Wednesday, 1 August 2018

TEXTS AND READINGS IN MATHEMATICS ANALYSIS-2 BY TERENCE TAO

This is part one of a two-volume book on real analysis and is intended for seniorundergraduate students of mathematics who have already been exposed tocalculus. 


PAGE:-421
The emphasis is on rigour and foundations of analysis. Beginning withthe construction of the number systems and set theory, the book discusses thebasics of analysis (limits, series, continuity, differentiation, Riemannintegration), through to power series, several variable calculus and Fourieranalysis, and then finally the Lebesgue integral. These are almost entirely setin the concrete setting of the real line and Euclidean spaces, although thereis some material on abstract metric and topological spaces. The book also has appendiceson mathematical logic and the decimal system. The entire text (omitting someless central topics) can be taught in two quarters of 25Â30 lectures each. Thecourse material is deeply intertwined wit.


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