2008;
193 pp;
Hardcover

MSC: Primary 26;
Secondary 12

Print ISBN: 978-0-8218-4634-6

Product Code: MBK/55

List Price: $53.00

Individual Member Price: $42.40

**Electronic ISBN: 978-1-4704-1202-9
Product Code: MBK/55.E**

List Price: $53.00

Individual Member Price: $42.40

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#### Supplemental Materials

# Tools of the Trade: Introduction to Advanced Mathematics

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*Paul J. Sally, Jr.*

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.

#### Readership

Undergraduate and graduate students interested in studying advanced mathematics.

# Table of Contents

## Tools of the Trade: Introduction to Advanced Mathematics

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Introduction ix10 free
- Acknowledgments xiii14 free
- Sets, functions, and other basic ideas 116 free
- Linear algebra 4762
- The construction of the real and complex numbers 89104
- Metric and Euclidean spaces 125140
- Complete metric spaces and the 𝑝-adic completion of ℚ 167182
- Index 189204 free
- Back Cover Back Cover1210