## About this book

### Introduction

This innovative textbook bridges the gap between undergraduate analysis and graduate measure theory by guiding students from the classical foundations of analysis to more modern topics like metric spaces and Lebesgue integration. Designed for a two-semester introduction to real analysis, the text gives special attention to metric spaces and topology to familiarize students with the level of abstraction and mathematical rigor needed for graduate study in real analysis. Fitting in between analysis textbooks that are too formal or too casual,

*From Classical to Modern Analysis*is a comprehensive, yet straightforward, resource for studying real analysis.Instructors who want to demonstrate the uses of measure theory and explore its advanced applications with their undergraduate students will find this textbook an invaluable resource. Advanced single-variable calculus and a familiarity with reading and writing mathematical proofs are all readers will need to follow the text. Graduate students can also use this self-contained and comprehensive introduction to real analysis for self-study and review.

### Keywords

Lebesgue integral real analysis measure theory Euclidean spaces metric spaces numerical series power series Cauchy sequences

### Bibliographic information

- DOI https://doi.org/10.1007/978-3-319-94583-5
- Copyright Information Springer International Publishing AG, part of Springer Nature 2018
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-94582-8
- Online ISBN 978-3-319-94583-5
- Buy this book on publisher's site