**Math 47a (Intro to Mathematical Research)**
**Brandeis Math Department**
**Fall 2008**

Updated: 12/5/08, 2pm

What is new: new Tex template.

**Putnam sessions** Practice sessions for the Putnam competition will resume Thursdays 2:45-4. For more information click here.

**Special lecture:** * Catalan numbers and exceptional sequences.
*

I gave a lecture about my research in connection to Math 47a in the Everytopic Seminar on Friday, Sept 19, 1:30-3. Here are preliminary lecture notes.

**Information**

- This class meets MWR 10-11 in Room 101.
- In this course we will actually try to do research on an active area of 21st century mathematics. We will look at cluster categories. Here is the syllabus and its LateX source file.

**Instructor**

- Kiyoshi Igusa
- Goldsmith 305
- Office hours: MWR 11-12 (after class).
- Phone 63062.
- standard email: lastname@brandeis.edu

**TA's**

- ?

**Homework**

- Problem Set 1 (due Thursday, Sept 25). Answers 1
- Problem Set 2 (due Wednesday, Oct 22).Hints, Answers
- The midterm paper can be a long winded answer to a HW problem.
- Monday, Nov 3, tell me what you want to do for the midterm paper.
- Monday, Nov 10: First draft of midterm paper due.
- One week after you get it back: the final version is due.

- The final paper must be in TeX or LaTeX.
- You need to reserve a topic or problem. Two students cannot work on the same project for their final paper. (But you can help each other on your respective problems. Also you can separate one project into two parts if you have a clear idea what the separation is.)
- Thursday, Nov 13: Topic for your final paper is due.
- The first draft of the final paper is due Monday, Dec 8.

**Notes**

- Permutations and groups
- Roots and reflections (includes day 7)
- Catalan numbers
- Categories
- complete notes so far (continuously updated, with braids added, but we have to skip braids.)
- Notes on TeX
- Here is the sample paper that I wrote earlier. And here is the source
- (Nov 6 notes) Here are notes on TeX from class with source.
- Here is the new tex template.

**links**

- Webpage from the 2003 course (On a very closely related topic.)
- Ocneanu's mathematical sculpture
- Brandeis Mathematics Department