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 x2+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 X2 + 3 X Y + Y2 + 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.
Thursday, April 17, 2014 at 3:00 p.m. in Lytle Hall 214
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.