Fall 2015
Week 1: August 3 - 7: Recollection from group theory and Galois theory. Notes 1
Week 2: August 10 - 14: Galois' Theorem on solvability by radicals. Homework 1 (due on 21/08).
Week 3: August 17 - 21: Jordan-Holder series. Recollection of rings and modules. Chain conditions. Notes 2
Week 4: August 24 - 28: Jordan-Holder Theorem. Automorphisms of the symmetric group.
Week 5: August 31 - September 4: Class on 01/09, Midterm exam 1 on 04/09 covering material taught until 28/08.
Week 6: September 7 - 11: Split Exact Sequences, Semisimple modules. Notes 3. Homework 2 (due on 18/09).
Week 7: September 14 - 18: Semisimple rings, Schur’s Lemma
Week 8: September 21 - 25: Classes on 22/09 and 23/09, holiday on 25/09. Jacobson Radical.
Week 9: September 28 - October 2: Classes on 29/09 and 30/09, holiday on 02/10, extra class on 29/09 at 2-3pm. Krull-Schmidt Theorem. Homework 3 (due on 16/10).
Week 10: October 5 - 9: Midterm exam 2 on 07/10 covering material taught between 31/08 and 30/09. No class on 09/10. Projective and Injective Modules. Notes 4
Week 11: October 12 - 16: Tensor Product, Homology of complexes, Finitely presented modules, Divisible Modules.
Week 12: October 19 - 23: Midsemester break
Week 13: October 26 - 30: Faithfully Flat Modules.
Week 14: November 2 - 6: Wedderburn’s Principal Theorem. Homework 4 (due on 13/11). Notes 5.
Week 15: November 9 - 13: Presentations. Homework 5 (due on 01/12).
Week 16: November 16 - 20: Presentations on Central Simple Algebras, Brauer Group and Clifford algebras.
Week 17: November 23 - 27: Class only on 24/11. Review.
Week 18: November 30 - December 4: Final exam on 01/12.
* Several parts of the lecture notes are borrowed from a course taught by Prof. R. Sridharan at CMI.