Topology of numbers
Hatcher, Allen,
Topology of numbers - Rhode Island : American Mathematical Society, 2022. - ix, 341p. : illustrations ; 26 cm
Includes bibliographical references (pages 338-339) and index.
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.
9781470456115
Geometry of numbers.
Algebraic topology.
Number theory.
Number theory -- Instructional exposition (textbooks, tutorial papers, etc.).
515.14 / HAT-T
Topology of numbers - Rhode Island : American Mathematical Society, 2022. - ix, 341p. : illustrations ; 26 cm
Includes bibliographical references (pages 338-339) and index.
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.
9781470456115
Geometry of numbers.
Algebraic topology.
Number theory.
Number theory -- Instructional exposition (textbooks, tutorial papers, etc.).
515.14 / HAT-T
