Course Notes

Undergraduate algebra

• central functions
• Burnside pq theorem
• Hilbert Nullstellensatz
• examples of character tables
• character tables of S5 and A5
• solving cubic and quartic equations
• notes on semisimple algebras
• symmetric polynomials
• a short summary of elementary number theory

Graduate courses

Algebraic Number theory
• Fall 1993, by Jeff Achter
• Spring 1994, by Jeff Achter
• 1996-97
• Fall 2014
• Fall 2016
• Fall 2022
• Spring 2023
• Complex algebraic geometry, spring 1996
• Ellilptic functions, spring 2015
• Commutative algebra, spring 2025
• Faltings's original proof of the Mordell conjecture, fall 2023
• Faltings's proof of Lang's conjecture via diophantine approximation
• Algebras with involution and linear algebraic groups, fall 2024