Subject: Linear Algebra
Recommendation: Introduction to Linear Algebra by Gilbert Strang
Reason: Strang presents the subject so clearly and intuitively that you feel like an expert on the subject after reading each chapter. It is by the far the best textbook I have encountered.
He is also an excellent teacher and offers the lecture notes to the corresponding MIT class online.
Here are the books that our university uses for first-year students combined with books that I found to be useful:
Introduction to Programming (using Eiffel) [1]
Mathematics for Computer Science (or: Discrete Mathematics) [2]
Introduction to Datastructures and Algorithms [3]
Introduction to Digital Design [4]
Parallel Programming (using Java) [5]
Optional but highly recommended, you'll probably find it completely out of scope:
Real Analysis I [6]
Real Analysis II [7]
Introduction to Linear Algebra [8]
Introduction to Physics [9]
[1]: http://www.amazon.com/Touch-Class-Learning-Program-Contracts...
[2]: http://ocw.mit.edu/courses/electrical-engineering-and-comput...
[3]: http://www.amazon.de/Introduction-Algorithms-Thomas-H-Cormen...
[4]: http://www.amazon.com/Digital-Design-Computer-Architecture-E...
[5]: http://www.amazon.com/Java-Concurrency-Practice-Brian-Goetz/...
[6]: http://www.amazon.com/Analysis-Texts-Readings-Mathematics-No...
[7]: http://www.amazon.com/Analysis-II-Texts-Readings-Mathematics...
[8]: http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gil...
[9]: http://www.amazon.com/Fundamentals-Physics-Extended-David-Ha...