Instructor: Prof. Gregory G. Smith
Email: 

Registration Deadline: September 12th, 2022
Lecture Times: Tuesday and Thursday | 10:00 - 11:30 am (ET)
Office Hours: TBD
Course Dates: September 6th - December 1st, 2022
Mid-Semester Break: October 10th - 14th, 2022
Registration Fee: PSU Students - Free | Other Students - $500 CAD
Prerequisites: Familiarity with modules over a commutative ring, homomorphism between them, and some basic constructions such as direct sums and tensor products will be assumed. Most graduate-level courses in algebra would be more than sufficient preparation. Excellent knowledge of abstract linear algebra should also be enough.
Evaluation: Students are expected to attend lectures, work on assignments, and a short presentation. The final grade will be based on a combination of these activities.

Capacity Limit: N/A

Format: Online

Course Description

This course will be an introduction to homological algebra. Rather than regarding the subject as an abstract machine for proving non‐constructive existence theorems, we will present homological algebra as a vast generalization of linear algebra: matrices are replaced by appropriate sequences of linear maps. This novel perspective will emphasize “thinking in terms of complexes” and developing effective computational tools. Together, we will explore the fundamental structures and essential constructions within homological algebra. A wide range of examples, many explicitly illustrated via the Macaulay2 software system, will also enhance the learning experience.