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

Alejandro Uribe A. University of Michigan, Ann Arbor, MI
Daniel A. Visscher Ithaca College, Ithaca, NY
Available Formats:
Softcover ISBN: 978-1-4704-5270-4
Product Code: AMSTEXT/44
List Price: $85.00 MAA Member Price:$76.50
AMS Member Price: $68.00 Electronic ISBN: 978-1-4704-5685-6 EPUB ISBN: 978-1-4704-6827-9 Product Code: AMSTEXT/44.E List Price:$85.00
MAA Member Price: $76.50 AMS Member Price:$68.00
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List Price: $127.50 MAA Member Price:$114.75
AMS Member Price: $102.00 Click above image for expanded view Explorations in Analysis, Topology, and Dynamics: An Introduction to Abstract Mathematics Alejandro Uribe A. University of Michigan, Ann Arbor, MI Daniel A. Visscher Ithaca College, Ithaca, NY Available Formats:  Softcover ISBN: 978-1-4704-5270-4 Product Code: AMSTEXT/44  List Price:$85.00 MAA Member Price: $76.50 AMS Member Price:$68.00
 Electronic ISBN: 978-1-4704-5685-6 EPUB ISBN: 978-1-4704-6827-9 Product Code: AMSTEXT/44.E
 List Price: $85.00 MAA Member Price:$76.50 AMS Member Price: $68.00 Please Note: Purchasing the electronic version includes access to both a PDF and EPUB version Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$127.50 MAA Member Price: $114.75 AMS Member Price:$102.00
• Book Details

Volume: 442020; 178 pp
MSC: Primary 26; 40; 54; 37;

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.

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

• Chapters
• 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

• Reviews

• Perhaps the biggest challenge for those instructors wishing to use inquiry-based learning is developing suitable materials. In this text, that challenge has been nicely met. This is not simply a list of examples to work out and theorems to prove. Well, it is collection of statements to prove, but it also includes some questions designed to help students think about expanding examples and comments designed to help students connect ideas. The authors do a nice job, too, of developing expectations of rigor as the text advances. For example, as the book begins, the authors use words more than symbolic language, gradually increasing the amount of symbolic language as the chapters progress.

Michele Intermont, Kalamazoo College
• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 442020; 178 pp
MSC: Primary 26; 40; 54; 37;

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.

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

• Chapters
• 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
• Perhaps the biggest challenge for those instructors wishing to use inquiry-based learning is developing suitable materials. In this text, that challenge has been nicely met. This is not simply a list of examples to work out and theorems to prove. Well, it is collection of statements to prove, but it also includes some questions designed to help students think about expanding examples and comments designed to help students connect ideas. The authors do a nice job, too, of developing expectations of rigor as the text advances. For example, as the book begins, the authors use words more than symbolic language, gradually increasing the amount of symbolic language as the chapters progress.

Michele Intermont, Kalamazoo College
• 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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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