Some background: I have a degree in computer science, but the math was limited and this was 10 years ago. High school was way before that. A year ago I relearnt algebra (factoring, solving linear equations, etc). However, I have probably forgotten some of that. I never really studied trigonometry properly.

I want to self study calculus and other advanced math, but I feel there are some holes that I should fill before starting. I planned on using MIT OCW for calculus but they don't have a revision course. Is there a video course or book that covers all of this up to calculus? (No textbooks with endless exercises please.) I would like to complete this in a few weeks. Given my background, I think this is possible.

  • $\begingroup$ Maybe "Essential Calculus with Applications" by Richard Silverman? You can look at the table of contents on Amazon to see if it fits your needs (read also customer reviews). It's at a relatively basic level, but if you start from scratch, it's probably better. $\endgroup$ – Jean-Claude Arbaut Mar 29 '13 at 11:42
  • $\begingroup$ Thanks arbautjc, I was looking for something that covers pre calculus more, i.e. trig, functions, logs, complex numbers and more algebra. $\endgroup$ – Mark Mar 29 '13 at 12:01
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    $\begingroup$ here they suggest "Calculus" Apostol. Much more expensive, but also much more comprehensive. After a quick look ate TOC, it seems to be at the level of first two years in university in France (in scientific studies), and it covers the whole maths courses (I mean the two volumes). $\endgroup$ – Jean-Claude Arbaut Mar 29 '13 at 12:11
  • $\begingroup$ See my previous comment $\endgroup$ – Mark Mar 29 '13 at 12:32
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    $\begingroup$ Math, just like riding a bicicle, is learned by doing. So the "endless exercises" are an asset. Nobody forces you to do all of them, select some and work them over carefully. Perhaps check out Pólya's clasic "How to solve it", problem solving skills will be indispensable later on. $\endgroup$ – vonbrand Mar 29 '13 at 12:50

On my first day of college, my Calc III professor began by extending the properties of real numbers to $\mathbb{R}^n$ vector space. At the end of class, I came up to him, very much floored that the words "distributive property" ever made a reappearance in my life, and mumbled something about not being cut out for this and asking for a resource to do a massive review. He pointed simply to homework he just assigned and said, "That will do fine."

This is all to say that learning math is a little like learning English. The best way to improve your vocabulary is to read and look up unfamiliar words, not insist on finishing the dictionary first. Fill in holes when you get to them: the exponent rules comes first with limits and differentiation, then logarithms, then trig properties, and then all of them again with integration. Don't go back to high school, even if it is only a few weeks; you'll do just fine without it.

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    $\begingroup$ Very good. Very astute. Don't try to prepare in advance toooo much for a thing you don't-know-what-is... Rather, arrive there, discover your own needs, and respond then, with that information. $\endgroup$ – paul garrett Apr 1 '13 at 2:05
  • $\begingroup$ I think this is a great approach, I had been put off, however when I heard people warning, "if you don't have Algebra and Trig mastered you will struggle with Calculus". $\endgroup$ – Mark Apr 1 '13 at 9:20
  • $\begingroup$ But where do you start? $\endgroup$ – Surya Nov 27 '13 at 18:48

The lecture notes by William Chen cover the requested material nicely. The Trillia Group distributes good texts too.


Try Paul's Online Math notes covering algebra-precalculus, calculus and differential equations.

  • $\begingroup$ Thanks, they look good, it doesn't seem to cover Trig though, but I suppose it can be seen elswhere $\endgroup$ – Mark Mar 29 '13 at 12:29
  • $\begingroup$ @Mark there is a link near the bottom called "Algebra/Trig Review" in addition to the cheat sheets at the top of the page. $\endgroup$ – Tyler Mar 29 '13 at 12:55
  • $\begingroup$ @TylerBailey Ok I see. $\endgroup$ – Mark Mar 29 '13 at 13:43

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