Softcover ISBN:  9781470456115 
Product Code:  MBK/145 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Softcover ISBN:  9781470456115 
Product Code:  MBK/145 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 

Book Details2022; 341 ppMSC: 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.
ReadershipUndergraduate students interested in number theory who appreciate geometric pictures of mathematical objects.

Additional Material

Reviews

It is a beautiful book.
D.D. Long, Notices of the AMS 
Whether for hobbyists, undergraduates, graduates, or professionals, Topology of Numbers is a worthy member of every individual's personal mathematical library...The book is assiduously written and is of a rare breed of text capable of teaching through colloquy and ratiocination rather than through the slough of 'standard' approaches...This allows instructors to easily use this book as the primary or secondary text for students at the cost of only a single book.
Caleb McWhorter , MAA Reviews


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

It is a beautiful book.
D.D. Long, Notices of the AMS 
Whether for hobbyists, undergraduates, graduates, or professionals, Topology of Numbers is a worthy member of every individual's personal mathematical library...The book is assiduously written and is of a rare breed of text capable of teaching through colloquy and ratiocination rather than through the slough of 'standard' approaches...This allows instructors to easily use this book as the primary or secondary text for students at the cost of only a single book.
Caleb McWhorter , MAA Reviews