Not the same type of book, but you could do a lot worse than reading through Mathematics: Its Content, Methods and Meaning, by M. A. Lavrent’ev, A. D. Aleksandrov, A. N. Kolmogorov. It's an amazing book which gives a mathematical (but not rigorous in the sense of proofs etc.) overview of most of mathematics. http://www.amazon.com/Mathematics-Content-Methods-Meaning-Do... (http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/)
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Mathematics: Its Content, Methods and Meaning
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