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.