# Analysis I

## Third Edition

Part of the Texts and Readings in Mathematics book series (TRIM, volume 37)

Part of the Texts and Readings in Mathematics book series (TRIM, volume 37)

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.

natural numbers Set theory Integers and rationals real numbers Limits of sequences Series Continuous functions Dierentiation of functions Riemann integral

- DOI https://doi.org/10.1007/978-981-10-1789-6
- Copyright Information Springer Science+Business Media Singapore 2016
- Publisher Name Springer, Singapore
- eBook Packages Mathematics and Statistics
- Online ISBN 978-981-10-1789-6
- Series Print ISSN 2366-8717
- Series Online ISSN 2366-8725
- About this book