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Texts and Readings in Mathematics

Analysis I

Third Edition

Authors: Tao, Terence

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  • Discusses all major topics of analysis in a simple, lucid manner
  • Highlights the concrete setting of the real line and Euclidean spaces
  • Provides examples, and step-by-step instructions
  • Evolves from the author’s lectures delivered at the University of California, Los Angeles
  • Covers about 30 lectures, this is part one of the two-volume book
  • Is authored by the winner of the Fields Medal        
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eBook £45.59
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  • ISBN 978-981-10-1789-6
  • Digitally watermarked, DRM-free
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About this Textbook

This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally 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. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 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.

About the authors

Terence "Terry" Chi-Shen Tao, FAA FRS, is an Australian mathematician. His areas of interests are in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Professor Tao is a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics. He maintains a personal mathematics blog, which has been described by Timothy Gowers as “the undisputed king of all mathematics blogs”.  

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Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook £45.59
price for United Kingdom (gross)
  • ISBN 978-981-10-1789-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Analysis I
Book Subtitle
Third Edition
Authors
Series Title
Texts and Readings in Mathematics
Series Volume
37
Copyright
2016
Publisher
Springer Singapore
Copyright Holder
Springer Science+Business Media Singapore
eBook ISBN
978-981-10-1789-6
DOI
10.1007/978-981-10-1789-6
Series ISSN
2366-8717
Edition Number
1
Number of Pages
XIX, 350
Topics