David A. Cox Picture of David A. Cox

Professor of Mathematics Emeritus
Fellow of the American Mathematical Society

Department of Mathematics and Statistics

Amherst College



Lecture Notes

Here are some postscript or pdf files containing lecture notes for various lectures given between 2001 and 2012..

Recent Papers

Click here for some of my papers, posted on the Amherst College Octagon, which is a collection of open access articles written by Amherst College faculty.


Cover of CBMS Volume

Applications of Polynomial Systemss

Click here for the web page for my book Applications of Polynomial Systems, with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck and Jessica Sidman. This book is based on 10 CBMS lectures given in June 2018 and explores some wonderful applications of algebraic geometry. It is published by the American Mathematical Society.



Cover of Toric Varieties

Toric Varieties

Click here for the web page for my book Toric Varieties, written with John Little and Hal Schenck. This book is about a wonderful part of algebraic geometry that has deep connections with polyhedral geometry. It is published by the American Mathematical Society.



Cover of Galois Theory

Galois Theory

Click here for the web page for my ōbook Galois Theory. This book is about the wonderful interaction between group theory and the roots of polynomials. It is now in its second edition and is published by John Wiley & Sons. The book has been translated into Japanese.



Cover of Primes book

Primes of the Form x2 + ny2

Click here for the web page for my book Primes of the Form x2 + ny2, with contributions by Roger Lipsett. This book is about Fermat, class field theory, and complex multiplication, and was written for anyone who loves number theory. The third edition is published by the American Mathematical Society and includes complete solutions, written by Roger Lipsett and David Cox.



Cover of Ideals, Varieties and Algorithms

Ideals, Varieties, and Algorithms

Click here for the web page for my book Ideals, Varieties and Algorithms, written with John Little and Don O'Shea. This book is an introduction to algebraic geometry and commutative algebra, and was written for undergraduate math majors. It is now in its fourth edition and is published by Springer-Verlag. The book has been translated into Japanese, Russian and Persian. In January 2016, Ideals, Varieties and Algorithms was awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society.



Cover of Using Algebraic Geometry

Using Algebraic Geometry

Click here for the web page for my book Using Algebraic Geometry, also written with John Little and Don O'Shea. This book is an introduction to Gröbner bases and resultants, which are two of the main tools used in computational algebraic geometry and commutative algebra. It also discusses local methods and syzygies, and gives applications to integer programming, polynomial splines and algebraic coding theory. It is published by Springer-Verlag and is available in hardcover and paperback. The second edition appeared in the Spring of 2005. The book has also been translated into Japanese.


Cover of Mirror Symmetry and Algebraic 

Geometry

Mirror Symmetry and Algebraic Geometry

Click here for the web page for my book Mirror Symmetry and Algebraic Geometry, written with Sheldon Katz. This monograph is an introduction to the mathematics of mirror symmetry, with a special emphasis on its algebro-geometric aspects. Topics covered include the quintic threefold, toric geometry, Hodge theory, complex and Kähler moduli, Gromov-Witten invariants, quantum cohomology, localization in equivariant cohomology, and the work of Lian-Liu-Yau and Givental on the Mirror Theorem. The book is written for algebraic geometers and graduate students who want to learn about mirror symmetry. It is also a reference for specialists in the field and background reading for physicists who want to see the mathematical underpinnings of the subject. It is published by the American Mathematical Society.


You can contact me at

dacox@amherst.edu