Mathematics 380 : Topics in Mathematics: Galois Theory
Professor: Jeff Johannes
MWF 11:30a - 12:20p ISC 136
Office Hours: Monday 1:30 - 2:20p, Tuesday 8:00 -
9:00p, Wednesday 4:00 - 5:00p, Thursday 4:00 - 5:00p, Friday 3:00 -
4:00p (may cancel occasionally) and by
appointment or visit
Email Address: Johannes@Geneseo.edu
Galois Theory, Third
Edition, Ian Stewart
Errata, George Bergman
Additional exercises, George Bergman
Comments 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 (or 319).
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 number systems.
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
Problem Sets (4)
Take home exam
Oral Final exam
The four problem sets will be due on 6 February, 27
February, 2 April, and 23 April. The assignments will be
finalised no later than the Wednesday before they are due.
On 2 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 5 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.
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
which 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 entitled anonymous
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.
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.