MATH.4200-301 Honors Mathematical Problem Solving

Fall 2018

Instructor: Prof. K. Levasseur -- kenneth_levasseur@uml.edu

The class will meet on Wednesdays, 3:30 - 6:15 PM, but you must also be available from 10AM to 6 PM on Saturday December 1, 2018 to compete in the William Lowell Putnam Mathematical Competition - this will be your final exam for the course.

The main focus of the course will be to solve interesting, challeging mathematics problems. Here is one of the problems from the 2013 competition:

Recall that a regular icosahedron is a convex polyhedron having 12 vertices and 20 faces; the faces are congruent equilateral triangles. On each face of a regular icosahedron is written a nonnegative integer such that the sum of all 20 integers is 39. Show that there are two faces that share a vertex and have the same integer written on them.

Text

Kiran S. Kedlaya, Bjorn Poonen, Ravi Vakil, The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions, and Commentary (MAA Problem Book Series), 2002, ISBN: 088385807X

Course Requirements, Grading

To earn a grade in this course you will need to do the following:

  1. Attend all classes. Unless you have valid medical or legal excuse for missing a class, you will be considered absent. You get one free absence, and then your starting grade will be moved down the list {A, A-, B+, B, B-,...}. Your starting grade will then be the highest possible grade you can earn in the course, assuming you do "A" work for everything.
  2. The bulk of your grade will be based on your participation and effort both inside and outside of the class. There will be a few problem sets assigned for work outside of class. If you attend all classes and make an honest effort, you don't have to be a mathematics prodigy to earn a good grade in the course. This component of the grade represents 70% of the final grade.
  3. You must compete in the William Lowell Putnam Mathematical Competition on December 2. Competing is 20% of the grade. The scores are announced long after grades are due, so everyone who shows up gets an "A" in this part of the course. We will meet on Wednesday, December 5 to "debrief."
  4. The final requirement for the course will be to write up a reflection on the course and the competition. In this 3-5 page paper, you can describe your efforts, preferably highlighting one of the Putnam problems. In addition, you can comment on what you've learned about mathematics and the problem solving process. This will count for 10% of the course and will be due Wednesday, December 12 at noon.