**Pure and Applied Undergraduate Texts**

Volume: 44;
2020;
178 pp;
Softcover

MSC: Primary 26; 40; 54; 37;

**Print ISBN: 978-1-4704-5270-4
Product Code: AMSTEXT/44**

List Price: $85.00

AMS Member Price: $68.00

MAA Member Price: $76.50

**Electronic ISBN: 978-1-4704-5685-6
Product Code: AMSTEXT/44.E**

List Price: $85.00

AMS Member Price: $68.00

MAA Member Price: $76.50

#### Supplemental Materials

# Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics

Share this page
*Alejandro Uribe A.; Daniel A. Visscher*

This book is an introduction to the theory of calculus in the style of
inquiry-based learning. The text guides students through the process
of making mathematical ideas rigorous, from investigations and
problems to definitions and proofs. The format allows for various
levels of rigor as negotiated between instructor and students, and the
text can be of use in a theoretically oriented calculus course or an
analysis course that develops rigor gradually. Material on topology
(e.g., of higher dimensional Euclidean spaces) and discrete dynamical
systems can be used as excursions within a study of analysis or as a
more central component of a course. The themes of bisection,
iteration, and nested intervals form a common thread throughout the
text.

The book is intended for students who have studied some calculus
and want to gain a deeper understanding of the subject through an
inquiry-based approach.

#### Readership

Undergraduate students interested in an introduction to proof-based Elementary Topology and Analysis.

#### Reviews & Endorsements

Picking up this slim volume with its conversational tone will make for a friendly beginning to the study of real analysis.

-- Michele Intermont, Kalamazoo College

#### Table of Contents

# Table of Contents

## Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics

- Cover Cover11
- Title page iii5
- Copyright iv6
- Contents vii9
- Preface ix11
- Chapter 1. Real Numbers and Sequences 117
- Chapter 2. An Introduction to Point-Set Topology and Continuity 3551
- Chapter 3. Differential Calculus 5975
- Chapter 4. Integral Calculus 7995
- 4.1. The Riemann integral 8197
- 4.2. The First Fundamental Theorem of Calculus (a telescoping sum) 88104
- 4.3. Change of variables for integration 91107
- 4.4. Averages and the Mean Value Theorem for Integrals 92108
- 4.5. Accumulation and the Second Fundamental Theorem of Calculus 93109
- 4.6. Methods for finding antiderivatives 95111

- Chapter 5. Discrete Dynamical Systems 101117
- Chapter 6. Iterating Algorithms and Representations of Real Numbers 133149
- Appendix A. Definitions, Proofs, and Mathematical Language 151167
- Appendix B. Sets and Functions between Sets 159175
- Appendix C. Graphs 167183
- Appendix D. Hints to Selected Problems 173189
- Index 177193
- Back Cover Back Cover1197