This course in algebra develops the foundation required by all graduate
students in the mathematical sciences. Together, we will explore some
fundamental algebraic structures including groups, commutative rings,
modules, and categories. A wide range of examples should also enhance
the learning experience.
There are no required or optional textbooks for this course. Total cost $0.
Learning Outcomes
Upon successful completion of the course, students will be able to:
Define and illustrate fundamental algebraic structures (such as
groups, rings, fields, and modules) using both examples and
counterexamples.
Demonstrate mastery of key topics, including automorphism groups,
group actions, Noetherian rings, unique factorization, and the
structure theorem for finitely generated modules over a principal
ideal domain.
Explain foundational categorial concepts, including isomorphisms,
products/coproducts, universal constructions, and functors.
Construct rigorous solutions to problems and write logically sound
proofs of theorems.
Assessment
The course grades will be computed as follows:
5% Feedback
40% Homework
30% "In-class" exam
25% "Take-home" exam
Feedback
Students are expected to provide constructive feedback on the course
notes. Each original correction, helpful comment, or actionable
suggestion will add 1% to your final grade.
Homework
Weekly problem sets consist of approximately 3 questions and are posted
in Portable Document Format (PDF) on the course website. Solutions will
be collected using the Crowdmark software. The best 10 of 12 problem sets
will determine your homework grade.
Academic Integrity
Students are responsible for familiarizing themselves with all of the
regulations concerning academic integrity and for ensuring that their
assignments and their behaviour conform to the principles of academic
integrity. Students are welcome to discuss problems, but should write up
the solutions individually. Students must explicitly acknowledge any
assistance including books, software, technology, websites, students,
friends, professors, references, etc.
Accommodations
The instructor is committed to achieving full accessibility for people
with disabilities. Part of this commitment includes arranging academic
accommodations for students with disabilities to ensure they have an
equitable opportunity to participate in all of their academic
activities. If you are a student with a disability and think you may
need academic accommodations, then you are strongly encouraged to
contact both the instructor and the
Queenʼs Student Accessibility Services (QSAS) as
early as possible.
Licensing
Materials generated by the instructor may not be used for commercial
advantage or monetary compensation. Some material is clearly copyrighted
and may not be reproduced or retransmitted in any form without express
written consent. Other material, licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 International License, may be
remixed, adapted, or built upon it, as long as appropriate credit is given
and the new creation is distributed under the identical terms.
