: Topics in Mathematics: Galois Theory
Professor: Jeff Johannes
Section 1 MWF 12:30 -
1:20p Sturges 103
Office Hours: Monday 11:30a - 12:20p, Tuesday 8:00 -
9:00p, Wednesday 11:30a - 12:20p, Thursday 10:15 - 11:15a, Friday 1:30 -
2:20p, and by appointment or visit
Email Address: Johannes@Geneseo.edu
Galois Theory, Fourth Edition, Ian Stewart
exercises, George Bergman
to student questions, George Bergman
In this course we will explore the question of
solvability of polynomials. We will consider finding and permuting
roots from Galois’ original historical perspective. Along the way we
will settle some of the classical construction problems and see the power of
applying seemingly theoretical ideas to the more practical question of
finding roots of polynomials. Prerequisite: Math. 330.
I Background and field extensions
II Galois Correspondence
III Examples and Applications
Much like Galois himself, we will be heavily driven by
examples. We will consider how permutation of roots allows us to
understand polynomials and discover ways to solve them. We will see a
deep connection among factoring, permutations of roots, and extensions of
Upon successful completion students will be able to
Explain how modern algebra grew out of Galois’
permutations of roots of polynomials.
Analyse particular polynomials – compute their Galois
groups and assess their solvability by radicals.
Your grade in this course will be based upon your
performance on four problem sets, one take home exam and one oral final
exam. The weight assigned to each is designated below:
Problem sets (4)
Take home exam
Oral final exam
Class presentation(s) 10%
The four problem sets will be due on 6 February, 27
February, 3 April, and 24 April. The assignments will be finalised no
later than the Wednesday before they are due.
Class presentations will be evaluated however we agree to
On 3 March in class you will be given your take home exam
related to course material included in the first two problem sets. It
will be due on 6 March at the beginning of class.
Oral Final Exam
Sometime after our last class, each student will present
a discussion about topics overviewing the course. Details will be
discussed after spring break. Probably will occur Thursday 4 May,
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for how the
course is running. Remember, the sooner you tell me your concerns, the
more I can do about them. I have also created a web-site
accepts anonymous comments. If we have not yet discussed this in
class, please encourage me to create a class code. This site may also
be accessed via our course page on a link
feedback. Of course, you are always welcome to approach me
outside of class to discuss these issues as well.
While working on homework with one another is encouraged,
all write-ups of solutions must be
your own. You are expected to be able to explain any solution you
give me if asked. The Student Academic Dishonesty Policy and Procedures will
be followed should incidents of academic dishonesty occur.
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning disabilities.
Students should consult with the Director in the Office of Disability
Services (Tabitha Buggie-Hunt, 105D Erwin, firstname.lastname@example.org)
and their individual faculty regarding any needed accommodations as early as
possible in the semester.
It is my policy to give students who miss class because
of observance of religious holidays the opportunity to make up missed
work. You are responsible for notifying me no later than January 30 of
plans to observe the holiday.
Since this course has a 300-level prerequisite of
theoretical mathematics, I find it reasonable to assume that all students
taking this class are interested in pursuing graduate study in mathematics.
Therefore I will attempt to run this course as an emulation of a
graduate school course. In particular, you may notice fewer
evaluations in the course, and fewer checks. You have more
responsibility for your own motivation and your own understanding. You
may also notice a challenging (to me) attempt on my part to be less
"nurturing", and for you to learn material on your own, with my skipping
sections for outside reading and similar. The good habits you have
developed of working with other students are now even more important than
before, as are your skills at reading and learning materials from a text.
For those who know me, this course should be a divergence from our
prior experiences. Please know that this is intentional.