Books and Articles / Number Theory and Geometry
Free version
Number Theory and Geometry
An Introduction to Arithmetic Geometry
In this page you can find a free version of my book “Number Theory and Geometry”, which was published by the American Mathematical Society in 2019, as part of their Pure and Applied Undergraduate Mathematics Texts Series.
PDF, 4.4 MB.
Some notes
- I would like to thank the AMS for allowing me to post a free version of the book.
- Please note that the free version is not equivalent to the published version. The AMS put many hours into polishing and editing the manuscript before printing, so please consider supporting the AMS publishing by purchasing their books! The official page for the book is here: https://bookstore.ams.org/amstext-35
- I keep a page with updates/comments/errata (which will hopefully be incorporated in a later version/edition of the book). Thanks to all who have contacted me with comments!
Contents
- Front matter
- Preface
- 1Introduction
- Part 1 · Integers, Polynomials, Lines, and Congruences
- 2The Integers
- 3The Prime Numbers
- 4Congruences
- 5Groups, Rings, and Fields
- 6Finite Fields
- 7The Theorems of Wilson, Fermat, and Euler
- 8Primitive Roots
- Part 2 · Quadratic Congruences and Quadratic Equations
- 9An Introduction to Quadratic Equations
- 10Quadratic Congruences
- 11The Hasse–Minkowski Theorem
- 12Circles, Ellipses, and the Sum of Two Squares Problem
- 13Continued Fractions
- 14Hyperbolas and Pell’s Equation
- Part 3 · Cubic Equations and Elliptic Curves
- 15An Introduction to Cubic Equations
- 16Elliptic Curves
- Back matter
- Bibliography
- Index
Also on my UConn page. Contents from the AMS Bookstore.