Recommended books to stay sharp

Question

Alight dudes, so I'm starting a CS/Math major in March ( well hopefully at least ) and I'm scared I might be a little rusty to start ( I'm 22 so not directly after school ), now my intention is to prepare myself for the rigorous ordeal ahead by being on top of things and sharpening my math skills and intuition, so I'd like some of you guys to help me out by suggesting some books ( preferably available online ) with a LOT of exercises to help me out, anything that includes an introduction to calculus I & II, linear algebra and some basic integration techniques would be good. Thanks in advance!

Answer 1

Highly recommend Apostol's Calculus I & II. These can be found online for free at http://www.matematica.net/portal/e-books/Apostol%20-%20CALCULUS%20-%20VOLUME%201%20-%20One-Variable%20Calculus,%20with%20an%20Introduction%20to%20Linear%20Algebra.pdf and http://www.matematica.net/portal/e-books/Apostol%20-%20CALCULUS%20-%20VOLUME%202%20-%20Multi%20Variable%20Calculus%20and%20Linear%20Algebra,%20with%20Applications%20to%20Differential%20Equations%20and%20Probability.pdf, respectively.

The second volume covers linear algebra, so you should be good, but it can get pretty pedantic. Another good lin alg book is Linear Algebra Done Wrong which can be found online for free at https://sites.google.com/a/brown.edu/sergei-treil-homepage/linear-algebra-done-wrong.

Answer 2

Not exactly what you are asking for, but to start your leveling up I recommend to read

A mathematical bridge: an intuitive journey in higher mathematics (second edition)

Answer 3

You might like Erdman's Exercises and Problems in Calculus. It contains a lot more than you will need, but starts from the beginning and seems quite exhaustive. It also contains answers to the odd-numbered exercises.

As for linear algebra, I would recommend Sergei Treil's Linear Algebra Done Wrong. It covers a nice selection of topics, is quite well written and has lots of good exercises.