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by rramadass 255 days ago
There is no one book which can give you the overall sweep of Mathematics. However, you might find the following (though not textbooks per se) useful.

1) The Princeton Companion to Mathematics by Timothy Gowers et al. and The Princeton Companion to Applied Mathematics by Nicholas Higham et al. - The closest you have to a Modern Encyclopedia of Mathematics. You get unmatched breadth after which you can move on to dedicated books as needed. Well worth the money.

2) Mathematics: Its Content, Methods and Meaning by Aleksandrov, Kolmogorov et al. - Absolutely brilliant overview of Basic Mathematics. Published by Dover and hence very affordable.

3) Elements of Mathematics: From Euclid to Gödel by John Stillwell - Written as sort of an update to the great Felix Klein's Elementary Mathematics from an Advanced Standpoint books. The Topics are particularly well chosen given modern advances; they include Arithmetic, Computation, Algebra, Geometry, Calculus, Combinatorics, Probability, Logic.