Lecture Notes

Arithmetic of Quadratic Forms. This is the expanded version of the lecture notes of a graduate course I taught. Most of the material is taken from O’Meara’s book Introduction to quadratic forms, Kitaoka’s book Arithmetic of quadratic forms, and Kneser’s book Quadratische Formen. I am sure that it still has a lot of typos and even errors; so please use it at your own risk. I appreciate and welcome any comment.

Arithmetic of Quaternion Algebras. This is the shortened version of the lecture notes I wrote for a graduate course I taught many years ago. It is hardly a polished product. Nevertheless, I think that it may be of interest to some people. A lot of the material is picked from Marie-France Vigneras’s Springer lecture notes Arithmetique des Algebres de Quaternions and the book Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan and Alan Reid.  Again, comments are welcome.