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9780821846346

Tools of the Trade

by
  • ISBN13:

    9780821846346

  • ISBN10:

    0821846345

  • Format: Hardcover
  • Copyright: 2008-08-12
  • Publisher: Amer Mathematical Society

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Summary

"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."--BOOK JACKET.

Table of Contents

Sets, functions, and other basic ideas
Linear algebra The construction of the real and complex numbers
Metric and Euclidean spaces
Complete metric spaces and the $p$-adic completion of $\mathbb{Q}$
Index
Table of Contents provided by Publisher. All Rights Reserved.

Supplemental Materials

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