# Courses

## 01:640:491 - Mathematics Problem Solving Seminar

This is a one credit seminar in mathematical problem solving.  It is aimed at undergraduate students who enjoy solving mathematical problems in a variety of areas, and want to strengthen their creative mathematical skills, and their skills at doing mathematical proofs.

A secondary goal of this seminar is to help interested students prepare for the William Lowell Putnam Undergraduate Mathematics Competition , which is an annual national mathematics competition held every December. Any full-time undergraduate who does not yet have a college degree is eligible to participate in the exam. (However, you are free to participate in the seminar without taking the exam, and vice versa.)

The meetings of the seminar will be a mixture of presentations by the instructors, group discussions of problems, and student presentations of solutions/ideas.

The seminar qualifies as an honors seminar for the honors track. It does not count as one of the required 300-400 level courses for the major or minor.

Students who have taken the seminar previously may not register for it, but are very welcome to attend.

All students taking the seminar are expected to:

• Attend regularly.
• Participate actively in group problem solving.
• Present problem solutions (or partial solutions) to the class.
• Work on some of the assigned problems and turn in a carefully written solution for at least one problem per week.
• Read assigned material prior to class.

Students taking the seminar for honors track credit may have additional requirements consisting either of doing additional problems or doing more extensive class presentations.

Some Appetizers:

• When you multiply the numbers 1, 2, 3, ..., 400, how many trailing 0's does the answer have?
• Suppose you have a finite collection of points on the plane, such that whenever you draw a line through any 2 of them, that line passes through a 3rd point. Must all the points be collinear?
• Is the 50000th Fibonacci number odd or even?
• Can the product of 2 consecutive integers be a perfect square?
• Suppose you have n red points and n blue points in the plane. Can you pair up the red points with the blue points (each red point is paired with one blue point) so that all the line segments between the pairs are nonintersecting?

This course is offered during the Fall semester.