# Colloquia

**2014-2015**

**2014-2015**

**Thursday, December 4, 2014 at 3:00 p.m. in Lytle Hall 228**

**Michelle Savescu, Ph.D., Professor of Mathematics, Kutztown University**

**Thursday, October 2, 2014 at 3:00 p.m. in Lytle Hall 228**

*"Fun with Factoring Fantastic Forms"*

Brian Kronenthal, Ph.D., Assistant Professor of Mathematics, Kutztown University

This talk is all about factoring polynomials, but not everyday ones like x^{2}+3x+2. We will be looking at polynomials which have more than one variable and whose exponents in every term add to two. For example, consider 2 X^{2} + 3 X Y + Y^{2} + 2 X Z + Y Z; can you figure out whether or not it factors (without a computer or calculator)? These special polynomials are called **quadratic forms**. We will discuss several criteria that help us determine, without using technology and without guessing and checking, which quadratic forms factor and which do not.

**2013-2014**

## Thursday, April 17, 2014 at 3:00 p.m. in Lytle Hall 214

*"Catalan Numbers"*

W. H. Tony Wong, Ph.D., Assistant Professor of Mathematics, Kutztown University

The associative law of addition in real numbers tells us that (1 + 2) + 3 = 1 + (2 + 3). In other words, there are two ways to put the parentheses in the expression 1 + 2 + 3. If there are four numbers adding up, e.g., in the expression 1 + 2 + 3 + 4, how many ways are there to put the parantheses? How about 1 + 2 + 3 + 4 + 5?

The answers to the above questions are called Catalan numbers. Catalan numbers appear in countless combinatorial problems, and some of them will be introduced in this talk. We will show a couple interesting pictorial proofs of bijections in combinatorics.

Part of the materials in this talk originates from my Research Experience for Undergraduates (REU) at Cornell University 2007.

## Wednesday, March 12, 2014 at 5:00 p.m. in Boehm Hall 260

# Seventh Annual Thomas Pirnot Lecture in Mathematics

*"Pondering Packing Puzzles: Research in Recreational Mathematics"*

Derek Smith, Ph.D., Associate Professor of Mathematics, Lafayette College

Here is a puzzle for you: Is it possible to assemble six 1 x 2 x 2 blocks and three 1 x 1 x 1 blocks into a 3 x 3 x 3 cube? If so, in how many ways can this be done? Don't look up the solution! Try to figure this out on paper or with a model first. But let me tell you that this is the Slothouber-Graatsma-Conway Puzzle, often called the smallest non-trivial 3-dimensional block-packing puzzle.

I will describe an infinite family of packing puzzles that includes the Slothouber-Graatsma-Conway Puzzle, and I will prove a nice result about them. I will also introduce you to Burr Tools, a cool computer program that helps with investigations of packing and other types of puzzles.