Overview
- Presents a foundation text on real analysis for undergraduate and graduate students of mathematics
- Emphasizes on number systems and set theory than in comparable analysis
- Is the first book of a two-volume textbook on real analysis
Part of the book series: Texts and Readings in Mathematics (TRIM, volume 37)
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About this book
This is the first book of a two-volume textbook on real analysis. Both the volumes—Analysis I and Analysis II—are intended for honors undergraduates who have already been exposed to calculus. The emphasis is on rigor and foundations. The material starts at the very beginning—the construction of number systems and set theory (Analysis I, Chaps. 1–5), then on to the basics of analysis such as limits, series, continuity, differentiation, and Riemann integration (Analysis I, Chaps. 6–11 on Euclidean spaces, and Analysis II, Chaps. 1–3 on metric spaces), through power series, several variable calculus, and Fourier analysis (Analysis II, Chaps. 4–6), and finally to the Lebesgue integral (Analysis II, Chaps. 7–8). There are appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) is in two quarters of twenty-five to thirty lectures each.
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Table of contents (11 chapters)
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Authors and Affiliations
About the author
Terence Tao has been a professor of Mathematics at the University of California Los Angeles (UCLA), USA, since 1999, having completed his Ph.D. under Prof. Elias Stein at Princeton University, USA, in 1996. Tao's areas of research include harmonic analysis, partial differential equations, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal in 2006, the MacArthur Fellowship in 2007, the Waterman Award in 2008, the Nemmers Prize in 2010, the Crafoord Prize in 2012, and the Breakthrough Prize in Mathematics in 2015. Terence Tao also currently holds the James and Carol Collins chair in Mathematics at UCLA and is a fellow of the Royal Society, the Australian Academy of Sciences (the corresponding member), the National Academy of Sciences (a foreign member), and the American Academy of Arts and Sciences. He was born in Adelaide, Australia, in 1975.
Bibliographic Information
Book Title: Analysis I
Book Subtitle: Fourth Edition
Authors: Terence Tao
Series Title: Texts and Readings in Mathematics
DOI: https://doi.org/10.1007/978-981-19-7261-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Hindustan Book Agency 2022
eBook ISBN: 978-981-19-7261-4Published: 22 February 2023
Series ISSN: 2366-8717
Series E-ISSN: 2366-8725
Edition Number: 2
Number of Pages: X, 340
Topics: Analysis