Once, when I Was doing calculus 2, someone challenged me to calculate and prove the Gaussian integral, with a few hints, and a few days, I managed to.
It was a great feeling to solve a “deep” multi step long math problem.
My question:
Do any of you know of resources for problems of this kind?
I’m looking for an online resource, in the level of calculus 2.
As a person planning on being a pure mathematician, I know that I will be presented with a problem and I will need to find an approach to solve it, most calculus textbooks provide a step by step explanation on the problem, detailing someone else’s reasoning.
When I see someone else’s reasoning it makes sense but I always wondered if I was presented with the problem what I would have done.

  • $\begingroup$ Since you are already MSE user, I really think that it is a very good source of quite deep problems. $\endgroup$ Commented Jun 19, 2020 at 11:13
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    $\begingroup$ @ClaudeLeibovici - How do you filter the good questions out from all the noise though? $\endgroup$
    – Alec
    Commented Jun 19, 2020 at 17:01
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    $\begingroup$ What do you mean by "deep" in that context? $\endgroup$ Commented Jun 19, 2020 at 17:41
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    $\begingroup$ I'm a fan of problems on brilliant.org and artofproblemsolving.com, but I don't think this is a full answer so I'm leaving it as a comment. Another great source of questions, though perhaps not 'deep' in the sense that they require lots of calculation but 'deep' in the sense that they require good reasoning, includes the good questions project: pi.math.cornell.edu/~GoodQuestions/materials.html $\endgroup$
    – Opal E
    Commented Jun 19, 2020 at 17:50
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    $\begingroup$ As these are surely known to you — Calculus by Spivak, Introduction to Calculus and Analysis by Courant/John, and A Course of Pure Mathematics by Hardy — perhaps you could indicate in what ways none of these has what you want (especially Courant/John), since each has many problems that appear to be what you're looking for. See also the books listed here. $\endgroup$ Commented Jun 20, 2020 at 18:18

1 Answer 1


razivio, look at Joseph Edwards Treatise on Integral Calculus froim 1920 (can find pdf on the web). Full of challenge problems from Cambridge Tripos exams. (Warning, stay in the earlier part of the text as that is calc 2. But he also has calc 3 and really complex analysis in there also.)

  • $\begingroup$ Thanks, the book is interesting and provides good explanations (from what I read) but it doesn’t provide the problems I’m looking for, thanks for recommending it though. $\endgroup$
    – razivo
    Commented Jun 20, 2020 at 9:25

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