Mathematics and Logic (Dover Books on Mathematics) by Mark Kac, Stanislaw M. Ulam
Mathematics and Logic (Dover Books on Mathematics) by Mark Kac, Stanislaw M. Ulam PDF, ePub eBook D0wnl0ad
The volume begins with a discussion of problems involving integers in which ideas of infinity appear and proceeds through the evolution of more abstract ideas about numbers and geometrical objects. The authors show how mathematicians came to consider groups of general transformations and then, looking upon the sets of such subjects as spaces, how they attempted to build theories of structures in general. Also considered here are the relations between mathematics and the empirical disciplines, the profound effect of high-speed computers on the scope of mathematical experimentation, and the question of how much mathematical progress depends on "invention" and how much on "discovery." For mathematicians, physicists, or any student of the evolution of mathematical thought, this highly regarded study offers a stimulating investigation of the essential nature of mathematics.
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