Description

Book Synopsis
The field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book provides an introduction to number theory and arithmetic geometry, the goal being to use geometry as the motivation to prove the main theorems in the book.

Table of Contents
  • Introduction
  • 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
  • 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
  • Cubic equations and elliptic curves: An introduction to cubic equations
  • Elliptic curves
  • Bibliography
  • Index

    Number Theory and Geometry An Introduction to

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      £78.30

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      Order before 4pm today for delivery by Mon 22 Jun 2026.

      A Hardback by Alvaro Lozano-Robledo

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        View other formats and editions of Number Theory and Geometry An Introduction to by Alvaro Lozano-Robledo

        Publisher: American Mathematical Society
        Publication Date: 30/06/2019
        ISBN13: 9781470450168, 978-1470450168
        ISBN10: 147045016X

        Description

        Book Synopsis
        The field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book provides an introduction to number theory and arithmetic geometry, the goal being to use geometry as the motivation to prove the main theorems in the book.

        Table of Contents
        • Introduction
        • 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
        • 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
        • Cubic equations and elliptic curves: An introduction to cubic equations
        • Elliptic curves
        • Bibliography
        • Index

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