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Background: I have a graduate degree in computer science. I was exposed to single var calculus, some linear algebra (not theoretical), linear programming, some basic convex optimization, basic probability theory and random process. Those were a long time ago though, I am sure I need a thorough review to get them back.

Purpose & Goal: Recently I feel my math skill is not enough to keep up with some of the literature I need to understand. Picked up an algebraic graph theory book, and found it too challenging to understand. I also have a plan of getting to the bottom of some of the ML topics.

So the learning goal is to first review and learn more in calculus, some analysis would be fine, as long as it is fun, but not the goal.

I am thinking of these two books:

1) Advanced Calculus, geometric view, by James Callanhan

2) Multi-variable Calculus with Application, by Lax

Which one is better? Or if one book is not enough, which combination I should get and make them complementary to each other? Suggestions?

Also, while picking a book for self-study, other criteria would be worth consideration: 1) more recent published book is preferred, b/c of the notation used etc; 2) A solution manual is easy to get access to.

Roy Huang
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    If you've never had a basic introduction to multivariable calculus, and given that you'll be studying on your own, I recommend first going through Calculus of Several Variables by Lang. Lang's book gives a crisp and non-nonsense coverage of the subject, where the big picture doesn't get lost in the details and the details aren't omitted or over-simplified. In Lang's book the discussions, examples, and main results (theorems) (continued) – Dave L. Renfro Aug 23 '22 at 07:34
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    are clearly displayed in a way that reminds me more of a Schaum's Outline book than some often praised books that may seem overwhelming by including everything under the sun (and sometimes a bunch of stuff in the shade), and thus Lang's book works well for self-study. Incidentally, when you're reading what others say about a book, the word "rigorous" is often used in two different ways -- see the first and subsequent comments to this question (click on "Show 9 more comments" at the bottom of the comments). – Dave L. Renfro Aug 23 '22 at 07:34
  • Thank you @DaveL.Renfro . Much appreciated. – Roy Huang Aug 23 '22 at 16:20
  • Of course, "non-nonsense" was intended to be "no-nonsense". I wrote some comments about Lang's book in a Stack Exchange answer within the past couple of years, but earlier today I couldn't find it. It just occurred to me which answer it might be, although I don't know why my many earlier google searches didn't find it, as the words I used in the searches (sometimes only giving 4 or 5 google hits) are all in that answer. Anyway, see the 2nd paragraph of my answer to What is a good way to teach Taylor expansion of multi-variable calculus? – Dave L. Renfro Aug 23 '22 at 17:23

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