Summer projects for students

Three students are in the midst of summer reading projects under my supervision, Acyr Locatelli, Alex Tao, and Nikhil Mehrotra.

Acyr is reading Ideals, Varieties, Algorithms by Cox, Little, and O’Shea, a very nice introduction to computational algebraic geometry.

Alex is reading Rational Points on Elliptic Curves by Silverman and Tate. This book deals with integral and rational solutions to cubic equations like

y^2=x^3+x-1000.

This class of problems, seemingly limited in scope, turns out to have many remarkable attendant structures, making it one of the most important directions of contemporary number theory.

Nikhil is reading Goedel, Escher, Bach by Douglas Hofstadter, a great classic on consciousness, mathematics, and the possibility of artificial intelligence.

I will be posting here their weekly reports, in case someone else wants to follow along. For now, here are

Alex’s report 1

Acyr’s report 1

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