MAT 1100: Algebra I, Fall 2015
Instructor: Florian Herzig;
my last name at math dot toronto dot edu
Office Hours: by appointment, at BA 6186
TA: John Enns
Lectures: Mondays 1-2pm, Fridays 2-4pm at BA 6183
Basic notions of linear algebra: brief recollection. The language of Hom spaces and the corresponding canonical isomorphisms. Tensor product of vector spaces.
Group Theory: Isomorphism theorems, group actions, Jordan-Hoelder theorem, Sylow theorems, direct and semidirect products, finitely generated abelian groups, simple groups, symmetric groups, linear groups, nilpotent and solvable groups, generators and relations.
Ring Theory: Rings, ideals, Euclidean domains, principal ideal domains, and unique factorization domains.
Modules: Modules and algebras over a ring, tensor products, modules over a principal ideal domain
Useful books for reference (I will not really follow any of them)
- Lang, Algebra, 3rd ed.
- Dummit and Foote, Abstract Algebra, 2nd ed.
The term test will be on Fri, October 23, 2:10-4pm in BA6183 (instead of class).
There will be no makeup test! If you miss the test for a valid reason, the grade will be reweighted as 35% homework and 65% final.
- Homework (roughly 5 assignments): 25%
- Term test: 25%
- Final: 50%
The final will be on Mon, December 14, 2-5pm in BA6183.
Homework (to be posted every 2-3 weeks)