Hardcover ISBN:  9780821846346 
Product Code:  MBK/55 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470412029 
Product Code:  MBK/55.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Hardcover ISBN:  9780821846346 
eBook: ISBN:  9781470412029 
Product Code:  MBK/55.B 
List Price:  $124.00 $94.50 
MAA Member Price:  $111.60 $85.05 
AMS Member Price:  $99.20 $75.60 
Hardcover ISBN:  9780821846346 
Product Code:  MBK/55 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $52.00 
eBook ISBN:  9781470412029 
Product Code:  MBK/55.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Hardcover ISBN:  9780821846346 
eBook ISBN:  9781470412029 
Product Code:  MBK/55.B 
List Price:  $124.00 $94.50 
MAA Member Price:  $111.60 $85.05 
AMS Member Price:  $99.20 $75.60 

Book Details2008; 193 ppMSC: Primary 26; Secondary 12;
This book provides a transition from the formulafull aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics.
Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as selfstudy projects for students, or for Inquiry Based Learning activities presented by the students.ReadershipUndergraduate and graduate students interested in studying advanced mathematics.

Table of Contents

Chapters

Chapter 1. Sets, functions, and other basic ideas

Chapter 2. Linear algebra

Chapter 3. The construction of the real and complex numbers

Chapter 4. Metric and Euclidean spaces

Chapter 5. Complete metric spaces and the $p$adic completion of $\mathbb {Q}$


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This book provides a transition from the formulafull aspects of the beginning study of college level mathematics to the rich and creative world of more advanced topics. It is designed to assist the student in mastering the techniques of analysis and proof that are required to do mathematics.
Along with the standard material such as linear algebra, construction of the real numbers via Cauchy sequences, metric spaces and complete metric spaces, there are three projects at the end of each chapter that form an integral part of the text. These projects include a detailed discussion of topics such as group theory, convergence of infinite series, decimal expansions of real numbers, point set topology and topological groups. They are carefully designed to guide the student through the subject matter. Together with numerous exercises included in the book, these projects may be used as part of the regular classroom presentation, as selfstudy projects for students, or for Inquiry Based Learning activities presented by the students.
Undergraduate and graduate students interested in studying advanced mathematics.

Chapters

Chapter 1. Sets, functions, and other basic ideas

Chapter 2. Linear algebra

Chapter 3. The construction of the real and complex numbers

Chapter 4. Metric and Euclidean spaces

Chapter 5. Complete metric spaces and the $p$adic completion of $\mathbb {Q}$