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?