Analysis Vol I & II_Terence Tao

Analysis Volume 1 & 2
Terence Tao

The two volume introduction to real analysis 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 consideration of the number system and set theory and 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 real line and Euclidean space, 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 students to actively learn the material and practice thinking and writing rigorously

About the Author:
Terence "Terry" Chi-Shen Tao FAA FRS (born 17 July 1975, Adelaide), is an Australian mathematician working in harmonic analysis, partial differential equations, additive combinatorics, ergodic Ramsey theory, random matrix theory, and analytic number theory. He currently holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. He was one of the recipients of the 2006 Fields Medal.

Tao was a child prodigy, one of the subjects in the longitudinal research on exceptionally gifted children by education researcher Miraca Gross. His father told the press that at the age of two, during a family gathering, Tao attempted to teach a 5-year-old child arithmetic and English. According to Smithsonian Online Magazine, Tao could carry out basic arithmetic by the age of two. When asked by his father how he knew numbers and letters, he said he learned them from Sesame Street.Aside from English, Tao speaks Cantonese, but cannot write Chinese.

Tao exhibited extraordinary mathematical abilities from an early age, attending university level mathematics courses at the age of nine.
He is one of only two children (besides Lenhard Ng) in the history of the Johns Hopkins' Study of Exceptional Talent program to have achieved a score of 700 or greater on the SAT math section while just 8 years old (he scored a 760).In 1986, 1987, and 1988, Tao was the youngest participant to date in the International Mathematical Olympiad, first competing at the age of ten, winning a bronze, silver, and gold medal respectively. He remains the youngest winner of each of the three medals in the olympiad's history winning the gold medal when he barely turned thirteen. At age 14, Tao attended the Research Science Institute. When he was 15 he published his first assistant paper. He received his bachelor's and master's degrees (at the age of 16) from Flinders University under Garth Gaudry. In 1992 he won a Fulbright Scholarship to undertake postgraduate study in the United States. From 1992 to 1996, Tao was a graduate student at Princeton University under the direction of Elias Stein, receiving his Ph.D. at the age of 20.He joined the faculty of the University of California, Los Angeles in 1996. When he was 24, he was promoted to full professor at UCLA and remains the youngest person ever appointed to that rank by the institution.

Product Details
Volume 1
Series: Texts and Readings in Mathematics
Hardcover: 347 pages
Publisher: Hindustan Book Agency; 2nd edition (November 12, 2009)
Language: English
ISBN-10: 8185931941
ISBN-13: 978-8185931944
Volume 2
Series: Texts and Readings in Mathematics
Hardcover: 218 pages
Publisher: Hindustan Book Agency; 2 edition (November 12, 2009)
Language: English
ISBN-10: 818593195X
ISBN-13: 978-8185931951