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Number Systems: An Introduction to Algebra and Analysis
 
Sergei Ovchinnikov San Francisco State University, San Francisco, CA
Number Systems
Hardcover ISBN:  978-1-4704-2018-5
Product Code:  AMSTEXT/23
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-2218-9
Product Code:  AMSTEXT/23.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-1-4704-2018-5
eBook: ISBN:  978-1-4704-2218-9
Product Code:  AMSTEXT/23.B
List Price: $154.00 $116.50
MAA Member Price: $138.60 $104.85
AMS Member Price: $123.20 $93.20
Number Systems
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Number Systems: An Introduction to Algebra and Analysis
Sergei Ovchinnikov San Francisco State University, San Francisco, CA
Hardcover ISBN:  978-1-4704-2018-5
Product Code:  AMSTEXT/23
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-2218-9
Product Code:  AMSTEXT/23.E
List Price: $75.00
MAA Member Price: $67.50
AMS Member Price: $60.00
Hardcover ISBN:  978-1-4704-2018-5
eBook ISBN:  978-1-4704-2218-9
Product Code:  AMSTEXT/23.B
List Price: $154.00 $116.50
MAA Member Price: $138.60 $104.85
AMS Member Price: $123.20 $93.20
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 232015; 144 pp
    MSC: Primary 97

    This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers.

    The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.

    Ancillaries:

    Readership

    Undergraduate students interested in foundations of algebra and analysis.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Preface
    • Chapter 1. Natural numbers
    • Chapter 2. Integers
    • Chapter 3. Rational numbers
    • Chapter 4. Real numbers
    • Chapter 5. Complex numbers
    • Appendix A. Sets, relations, functions
    • Bibliography
    • Index
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    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
Volume: 232015; 144 pp
MSC: Primary 97

This book offers a rigorous and coherent introduction to the five basic number systems of mathematics, namely natural numbers, integers, rational numbers, real numbers, and complex numbers. It is a subject that many mathematicians believe should be learned by any student of mathematics including future teachers.

The book starts with the development of Peano arithmetic in the first chapter which includes mathematical induction and elements of recursion theory. It proceeds to an examination of integers that also covers rings and ordered integral domains. The presentation of rational numbers includes material on ordered fields and convergence of sequences in these fields. Cauchy and Dedekind completeness properties of the field of real numbers are established, together with some properties of real continuous functions. An elementary proof of the Fundamental Theorem of Algebra is the highest point of the chapter on complex numbers. The great merit of the book lies in its extensive list of exercises following each chapter. These exercises are designed to assist the instructor and to enhance the learning experience of the students.

Ancillaries:

Readership

Undergraduate students interested in foundations of algebra and analysis.

  • Cover
  • Title page
  • Contents
  • Preface
  • Chapter 1. Natural numbers
  • Chapter 2. Integers
  • Chapter 3. Rational numbers
  • Chapter 4. Real numbers
  • Chapter 5. Complex numbers
  • Appendix A. Sets, relations, functions
  • Bibliography
  • Index
  • Back Cover
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
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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