# Math 4513 (Senior Mathematics Seminar)

# Spring 2008

** Instructor: **

John Albert Office: PHSC 1004, Ext.
5-3782. Office hours: Mon, Wed 2:30 to 3:30, Thurs 10:30 to 11:30 (or by
appointment) E-mail: jalbert@ou.edu

Here is the syllabus for this course.
For a careful treatment of the problem we discussed in class on March 14, see
section 2.1, "The Classical Secretary Problem", of Thomas Ferguson's book "Optimal Stopping and Applications",
which you can find online at
http://www.math.ucla.edu/~tom/Stopping/Contents.html. Also check out an interesting historical
account of the article by Prof. Ferguson at http://projecteuclid.org/euclid.ss/1177012493.
What would a musical piece based on the Fibonacci sequence sound like? Maybe this?

## Take-home final

Here is the take-home final for the class. It's due next Wednesday. Instructions are on the exam.
## Presentations

Here are scans of the write-ups submitted so far for the presentations:

Byrnes/Glascock: Palindromic numbers
Millikin/Rainey: Game theory part 1
Brown/Daifi/Perkins: Random Fibonacci numbers part 1 and part 2
Rees/Thomas: Combinatorial game theory
Lively/Mello de Almeida/Welch: Penrose tilings
Anderson/Smith: Harmonic functions on the sphere part 1 and part 2
Davis/Miller: Pythagorean triples and Fermat's Last Theorem
Conrad/Roper: Twin primes
Morris/Vance: RISK and Markov chains

Here is the current revision of the schedule for the student presentations.
This was the list of possible ideas for presentations that I handed out earlier, based on random interesting things I've come across recently.
You can also see lists from a previous semester of this course here (these problems
are mostly taken from geometry) and here (these problems are taken mostly from number theory).
## Midterm

Here are answers to the problems on the midterm.

These were some practice problems for the exam.
## Assignments

Assignment 1.
Assignment 2 consists of problems #3 and #7 from page 2 of this problem sheet.
(There are other interesting problem sheets where this came from: see http://math.stanford.edu/~vakil/putnam07.)
Assignment 4.