I'm a bachelor student majoring in math, and pretty interested in physics. I would like a book to study for classical mechanics, that will prepare me to work through Goldstein's Classical Mechanics. What books would be good for a beginner?
Goldstein's Classical Mechanics is a masterpiece. That's why it's still held in such high regard as one of the best mechanics books available 60 years later after after 3 revisions.
I would suggest that you should stick with this book and work through it slowly. If that is too difficult then slooooowly. I'm pretty thick, to be honest, which is why I had no problem over the embarrassment of taking a week trying to understand a page of the first chapter sometimes. Others would take a month, and others I still don't understand fully.
I don't think any book comes anywhere close to explaining mechanics concisely and accurately in the first chapter, where others take 300 pages and yet still gloss over the details.
Assuming that you have studied introductory mechanics at the level of freshman physics, The best book on mechanics after that to tackle is Classical Mechanics by John R. Taylor. It is very clear and insightful. The author is a very good writer, he has written also the best introductory book on error analysis.
Besides Classical Mechanics What I have used in my studies is An Introduction to Mechanics.
I think Goldstein is a great book which should be supplemented by the internet, rather than a mass of books to clarify every detail.
There's the MIT OpenCourseWare program for classical mechanics:
Here you'll find the videos by prof Lewin, lectures notes, exam questions, study groups etc.
There's also the 10 classical mechanics videos by Prof Susskind of Stanford, but on a level around that of Goldstein:
Since I'm not a math major and have little direct experience with math people learning physics, my answer here is pure speculation. I'll offer it anyway.
You don't want something like Arnold's mathematical book on mechanics. That would be new material, but essentially familiar to you and inside your comfort zone. If you're interested in learning physics for its own sake, what you want to focus on isn't the mathematical structure of the theory, but the physical intuition, since that's where you pick up something new and exciting.
In that vein, I recommend
Thinking Physics by Lewis Carroll Epstein
The Feynman Lectures on Physics
The Mathematical Mechanic by Mark Levi
You might be interested in Eugene Hecht's book: http://www.amazon.com/Physics-Calculus-Eugene-Hecht/dp/0534339859
What I like about it is that both fundamental principles (notably Noether's principle) and basic but important techniques (like dealing with significant digits) are consistently mentioned and enforced throughout the book. It also contains a lot of examples and exercices of varying levels of difficulty.