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Tools of the Trade: Introduction to Advanced Mathematics
 
Paul J. Sally, Jr. University of Chicago, Chicago, IL
Tools of the Trade
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
Tools of the Trade
Click above image for expanded view
Tools of the Trade: Introduction to Advanced Mathematics
Paul J. Sally, Jr. University of Chicago, Chicago, IL
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
  • Book Details
     
     
    2008; 193 pp
    MSC: 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.

    Readership

    Undergraduate 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 $\mathbb {Q}$
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
2008; 193 pp
MSC: 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.

Readership

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 $\mathbb {Q}$
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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