The Tao of Mathematics

Terence Tao is amazing. Of course he is extremely gifted- he was awarded the Fields Medal at the last ICM in Madrid in 2006- but in addition, he is articulate, prolific, and intellectually very generous. He can not only write at the most advanced level- we have his Analysis I and II listed in our Mathematics section (both a part of the superb TRIM series of books in mathematics from the HBA, New Delhi), but also for a less specialist audience.

This two-volume introduction to real analysis by Fields medalist Terence Tao, is intended for honours undergraduates, who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning - the construction of the number systems and set theory, then goes onto the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The course material is deeply intertwined with the exercises, as it is intended for the student to actively learn the material and to practice thinking and writing rigorously.

Vol I: Rs 550, 365 pages, ISBN: 9788185931944
Vol II: Rs. 350, 236 pages, ISBN: 9789380250656