Analysis II (Texts and Readings in Mathematics) - Hardcover

Tao, Terence

Hardcover

ISBN 10: 9380250657 ISBN 13: 9789380250656

Publisher: Hindustan Book Agency, 2014

Synopsis

This is part two of a two-volume introduction to real analysis and 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 on to 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 entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.

The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.

In the third edition, several typos and other errors have been corrected and a few new exercises have been added.

About this title

About the Author

Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Applied Mathematics (2010), the Alan T Waterman Award from the National Science Foundation (2008), the SASTRA Ramanujan Prize (2006), the Clay Research Award from the Clay Mathematical Institute (2003), the Bocher Memorial Prize from the American Mathematical Society (2002) and the Salem Prize (2000).

From the Back Cover

Thisis part two of a two-volume book on real analysis and is intended for seniorundergraduate students of mathematics who have already been exposed tocalculus. 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 25 30 lectures each. Thecourse material is deeply intertwined with the exercises, as it is intendedthat the student actively learn the material (and practice thinking and writingrigorously) by proving several of the key results in the theory.

Edition details

• Publisher: Hindustan Book Agency
• Publication date: 2014
• Language: English
• ISBN 10: 9380250657
• ISBN 13: 9789380250656
• Binding: Hardcover
• Edition number: 3
• Number of pages: 236