We study systems of polynomial equations in several variables. As an
introduction to this branch of mathematics, we will examine the
computational foundations, the dictionary between ideals in a polynomial
ring and affine varieties, and projective geometry.
Monday at 12:30–13:20 in
306 MacLaughlin
Wednesday at 11:30–12:20 in 306 MacLaughlin
Thursday at 13:30–14:20 in 306 MacLaughlin
Office Hour
Thursday at 16:30–17:20 in
201 Jeffery Hall (aka
Math Help Center)
Assessment
The course grades will be computed as follows:
40% Homework
40% Project
20% Exam
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 17:00;
late homework will receive no credit. Your best five of
six solution sets will determine your homework grade.
Exam
There will be a three-hour exam on Sunday, 16 April 2023 at
14:00–17:00 in Gym 5.
Learning Outcomes
Upon successful completion of the course, students will be able to do
the following:
Execute accurate and efficient calculations with ideals in a
multivariate polynomial ring involving Gröbner bases, membership,
intersections, and quotients.
Explain and use elimination theory to solve systems of polynomial
equations.
Define and illustrate the correspondence between ideals and
varieties by translating between algebraic and geometric
statements.
Describe and demonstrate a basic understanding of projective
geometry.
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 office hours,
persistently complete all homework assignments and all steps in the project, and
continually discuss mathematics with other students.
Writing
We write to communicate. Please bear this in mind as you complete the
homework, the project, 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 remix, adapt, 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
and project, but these aids will not be allowed during the exam.
