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This is a good reference. It is basically an encyclopedia, so some sections are better than others. I'm not a big fan of Gowers' intro, it is very heavy and could have done much more in the way of explaining how to navigate the volume itself. It is generally assumed that you know integral and differential calculus.

If you are daunted by mathematical formulas and don't have a solid basis in math generally, I would recommend Pickover's "The Math Book"[1]. Very engaging; good short, non-technical descriptions of many of the same topics in Princeton; lots of pretty pictures.

[1] http://www.amazon.com/Math-Book-Pythagoras-Milestones-Mathem...

How deep does Pickover's book go? I read in the reviews that each topic is limited to one page only, so I presume the real mathematics would not be covered. In other words, after reading this, will I understand the topics or would just understand things about them?

I also see a Physics book by the same author, but have the same question there too: http://www.amazon.com/Archimedes-Hawking-Science-Great-Behin...

IIRC there are a few things that are simple enough to actually explain in a page, but yes, one page per...artifact? Very little real mathematics, you will just understand things about them. It is, however, the best written of these pop-math type books that I've come across. If you are comfortable with undergraduate-level mathematics, the Princeton Guide is a much better book for getting an idea about a specific topic. Pickover's book is more for getting a feel for what topics are out there. They were written for two very different audiences and I like them both for different reasons.

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