This is a repository of course materials for Math 611: Graduate Algebra. More information can be found on Canvas. If you don't have access to Canvas for any reason, let me know ASAP.
Class information:
Syllabus
Tentative schedule
Office hours: Tuesday 10 - 11, Thursday 11:30 - 12:30, Friday 11:45 - 12:45, or by appointment.
There will be a class Discord server and we will use Gradescope for homework submission. Check Canvas for links.
Class notes:
September 5: Group basics and examples
September 7: Dihedral groups, symmetric groups, matrix groups, and the quaternions
September 12: Homomorphisms, isomorphisms, and group actions
September 14: Subgroups and examples of subgroups
September 19: Subgroups and cyclic groups
September 21: More on cyclic groups and subgroups generated by subsets
September 26: Subgroup lattices and quotient groups
September 28: Quotient groups and Lagrange's Theorem
October 3: The Isomorphism Theorems, simple and solvable groups
October 5: The alternating group, group actions, and the left multiplication action
No class October 10
October 12: Conjugation and classification results with group actions
October 17: Automorphisms and the Sylow Theorems
October 19: Applications of the Sylow Theorems to classifying groups of small order
October 24: More Sylow and semi-direct product examples
Practice Problems for the exam. The midterm exam was on October 26, in class. Students have the opportunity to re-submit two problems from the exam; see Canvas for more details.
October 31: Introduction to rings
November 7: Rings: examples, properties, homomorphisms
November 9: Ideals and properties of ideals
November 14: Prime ideals, maximal ideals, fields of fractions, and the Chinese remainder theorem
November 16: Euclidean domains, principal ideal domains, and unique factorization domains
November 28: Introduction to modules
November 30: Generation of modules, free modules, tensor products
December 5: Tensor products
December 7: Tensor algebras and finitely generated modules over PIDs
Homework assignments:
Homework 1: due September 15, at 11:59 pm
Homework 2: due September 22, at 11:59 pm
Homework 3: due TUESDAY October 3, at 11:59 pm
Homework 4: due October 15, at 11:59 pm
Homework 5: due October 20, at 11:59 pm
Optional Homework 6: here are a few problems that you may wish to do as midterm practice, but they are optional and do not need to be submitted.
Homework 7: due November 12, at 11:59 pm
Homework 8: due November 19, at 11:59 pm
Homework 9: due December 1, at 11:59 pm
Homework 10: due December 8, at 11:59 pm