UCR's Mathematics Department holds its Written Qualifying Exams at the end of summer every year, and graduate students are required to pass two exams out of the following six subjects:
Algebra
Real Analysis
Complex Analysis
Differential Equations
Applied Mathematics
Topology
To assist the Graduate student body's success, the department appoints a graduate student working in each of the six fields to run a seminar devoted to helping them review material from the year and prepare for the exams. I had the privilege of running this seminar for Algebra in 2023 and 2024. Here, I've collected some of the materials that I've created. If you'd like solutions to any of these, please let me know and I'll be happy to send them to you or discuss them with you!
Mock Qualifying Exams
Worksheets
Worksheet 1 - Groups and Rings
Worksheet 2 -Â Module Theory and Linear Algebra
Worksheet 3 - Field and Galois Theory