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Analysis I: Third Edition

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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.

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Detail Information

Series Title

Texts and Readings in Mathematics

Call Number

515 TAO a

Publisher

Singapore : Springer Singapore., 2016

Collation

XIX, 350

Language

English

ISBN/ISSN

978-981-10-1789-6

Classification

515

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

Ed. 1

Subject(s)

Analysis

Specific Detail Info

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Statement of Responsibility

Terence Tao

Other Information

Cataloger

umi

Source

https://link.springer.com/content/pdf/10.1007/978-981-10-1789-6.pdf?pdf=button

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