MTH 190 "Topics in Problem Solving"

Course Number	Time	Location	Instructor	Office Hours	E-mail
66785	Every other Monday 6:15-7:30pm	310 Gavett	Dan-Andrei Geba	MW 9-10am, 806 Hylan	dangeba@math.rochester.edu

Description

Building on the success of previous years, this class is primarily aimed at students with an interest in problem solving in mathematics, and, in particular, at participants in mathematical contests at college level. What we try to do here is pick up where the usual mathematical curriculum stops and investigate interesting topics (some of them quite advanced) that are either marginally touched or downright omitted. By doing that, we hope on one hand to create enough spark for the audience to follow up this class with independent readings and even research projects, while advocating at the same time for the importance of problem solving techniques. We are going to try and keep this class as self contained as possible, with some of the topics requiring nothing more than a strong high-school mathematical background. This is why I would encourage the advanced freshmen to consider it.

I would expect for all the students enrolled in the class to participate in the two math competitions organized in the fall:

The William Lowell Putnam Mathematical Competition (70th edition, 12/5)

Virginia Tech Regional Mathematics Contest (31th edition, 10/24)

Grading

The grade will be entirely based on class participation (30%) and homework (70%). Each student will have to turn in for the following meeting detailed solutions to 3 problems from the assigned problem set.

Extra reading material

For those willing to go beyond the scope of this course, I strongly recommend taking a look at:

"Problem-Solving Through Problems" by Loren C. Larson.
"Problem-Solving Strategies" by Arthur Engel.
"The William Lowell Putnam Mathematical Competition 1985-2000" by Kiran S. Kedlaya, Bjorn Poonen, and Ravi Vakil.
"Putnam and Beyond" by Razvan Gelca and Titu Andreescu.

All these books will be on reserve at the Carlson Library reserve collection.

You might find useful also the largest online forum dedicated to problem solving: The MathLinks Forum, organized by Valentin Vornicu.

Weekly schedule


Date	Lecture	Homework
9/14	Polynomials	Problem set 1
9/28	Recurrent sequences	Problem set 2
10/12	Functional equations	Problem set 3
10/26	VTRM contest discussion
11/9	Topics in differential equations	Problem set 4
11/23	Review for the Putnam exam	Last homework: write down complete solutions to 3 problems from previous Putnam exams.
12/7	Putnam contest discussion