Tools of the Trade Review

Tools of the Trade
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Tools of the Trade ReviewMr. Sally's book starts with basic, almost obvious elements of the set theory that provide the logical foundation of essentially all modern mathematics. In this way, he mines the best of the 20th century's progress in solidifying those foundations. But fear not, he does not become mired in Russelian logic.
Instead, he goes on to derive and define the properties of myriad basic mathematics, up through some of the basics of topology, complex analysis and so on. A variety of statements are left for the reader to prove, though all important theorems at this level are at least stated explicitly.
The reader will go through essentially the same mental development undergone by students fortunate enough to take the famous U of Chicago Math 207 course. Budding mathematicians have been inspired by that course for generations. The proofs, where provided, are pithy and crystal clear while the exercises have a fine distribution of difficulty from trivial to tricky.
This is not a reference text by any means, but rather, as the title implies, a means to give you the skill set necessary to understand and invent real mathematics.Tools of the Trade Overview

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