Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics
Author:   Alejandro A. Uribe ,  Daniel A. Visscher
Publisher:   American Mathematical Society
ISBN:  

9781470452704


Pages:   182
Publication Date:   30 July 2020
Format:   Hardback
Availability:   In Print   Availability explained
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Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics


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Overview

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 rigour 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.

Full Product Details

Author:   Alejandro A. Uribe ,  Daniel A. Visscher
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Weight:   0.350kg
ISBN:  

9781470452704


ISBN 10:   1470452707
Pages:   182
Publication Date:   30 July 2020
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print   Availability explained
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Real numbers and sequences An introduction to point-set topology and continuity Differential calculus Integral calculus Discrete dynamical systems Iterating algorithms and represenations of real numbers Appendix A: Definitions, proofs, and mathematical language Appendix B: Sets and functions between sets Appendix C: Graphs Appendix D: Hints to selected problems Index.

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Author Information

Alejandro Uribe A., University of Michigan Ann Arbor, MI, USA Daniel A. Visscher, Ithaca College, NY, USA.

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