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I am a computer engineering student and lately every thing I see includes math. I have taken all the math courses any one in college should have taken (high school : alg,trig & geom, -sophomore: calc1,clc2,linear algbra & diff eqt). But because most math taught these days is in a way that is here is the equation here some example here the exam, I really hated math and just took those courses as a pass/fail ones.

Now I need to do something about this and I have seen the promotion of the coursera course about how to think mathematically, after that I realized that there exist a way to really understand the "WHY" behind all those equations and that math isn't as dry and dull as it sounds.

So basically I thought I could start with calculus, but I read you should be very good in algebra, trig and geometry to do that.

So my Question are:

1) Do I really need to start it from the beginning and read books on the ALG,TRIG & GEOM?! Or should I just jump into calculus.

2) I have found several books : "Calculus Made Easy", "Calculus: An Intuitive Approach", " Calculus, 4th edition by Michael Spivak" which one of those should I choose?

3) After calculus where should I go next to continue on other topics on math that would benefit me?

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  • $\begingroup$ Spivak's calculus is a popular book for your sort of purpose. After that, you'd probably want an introductory text to Real Analysis and one for Algebra. $\endgroup$ – Newb Oct 28 '13 at 3:38
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    $\begingroup$ I hate to break it down to you, but it looks like you had crap teachers. This definitely is not the way mathematics is taught at most universities. Mathematics is about deep understanding and writing proofs, that's the way I've been taught math, and I was an engineering major. $\endgroup$ – Phonon Oct 28 '13 at 3:38
  • $\begingroup$ What I've learned about CS is that it needs solid Math. By Math, people usually understand "formula" and "triangle", but there is so much more to it. That being said, I would go over almost all of it again. Assuming you have the time for it, checking the basics to finally get to calculus might be a good idea. If you want to go really deep and very math-thinking like, check basic Set Theory. After you get the idea of how Math "works", then you will see theorems and proofs from a completely different angle! $\endgroup$ – Cehhiro Oct 28 '13 at 3:39
  • $\begingroup$ If you really want to know the "WHY" behind calculus by self-learning, then Hardy's "A Course of Pure Mathematics" is best choice. It is much less formal compared to Spivak. What Spivak does in 630 pages, Hardy does in 512 pages and he does it much better. As a side benefit you get the literary enjoyment due to very well written prose. Hardy's book is specially written to be read without any external help from any kind of tutor/teacher. $\endgroup$ – Paramanand Singh Oct 28 '13 at 3:51
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To answer your first question, you should self-test on algebra, trigonometry, and geometry. But truthfully, you do need a good foundation on all three, except formally with geometry. I got by without knowing much of the definitions in geometry, but I certainly had to think within the bounds of the Cartesian plane a lot.

Calculus will be work.

To answer your second question, I would use Stewart's version. It is not pedantic in the single bit.

Third, after covering the entire calculus book you should proceed to take a class that is proof-based and concentrates on proof-writing. Then come the Real Analysis, Algebra, etc. courses you can take because you know how to write and understand these proofs. It is basically just formal writing.

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  • $\begingroup$ I think we used the stewart book in calc1 & 2 but I didnt find it helpful to really understand derivatives nor limits, and couldnt find a solution manual for it. $\endgroup$ – Karim Tarabishy Oct 28 '13 at 3:48
  • $\begingroup$ If you didn't understand derivatives, how can you understand change?! "Mathematics is the abstract study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change." There is a solution for odd-numbered exercises however. $\endgroup$ – Don Larynx Oct 28 '13 at 3:51

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