**Pure and Applied Undergraduate Texts**

Volume: 36;
2019;
303 pp;
Hardcover

MSC: Primary 26;

**Print ISBN: 978-1-4704-4928-5
Product Code: AMSTEXT/36**

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

**Electronic ISBN: 978-1-4704-5233-9
Product Code: AMSTEXT/36.E**

List Price: $99.00

AMS Member Price: $79.20

MAA Member Price: $89.10

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#### Supplemental Materials

# Invitation to Real Analysis

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*Cesar E. Silva*

This book is an introduction to real analysis for a one-semester
course aimed at students who have completed the calculus sequence and
preferably one other course, such as linear algebra. It does not
assume any specific knowledge and starts with all that is needed from
sets, logic, and induction. Then there is a careful introduction to
the real numbers with an emphasis on developing proof-writing
skills. It continues with a logical development of the notions of
sequences, open and closed sets (including compactness and the Cantor
set), continuity, differentiation, integration, and series of numbers
and functions.

A theme in the book is to give more than one proof for interesting
facts; this illustrates how different ideas interact and it makes
connections among the facts that are being learned. Metric spaces are
introduced early in the book, but there are instructions on how to
avoid metric spaces for the instructor who wishes to do so. There are
questions that check the readers' understanding of the material, with
solutions provided at the end. Topics that could be optional or
assigned for independent reading include the Cantor function, nowhere
differentiable functions, the Gamma function, and the Weierstrass
theorem on approximation by continuous functions.

#### Readership

Undergraduate and graduate students interested in learning and teaching undergraduate real analysis.

#### Table of Contents

# Table of Contents

## Invitation to Real Analysis

- Cover Cover11
- Title page iii4
- Preface vii8
- Chapter 0. Preliminaries: Sets, Functions, and Induction 112
- Chapter 1. The Real Numbers and the Completeness Property 4758
- Chapter 2. Sequences 7990
- Chapter 3. Topology of the Real Numbers and Metric Spaces 109120
- Chapter 4. Continuous Functions 145156
- Chapter 5. Differentiable Functions 175186
- Chapter 6. Integration 197208
- Chapter 7. Series 223234
- Chapter 8. Sequences and Series of Functions 241252
- Appendix A. Solutions to Questions 283294
- Bibliographical Notes 293304
- Bibliography 295306
- Index 299310
- Back Cover Back Cover1318