عنوان

Number theory and geometry :

(Number (ISBN

147045016X

(Number (ISBN

9781470450168

Title Proper

Number theory and geometry :

General Material Designation

[Book]

Other Title Information

an introduction to arithmetic geometry /

First Statement of Responsibility

Álvaro Lozano-Robledo.

Place of Publication, Distribution, etc.

Providence, Rhode Island :

Name of Publisher, Distributor, etc.

American Mathematical Society,

Date of Publication, Distribution, etc.

[2019]

Specific Material Designation and Extent of Item

xv, 488 pages ;

Dimensions

27 cm.

Series Title

Pure and applied undergraduate texts ;

Volume Designation

35

Text of Note

Includes bibliographical references and index.

Text of Note

Introduction -- Part 1. Integers, Polynomials, Lines, and Congruences: The Integers -- The Prime Numbers Congruences -- Groups, Rings, and Fields -- Finite Fields -- The Theorems of Wilson, Fermat, and Euler -- Primitive Roots -- Part 2. Quadratic Congruences and Quadratic Equations: An Introduction to Quadratic Equations -- Quadratic Congruences -- The Hasse-Minkowski Theorem -- Circles, Ellipses, and the Sum of Two Squares Problem -- Continued Fractions -- Hyperbolas and Pell's Equation -- Part 3. Cubic Equations and Elliptic Curves: An Introduction to Cubic Equations -- Elliptic Curves

0

Text of Note

Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level. -- Provided by publisher.

Arithmetical algebraic geometry, Textbooks.

Number theory, Textbooks.

Algebraic geometry -- Arithmetic problems. Diophantine geometry -- Arithmetic problems. Diophantine geometry.

Arithmetical algebraic geometry.

Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Arithmetic algebraic geometry (Diophantine geometry).

Number theory.

Number theory.

Number

Edition

Class number

Book number

Class number

System Code

Lozano-Robledo, Álvaro,1978-

Date of Transaction

20200823025858.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y