## Undergraduate courses

__A first course in number theory (used for Math 319)
__
__A first course in mathematics (used for Math 327)
__
## Graduate courses

__Algebra I and II (Math 520 and 521)__
__Topics in number theory I: algebraic number theory (Math 519)__
__Topics in number theory II: modular forms (Math 519)__
__Topics in number theory III: p-adic interpolation (Math 519)__
__Topics in number theory IV: Analogies between numbers and functions (Math 519) __
__Algebraic geometry, I (Math 530)__
__Algebraic geometry, II (Math 531)__
## Talks, mini-courses

__Differential calculus with integers (IHES 2011) __
__Correspondences, Fermat quotients, uniformization (Bonn, 2010) __
__Galois groups arising from arithmetic differential equations (Luminy, 2010) __
__Lectures on arithmetic differential equations (Leiden, 2009) __
__Differential algebra and diophantine geometry (Princeton, 1993)__
## Short notes

__Group actions__
__G(2,4), etc__
__SL(2,F)__
__Complex multiplication__
__Introduction to a course on zetas__
__Dwork's approach to congruence zeta__
__Schemes, moduli schemes__
__The totally ramified direction__
__Fractal dimension__
__Areas and volumes__
__Projective non-free modules__
__Introduction to "elliptic curves" or "modular forms"__
__Explicit computation of H^1(elliptic curve,O)__
__Turing, Godel, Matjiasevich__
__Some number theory exercises__
__Some algebra exercises__
__Langlangs philosophy__
__History of Galois theory__
__Some basic Galois groups__
__S_p as Galois group__
__Finite generation of invariants__
__History of p-adic analysis__
__Jordan normal form, etc__
__Artin-Hasse exponential__
__Plane curves__
__Probabilities__
__Particles and fields__
__SO(3), SU(2), etc__
__Lorentz transformations, E=mc^2__
__Gauge, matter, gravitation__
__Planck units__
__Universal gravitation__
__Classical vs quantum mechanics__
__Groups and quantum mechanics__
__Linear algebra of
quantum mechanics__
__Penrose diagram: mind/physics/mathematics__
__Galois groups Galois-style__
__Disciplines in modern university__
__Artin substitution__
__Interior, exterior, and Lie derivatives __
__Addition formulae __