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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
Explorations in Analysis, Topology, and Dynamics
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
eBook 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
Softcover ISBN:  978-1-4704-5270-4
eBook: ISBN:  978-1-4704-5685-6
Product Code:  AMSTEXT/44.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
Explorations in Analysis, Topology, and Dynamics
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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
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
eBook 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
Softcover ISBN:  978-1-4704-5270-4
eBook ISBN:  978-1-4704-5685-6
Product Code:  AMSTEXT/44.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    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.

    Readership

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

  • Table of Contents
     
     
    • 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 publishers of book reviews
    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.

Readership

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 publishers of book reviews
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
Please select which format for which you are requesting permissions.