| Hardcover ISBN: | 978-0-8218-4634-6 |
| Product Code: | MBK/55 |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| eBook ISBN: | 978-1-4704-1202-9 |
| Product Code: | MBK/55.E |
| List Price: | $59.00 |
| MAA Member Price: | $53.10 |
| AMS Member Price: | $47.20 |
| Hardcover ISBN: | 978-0-8218-4634-6 |
| eBook: ISBN: | 978-1-4704-1202-9 |
| 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: | 978-0-8218-4634-6 |
| Product Code: | MBK/55 |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $52.00 |
| eBook ISBN: | 978-1-4704-1202-9 |
| Product Code: | MBK/55.E |
| List Price: | $59.00 |
| MAA Member Price: | $53.10 |
| AMS Member Price: | $47.20 |
| Hardcover ISBN: | 978-0-8218-4634-6 |
| eBook ISBN: | 978-1-4704-1202-9 |
| 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 |
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Book Details2008; 193 ppMSC: Primary 26; Secondary 12
This book provides a transition from the formula-full 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 self-study projects for students, or for Inquiry Based Learning activities presented by the students.
ReadershipUndergraduate and graduate students interested in studying advanced mathematics.
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Table of Contents
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Chapters
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Chapter 1. Sets, functions, and other basic ideas
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Chapter 2. Linear algebra
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Chapter 3. The construction of the real and complex numbers
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Chapter 4. Metric and Euclidean spaces
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Chapter 5. Complete metric spaces and the $p$-adic completion of $\mathbb {Q}$
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk 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
- Requests
This book provides a transition from the formula-full 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 self-study 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 $\mathbb {Q}$
