Course 18.784: Seminar in Number Theory

Resources

Online text:
Stein, Modular Forms, A Computational Approach
Lecture notes:
Milne, Modular Functions and Modular Forms
Dolgachev, Lecture Notes
Ribet, Lecture Notes
Exercises:
Richard Borcherds's example sheets
Previous incarnations:
2008 course web page
Calculation:
SAGE
Helena Verrill's fundamental domain applet
Wikipedia:
Poincaré half-plane, Hyperbolic geometry, Möbius transformation
The modular group (e.g., PSL2(Z))
Modular form, cusp form, Hecke operator (needs work)
Eisenstein series, Tau function, eta function, E8 lattice
Biographies:
Eisenstein
Hecke
Jacobi
Weierstrass
Similar classes elsewhere:
Warwick
UT Austin