Softcover ISBN:  9781470452704 
Product Code:  AMSTEXT/44 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Electronic ISBN:  9781470456856 
EPUB ISBN:  9781470468279 
Product Code:  AMSTEXT/44.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 

Book DetailsPure and Applied Undergraduate TextsVolume: 44; 2020; 178 ppMSC: Primary 26; 40; 54; 37;
This book is an introduction to the theory of calculus in the style of inquirybased 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 inquirybased approach.ReadershipUndergraduate students interested in an introduction to proofbased Elementary Topology and Analysis.

Table of Contents

Chapters

Real numbers and sequences

An introduction to pointset 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


Additional Material

Reviews

Perhaps the biggest challenge for those instructors wishing to use inquirybased 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


RequestsReview Copy – for reviewers who would like to review an AMS bookDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This book is an introduction to the theory of calculus in the style of inquirybased 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 inquirybased approach.
Undergraduate students interested in an introduction to proofbased Elementary Topology and Analysis.

Chapters

Real numbers and sequences

An introduction to pointset 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 inquirybased 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