I am going to learn these math topics , please suggest me where to start?

Question

I always did poor in mathematics and i even quit my mathematics from 10th grade but since I was good in programming ( C++ and Java) I took course related to computers in my college where I am going to join now. I know Mathematics plays a vital role in programming, I am having below mentioned mathematical subjects / topics in my college, please tell me how can I learn them and what are the basics one should know to learn all the below mentioned Mathematics topics ?

1. Determinants.
2. Matrices.
3. Limit and Continuity.
4. Differentiation
5. Integration.
6. Vector Algebra.
7. Numerical Analysis ( sorry I dont have detailed info on this).
8. Differential Equations.

Now the problem is, I am really bad at Mathematics and I almost forgot few of the things I learned in my 10th std. I of course know the basics but since i never had maths in my high school, I am little scared on how will I deal with these topics. Someone please help me and suggest on how difficult these are and also tell me whether there is something I need to already know to learn these topics?

thanks a lot for your time.

Answer 1

I suggest before worrying about your college level courses, please revise the earlier material.

Udacity http://www.udacity.com has several courses which might be useful in this regard. I suggest you have a look at the following courses:
1. Intro to Algebra review
2. Visualizing Algebra
3. College Algebra
4. Introduction to Physics

I am suggesting "Introduction to Physics" because it covers some revision of Trignometry. Also the motivation for Vectors / Calculus / Differntial Equations comes from Physics.

You may also try Coursera
1. Algebra ( University of California, Irvine )
2. Pre-calculus ( University of California, Irvine )
3. Calculus: Single Variable ( University of Pennsylvania )
.

( You can try Coursera courses when they are offered. Udacity courses can be taken any time. )

Answer 2

I think every topic you mentioned has varying difficulties depending on how deeply you want to venture.. Linear Algebra (the field that includes matrices and determinants) is generally self contained and doesn't have prerequisites apart perhaps from basic algebra. It's also considered fairly straightforward. For everything else you just need to get your hands dirty!

Maybe the most important thing for you is to do exercises; Otherwise you just forget the theory.

Some Not-Overly-Rigorous Books (I only read Tenenbaum & Pollard):

Determinants and Matrices - Two simple books by Gilbert Strang are 'Introduction to Linear Algebra', and 'Linear Algebra and Its Applications'. They aren't pedantic so might be the place to start.

Limits, Continuity, Differentiation, Integration - Mark Ryan's book, 'Calculus for Dummies' has very free language. It might appeal to you if you're looking for some intuition rather than Definition-Lemma-Theorem structure.

If by Vector Algebra you mean operations on vectors such as scalar product and addition, you will find that material in Strang's books. If you mean multivariable calculus, try Morris Kline's 'Calculus: An Intuitive and Physical Approach'. This book covers everything Ryan's book does, and alot more. It also has free language, but it's more "serious" in the sense of not wasting words on irrelevant things like comforting the reader.

Differential Equations - Before learning these you need to know Calculus and Linear Algebra reasonably well. One of the classic books is 'Ordinary Differential Equations' by Tenenbaum and Pollard, but it's pretty rigorous. If you feel it's a bit hard, you can try this introductory text: 'An Introduction to Ordinary Differential Equations' by E.A Coddington.

Numerical Analysis - The programming approach to numerical analysis is probably very different from the mathematical one.. anyway, two highly reviewed Dover books (on mathematics) on Numerical Analysis are: 'Introduction to Numerical Analysis' by F.B Hilderbrand, and 'A First Course in Numerical Analysis' by Ralston and Rabinowitz.