A quiver is a directed graph whose properties give valuable insight into various areas of mathematics.
In this course we will introduce more advanced topics in
algebra---representation theory, homological algebra, algebraic
geometry, and category theory---through the common theme of a quiver and
the category repQ.
By choosing to work with quivers as our tool of choice we are able to
present examples very tangibly, overcoming difficulty associated to the
traditional abstractions that are present in these subjects.
The material requires only a familiarity with linear algebra, experience with proofs is necessary.
If time permits, we may also discuss special topics and/or workshops
(some ideas I have involve computer algebra systems, but we will discuss
this later).
Grading & Policies
The final grade is determined by Attendance/Participation (10%), Homework (40%), Midterm (20%), and a Final Project (30%).
Homework: See below. Midterm: There is one open-note midterm, on March 10 in class. Final Project: Students will research a topic related to quivers
in some form (research paper, famous theorem, etc...) and prepare a
short presentation for the rest of the course.
I can recommend topics for this presentation based on the students' interests.
References
A quick search will result in many notes on quivers, ones that I have used (including my own notes) are listed below.
There will be roughly five homework assignments, assigned on Friday and
due two weeks later. The pdf, as well as the associated tex file, will
be posted below. Solutions will also be posted after assignment due
dates.