Description
Book SynopsisThe 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
