Thursday, April 14, 2016 at 4:00 p.m. in Boehm Hall 260
Ninth Annual Thomas Pirnot Lecture in Mathematics
"The Joy of SET®: The Mathematics In a Card Game"
Dr. Elizabeth McMahon and Dr. Gary Gordon, Lafayette College
The card game SET® is played with a special deck of 81 cards. There is quite a lot of mathematics that can be explored using the game. We’ll look at questions in combinatorics, probability, linear algebra, and especially geometry. The deck is an excellent model for a 4-dimensional finite affine geometry. If you’d like some practice before the talk, go to www.setgame.com for the rules and a Daily Puzzle.
Tuesday, March 29, 2016 at 3:00 p.m. in Lytle Hall 218
"Soliton Solutions of the Nonlinear Schrödinger Equation"
Dr. Michelle Savescu, Department of Mathematics, Kutztown University of Pennsylvania
The presentation starts with a brief history of solitons followed by an introduction to optical solitons and related concepts. The dynamics of the propagation of solitons through optical fibers is governed by the Nonlinear Schrödinger Equation (NLSE).
Several methods have been applied to the NLSE in order to obtain analytical soliton solutions. The methods that will be presented here are the traveling wave hypothesis, the ansatz method, the semi-inverse variational principle, the tanh method, the G′/G expansion method and the Adomian decomposition method.
Research results using some of these methods will be presented for physical models such as nano optical fibers and birefringent fibers. Bright, dark and singular soliton solutions were obtained for nonlinearity laws such as the Kerr law, the parabolic law and the polynomial law of nonlinearity.
Thursday, March 24, 2016 at 11:00 a.m. in Boehm Hall 260
"Who's Who in the Politics of Math Education"
Dr. Mark Wolfmeyer, Department of Secondary Education, Kutztown University of Pennsylvania
The effort to standardize a US national mathematics curriculum culminated in 2010 when over 40 states adopted the Common Core State Standards for Mathematics. How did this come to be? Who was involved and what did they set as the primary issues in mathematics education? This talk aims to provide a landscape of mathematics education policy in the United States and draws on Dr. Wolfmeyer's research contained in Math Education for America? (Routledge, 2014).
In an interactive presentation he will offer examples of the people and organizations involved in mathematics policy, shedding insight into the debates that exist and priorities now established. Come, mathematicians and educators, and find out where you stand on today's most pertinent issues in K-12 mathematics teaching and learning!
Tuesday, March 22, 2016 at 3:00 p.m. in Lytle Hall 228
"An Evaluation of the Functional Assessment Questionnaire Using a Graded Response Model"
Dr. Tuan Nguyen, University of Southern California
Alzheimer's disease (AD) is widely believed to progress over many years before any clinical symptom appears; hence, an effective treatment should be started as early as possible, especially in the preclinical stage of AD. One of the challenges to achieve this end is to find endpoints that have good sensitivity to the longitudinal decline of global functional performance.
The currently available measurements are typically obtained by assessing the patient performance on a Likert scale and summing up the resulting sub-scores to yield overall performance. An alternative approach, explored in this work, is to compute the measurement under item response theory (IRT).
Using data on the Functional Assessment Questionnaire from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study, we found that IRT-based scoring increased the sensitivity to change in functional ability and improved the statistical power in future clinical trials.
Monday, February 29, 2016 at 3:00 p.m. in Lytle Hall 214
"An Analysis of Non-local Elements in Differential Equations and Fractional Calculus"
Dr. Christopher Goodrich, Creighton Preparatory School
In this talk we will discuss the effect of non-local elements in the discrete and continuous calculus. More specifically, we will investigate two different manifestations of non-local elements:
- the analysis of boundary value problems with nonlocal boundary conditions; and
- the nonlocal structure of the discrete fractional difference.
Finally, since we will begin by discussing the fundamentals of both the difference calculus and boundary value problems, no previous knowledge of each is assumed. A working knowledge of single-variable calculus and ordinary differential equations should be sufficient to understand a majority of the talk.
