- Fall 2016: This semester I am teaching Basic Number Theory (MA523).
- Summer 2016: This was a reading course on Representation Theory of Lie Algebras, (it covered Harish-Chandra's isomorphism theorem, Weyl's character formula) offered to Nagarjuna Chary, a BS-MS student at IISER, Pune.
- Fall 2015: Group Theory - for undergraduate students in their 5th semester. The material covered in this course included
the basic definitions (groups, subgroups, normal subgroups, normalizers, ...), quotient groups associated to normal subgroups,
their universal property (also known as one of the isomorphism theorems), group actions, Cauchy's theorem, Sylow's theorems, semidirect products. In the assignments finite abelian groups were classified up to isomorphism, it was shown that the alternating groups are simple
for n ≥ 5, among other interesting facts.
You can find the assignments here and a photograph of (most of) us here.
- Spring 2015: Algebraic Number Theory - We covered the material in the first 5 chapters of Marcus and the first chapter
of Washington's book on Cyclotomic fields, the latter contains a proof of Fermat's Last Theorem in a nontrivial special case.
An important aim of this course (at least for me) was to understand the proof of the Kronecker-Weber Theorem, as outlined
in the exercises in Daniel Marcus' Number Fields. You can find a photograph of us
- Fall 2014: Galois Theory - We proved the Galois correspondence for finite extensions and some other interesting theorems from Lang's Algebra. Along the way we also covered finite fields, cyclotomic polynomials and saw why the Galois correspondence (for finite extensions) does not work for infinite extensions, but we did not see how to rectify this. You can find a photograph of us here.