As a first undergraduate course in modern algebra, we study
rings—an algebraic structure in which addition and multiplication
are defined and have properties similar to those operations on the
integers. This theory unifies and generalizes many examples from
geometry and number theory. This course is intended for all students
majoring in mathematics.
Students are expected to provide constructive feedback on the course
notes. Each original correction, helpful comment, or actionable suggestion
will contribute 1% to your final grade (up to a maximum of 5%).
Homework
Problem sets are posted in PDF on the lectures webpage.
Your browser can be trained to open these files with the free
program
Acrobat Reader (or other
PDF viewer). Solutions to each problem set
will be submitted via the
Crowdmark system. Instructions for using
this software are
available. The solution to each problem must
be uploaded separately. Solutions are due on Fridays before 23:59 EST;
late homework will receive no credit. Your best ten of
twelve solution sets will determine your homework grade.
Midterm
There will be a two-hour midterm on Thursday, 13 February 2025 at 19:00–21:00 in ??.
Upon successful completion of the course, students will be able to do
the following:
Perform accurate and efficient computations with integers and
polynomials involving quotients, remainders, divisibility, greatest
common divisors, primality, irreducibility, and factorizations.
Define and illustrate basic concepts in ring theory using examples
and counterexamples.
Describe and demonstrate an understanding of equivalence classes,
ideals, quotient rings, ring homomorphisms, and some standard
isomorphisms.
Recognize and explain a hierarchy of rings that includes
commutative rings, unique factorization domains, principal ideal
domains, Euclidean domains, and fields.
Write rigorous solutions to problems and clear proofs of theorems.
To develop these abilities, students are expected to
independently read the course notes or at least one textbook,
regularly participate in the lectures and tutorials,
persistently complete all homework assignments, and
continually discuss mathematics with other students.
Writing
We write to communicate. Please bear this in mind as you complete the
homework, the midterm, and the exam. Work must be neat and legible to
receive consideration. You must explain your work in order to obtain
full credit; an assertion is not an answer.
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 think that you may need academic accommodations, then
you are strongly encouraged to contact the instructor and the Queenʼs Student Accessibility Services (QSAS) as
soon 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 build upon it, as long as
appropriate credit is given and the new creation is distributed under
the identical terms.
Technology
Students are encouraged to use any available technology on the homework,
but these aids (including calculators) will not be allowed during the
midterm and exam.
