Galois theory is one of the most beautiful parts of mathematics. As a
capstone to undergraduate algebra, this course invites students to
discover how questions about solving polynomial equations lead naturally
to the study of symmetry, revealing a powerful and unifying connection
between field extensions and group theory.
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 Tuesday, 24 February 2026 at 19:00–21:00.
Upon successful completion of the course, students will be able to do
the following:
Work fluently with minimal polynomials, towers of fields, and
simple extensions.
Define and illustrate normal, separable, and Galois extensions.
Interpret Galois groups as permutation groups acting on roots and
relate group-theoretic properties to field-theoretic structure.
Apply the Galois correspondence to classify intermediate fields
and subgroups in concrete examples.
Create and present rigorous solutions to problems and coherent
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.
