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.
Thursday, November 21, 2013 at 11:00 a.m. in Lytle Hall 228
"Those Summer Math Nights"
Lauren Williams, 2013 B.S. Mathematics & B.S.Ed. Mathematics
Zachary Bales, 2013 B.S. Mathematics & Physics
Lauren and Zach will speak on their involvement with a Research Experience for Undergraduates (REU) that each experienced last summer.
Thursday, October 17, 2013 at 11:00 a.m. in Lytle Hall 228
"Beliefs of Mathematics Majors"
Joshua Goodson, Ph.D., Assistant Professor of Mathematics, Kutztown University
Teachers' beliefs about content play a key role in the presentation of material to their students. Dr. Goodson will discuss a study on the influence of mathematical research on mathematics majors' beliefs, its implications on teacher education, and further possible research.