MATH 412 - Fall 2017
## MATH 412 - Topics in Algebra: Representation Theory

Fall 2017

Professor: Angélica Osorno

Office: Library 305

Phone: x5093 (503-517-5093)
This is the course information website for section Math 412: Topics in Algebra.

All other material for the class will be posted on the Moodle page.

### General Information

#### Schedule

- Lecture: MWF 3:10-4:00pm, Eliot 207.
- Office hours: Tu 11:00-11:50am, F 2:00-3:00pm; you can also make an appointment or stop by my office. If my door is open, you are welcome in.

**Text:** There is no required textbook. You might find the following texts useful:
- J.P. Serre,
*Linear representations of finite groups* (available on reserve at the library).
- G. James and M. Liebeck,
*Representations and characters of groups* (available at the library).

**Course description:** Representation theory studies symmetry in vector spaces. In this class, we will study finite groups via their actions on vector spaces (i.e., their representations), with the ultimate goal of understanding the classification or representations of finite groups over the complex numbers. If time permits, we will also talk about Lie groups and their representations.

**Participation:** I expect you to actively engage in conversations in class by asking questions and participating in classroom discussions.

**Problem sets:** Homework will be due at the beginning of class on Wednesdays. No late problem sets will be accepted, but the lowest score will be dropped. Please order and staple your solutions.
Solutions should be written neatly or typeset and should use complete sentences. An ideal solution is written as an explanation meant for other students in the class.

**Collaboration policy:** You are welcome to work on homework together, this is a great way of learning. But YOU MUST WRITE UP YOUR OWN SOLUTIONS INDEPENDENTLY. For total disclosure, write the names of your collaborators.

**Exams:** There will be one take-home exam and a final exam.
- Exam 1: due Wednesday, October 11 (distributed on October 9).
- Final Exam: During exam week

**Final project:** There will be a project on the topic of your choice (related to representation theory). This will entail a written document and an in-class presentation, and it will happen during the last week of class. A topic proposal will be due on Monday, November 13, and presentations will be scheduled for the last two weeks of classes.

**Technology:** The use of electronic devices (computers, cell phones, tablets, etc) is not allowed in the classroom without my authorization. Talk to me if you have a specific reason for needing to use technology (for example, note taking).

**Academic honesty:** As noted above, for homework you should write your own solutions and disclose your collaborators. For both exams, there is no collaboration allowed. The internet is a great source of information about mathematics; you are welcome to search information about the material of the course online, but you should not search for solutions to specific problems in the homework.

**A final remark:** Learning and understanding mathematics requires engaging with the material several times. You might not get what is happening on the first try. Struggling with the material is normal, and maybe even expected.
By actively participating in class, spending time working on the homework, reviewing the material, talking to classmates and talking to me, you will increase your understanding. Use the resources available!