '16 at 03:31
  • Thanks for reply, the comments there refer the books as drill-type, I would like to know some books that don't have 3000 exercises but 100 (or so) really good problems. –  Nov 03 '16 at 03:36

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I think Boris Demidovich's Problems in Mathematical Analysis is a good book if you are going for the problems.

Link and reviews: amazon

Henricus V.
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I think M. Spivak's Calculus could be an excellent source to help settle your theoretical understanding of Calculus, and its set of problems is challenging.

Also, in a more conceptualistic point of view, A Course of Pure Mathematics by G. H. Hardy can be a good approach to understand Calculus made-from-scratch.

  • Thanks for answering, I will be sure to take a look. But I am looking for books like "101 algebra problems" by Titu. The book should be purely problem based and theory should be included if possible as a mere review. –  Nov 03 '16 at 03:45
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    Maybe I should clarify that "theoretical" and "conceptualistic" here, if your intentions are to focus only in the practical sense (in the problema sets), are to be understood as "difficult"; not huge-calculations-kind-of-hard, but struggle-and-think-hard-kind-of-hard. –  Nov 03 '16 at 03:54
  • @dovakin123 I guessed that that was what you meant, and I am sure you will find a lot of those, but I just wanted to give you some alternatives that given a chance will help you for sure! –  Nov 03 '16 at 04:01
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    I actually did some chapters from Spivak, and it was really interesting, I was unaware of Hardy's book. I am asking for a problem book because in a theory (+problem) book I will have to read the theory to understand what is going on in the problem set and then some problem may refer to theory or previously solved example. –  Nov 03 '16 at 04:04
  • Is the book problems in real analysis by Titu Andresscu accessible to someone with a single variable course? –  Nov 03 '16 at 04:14
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    I don't know it, but probably it's not; a good rule of thumb might be to rule them out whenever you see "Fourier transform", "$L^p$ spaces", "measures", " Interpolation", "Lebesgue differentiation", " Banach spaces" or "'something' spaces" in the index of contents. –  Nov 03 '16 at 04:21