A little background: I'm a high school student enrolling at a local university next fall. I plan to pursue a mathematics degree, have studied this Calculus book. During the next semester, I plan to study this book. Given that I've already taken Calculus I at university and read these books, I have two questions:

1) Do universities allow students to take courses like Calculus II and III concurrently?

2) Given the amount of material studied, would it be wise to take both courses simultaneously?

This is pertinent because I wish to take part in a REU or summer internship in the future, and my current schedule makes it impossible without taking Calculus II and III in one semester.


I ended up taking Calculus II at a neighbor university. It's been working out so far, for it seems to be just an in-depth look at integrals and infinite series. Morris Kline's Calculus seems to be a solid, albeit not very rigorous, introduction to the intuition behind calculus. The first 400 or so pages of the book covered all the information needed for taking Calculus II.

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    $\begingroup$ 1) Sometimes, and 2) Maybe. Calculus courses vary enough that it's hard to say. If you want some kind of answer from Math.SE, it'd probably help to post the course descriptions of the specific Calc II/III that you're looking at. If you want a really reliable answer, you should talk to someone who's familiar with your university's specific math program... $\endgroup$ – Micah Nov 5 '14 at 0:06
  • $\begingroup$ It's a bit unclear how taking the two courses in different semesters affects your ability to do an internship or REU, though I suppose it might depend on where you go to university. (In the US, I had the impression that internships and REUs are generally for students with at least three or four semesters already completed.) $\endgroup$ – David K Nov 5 '14 at 18:38
  • $\begingroup$ You're right David, most REUs that I've looked at require at least 1 course in advanced calculus and analysis. However, I mapped out my current pace and I would be one semester late in taking those classes. Thus, I thought it would be better to try and fit two classes together than wait another year for an REU. $\endgroup$ – JMill. Nov 6 '14 at 16:21

If you have successfully studied Widder's Advance Calculus book (and don't fool yourself, work the problems to see if you really know the material!) then you have the chops to take two math courses together. But calc II and calc III are the wrong choices, since one leads into vector calculus and the other develops it. (Of course, at schools like MIT, the calc sequence is just I and II, covering vector calc in II.)

Your best approach is to ask for permission to take a first course in real analysis at the same time as Calc II. That is tough work, but if you already worked through that book, you should be able to handle it. And it will give you a connecdtion to a prof who can advise you what next to take while you take Calc III.

  • $\begingroup$ Hey Mark, I just worked on Kline's Calculus book (haven't read Widder's yet). Do you suggest a good book for self-studying vector calculus? $\endgroup$ – JMill. Nov 6 '14 at 19:09
  • $\begingroup$ If I remember correctly, Thomas and Finney (it may be volume 2) does a good job up to and including Stoke's theorem and Gauss'law. And a good but beginning student should be able to follow it. $\endgroup$ – Mark Fischler Nov 8 '14 at 4:39

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