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Topology of Numbers
 
Allen Hatcher Cornell University, Ithaca, NY
Topology of Numbers
Softcover ISBN:  978-1-4704-5611-5
Product Code:  MBK/145
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
Topology of Numbers
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Topology of Numbers
Allen Hatcher Cornell University, Ithaca, NY
Softcover ISBN:  978-1-4704-5611-5
Product Code:  MBK/145
List Price: $59.00
MAA Member Price: $53.10
AMS Member Price: $47.20
  • Book Details
     
     
    2022; 341 pp
    MSC: Primary 11

    This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the classical topic of quadratic forms with integer coefficients, a central topic of the book. Quadratic forms of this type in two variables have a very rich theory, developed mostly by Euler, Lagrange, Legendre, and Gauss during the period 1750–1800. In this book their approach is modernized by using the splendid visualization tool introduced by John Conway in the 1990s called the topograph of a quadratic form. Besides the intrinsic interest of quadratic forms, this theory has also served as a stepping stone for many later developments in algebra and number theory.

    The book is accessible to students with a basic knowledge of linear algebra and arithmetic modulo \(n\). Some exposure to mathematical proofs will also be helpful. The early chapters focus on examples rather than general theorems, but theorems and their proofs play a larger role as the book progresses.

    Readership

    Undergraduate students interested in number theory who appreciate geometric pictures of mathematical objects.

  • Reviews
     
     
    • It is a beautiful book.

      D.D. Long in Notices of the AMS
  • 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
2022; 341 pp
MSC: Primary 11

This book serves as an introduction to number theory at the undergraduate level, emphasizing geometric aspects of the subject. The geometric approach is exploited to explore in some depth the classical topic of quadratic forms with integer coefficients, a central topic of the book. Quadratic forms of this type in two variables have a very rich theory, developed mostly by Euler, Lagrange, Legendre, and Gauss during the period 1750–1800. In this book their approach is modernized by using the splendid visualization tool introduced by John Conway in the 1990s called the topograph of a quadratic form. Besides the intrinsic interest of quadratic forms, this theory has also served as a stepping stone for many later developments in algebra and number theory.

The book is accessible to students with a basic knowledge of linear algebra and arithmetic modulo \(n\). Some exposure to mathematical proofs will also be helpful. The early chapters focus on examples rather than general theorems, but theorems and their proofs play a larger role as the book progresses.

Readership

Undergraduate students interested in number theory who appreciate geometric pictures of mathematical objects.

  • It is a beautiful book.

    D.D. Long in Notices of the AMS
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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