**Instructor:**Dan Christensen**E-mail:**jdc@uwo.ca**Office:**Middlesex 103b.**Office Phone:**661-2111 x86530.**Office Hours:**after class**Class times and location:**Mondays and Wednesdays, 10-noon, starting May 5 and ending around July 2, in MC107. Exceptions: on Monday, May 5 and Monday, May 12, we meet 1:30-3:30 in MC108. Final exam July 14. I will be away July 6-12.**Prerequisites:**Group theory and linear algebra.

Basic representation theory: irreducibility, complete reducibility, Schur's lemma, character theory, induced representations, etc.

Possible further topics include:

- Fourier analysis on finite groups
- Applications to group theory, including theorems of Burnside.
- Representations of the symmetric groups: partitions, Young tableaux, Young symmetrizers, Specht modules, and lots more.
- Probability and random walks on graphs.

**Text:** The text is
*Representation Theory of Finite Groups: An Introductory Approach*,
by Benjamin Steinberg, 2012, Springer.
From on campus, you should be able to download it for free via
this link.

Other references you may find useful, but which are not required:

- J.P. Serre,
*Linear Representations of Finite Groups*, GTM 42, Springer, 1977. - A. Baker,
*Representations of Finite Groups*, pdf notes. - Shlomo Sternberg,
*Group theory in physics*. A pleasant book with a conversational style and lots of applications to motivate the material. - W. Fulton and J. Harris,
*Representation theory*, GTM 129, Springer, 1991. Starts with a very fast treatment of the representation theory of finite groups.

**Homework:** Homework will be due each Wednesday at
the beginning of class.
Doing problems and talking about the
material are both essential for learning the material in this course,
so you are encouraged to **discuss**
the problems with classmates and with me.
But you must write up the solutions **on your own** and must not
look at other students' written solutions nor should you attempt to
find solutions to problems online or in textbooks.
Your solutions should be **clear** and **carefully written** and
you should give **credit** to
those who helped you and to any references you used.
Homework will be graded based on both correctness and clarity.
Late problem sets will not be accepted unless arranged in advance
for a good reason.

**Copying solutions** from other students, online sources,
textbooks, etc. or showing your work to other students
constitutes a scholastic offense and will result
in a grade of **negative 100%** for the assignment and in some cases
expulsion from the program.
All academic offenses are added to your student record.

**Presentations:** In the second half of the semester,
each student will give a presentation on a topic related to the
course.

**Exam:** There will be a final exam on July 14, 1-4pm, MC107.

**Evaluation:** Evaluation will be based upon homework,
presentations and the final exam, with equal weight.

**Scholastic offences:** Scholastic offences are taken
seriously and students are directed to read the appropriate policy,
specifically, the definition of what constitutes a Scholastic Offence,
at the following Web site:
http://www.uwo.ca/univsec/handbook/appeals/scholastic_discipline_grad.pdf