Tuesday, February 23, 2016 at 3:00 p.m. in Lytle Hall 228
"A Snapshot of Complex Dynamics"
Dr. Sara W. Lapan, Northwestern University
Complex dynamics is a fascinating area of mathematics that lies at the intersection of complex analysis and dynamical systems. In pop-culture, complex dynamics is known for its beautiful fractals, like the Mandelbrot set and Julia sets. This talk will be a gentle introduction to complex dynamics and, along the way, we will see and explore many beautiful fractals.
More specifically, we will focus on polynomials P(z) in one complex variable that fix 0. Every time we apply P, 0 remains fixed, but what happens to points near 0? For instance, if z is close to 0, is P(P(z)) close to 0? In complex dynamics, this type of question is of great interest.
We will discuss some of the interesting things that can happen in one complex variable. This talk will build up to the famous Leau-Fatou Flower Theorem, which provides a beautiful description of the movement of points near the fixed point for a special type of polynomial. This theorem from the early 1900s serves as inspiration for research in higher dimensions.
Monday, February 15, 2016 at 11:00 a.m. in Lytle Hall 228
"Applications of Persistent Homology"
Ms. Leyda Almodovar, University of Iowa
Topological Data Analysis (TDA) is a relatively new area within data analysis that combines different disciplines, such as computational topology, statistics and geometry. Many different fields have benefited from this new way of visualizing and analyzing data, such as neuroscience, linguistics and chemistry, and it is especially helpful when applied to network data.
Networks, a set of vertices representing real-world objects and a set of edges denoting relations between vertices, are very useful to model certain relations between groups of objects. In particular, I am interested in the case where these objects are brain regions, and their relations are given by anatomical connections. While the theory points to a lack of connections in certain brain regions in schizophrenic patients, neuroscientists have not been able to identify these regions using standard network theory tools.
I will present the application of persistent homology, the cornerstone of TDA, to different data sets including linguistic data, evasion paths in mobile sensor networks, and brain networks, which will be emphasized.
Thursday, February 11, 2016 at 3:00 p.m. in Lytle Hall 228
"The Optimal Harvesting Policy for the Beverton-Holt Population Model"
Dr. Sabrina H. Streipert, Missouri University of Science and Technology
In this presentation, the exploitation of a single population modeled by the Beverton-Holt difference equation with periodic coefficients is established. The investigation begins with the harvesting of a single autonomous population with logistic growth and it is shown that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, the optimal harvesting policy that maximizes the annual sustainable yield is investigated in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model.
In the second part, the harvested Beverton - Holt model is presented and the unique periodic solution, which globally attracts all its solutions, is derived. The investigation continues by optimizing the sustainable yield with respect to the harvest effort. The results differ from the optimal harvesting policy for the continuous logistic model, which suggests a separate strategy for populations modeled by the Beverton-Holt difference equation.
Monday, November 9, 2015 at 11:00 a.m. in Lytle Hall 228
"Hands-on Dynamical Systems"
Dr. Karen Keene, North Carolina State University
In her talk, Dr. Keene will offer a hands on way for students to be introduced to the notion of solutions for dynamical systems. Participants in the colloquium will use pipe cleaners to construct an understanding of what a solution to a dynamical system looks like. Then specialized technology will move students into a more formal understanding.
Come prepared to listen, talk and work in a fun area of mathematics.
Tuesday, November 3, 2015 at 4:00 p.m. in Lytle Hall 228
"Classical and Generalized Iteration"
Dr. Jesse Feller, Kutztown University
The study of holomorphic dynamical systems (discrete time) is a relatively new area of study involving the repeated composition of a single function f(z) in a process called iteration. Thus we are studying the convergence of the sequence of functions fn(z) = (f ◦ f ◦ ... ◦ f)(z) (n times). We will discover the concept of periodic points and classify them into the three categories of attracting, repelling or neutral. Most of our examples have dynamical properties that are easily understood. Other examples have dynamical properties that are called chaotic due to their unpredictability. We will take a look at several computer generated images of the important Julia and filled Julia sets for several examples.
Some mathematicians studying dynamics focus on composing a different function at each step of the iteration process where the function is chosen from a family according to some probability distribution. This is called random iteration. We will learn about a few recent results in this area regarding the probability that a random iteration ends up “close” to an attracting periodic point.
Wednesday, October 14, 2015 at 4:00 p.m. in Lytle Hall 228
"Factor Pair Latin Squares: Be There or Be Square"
Dr. James Hammer, Cedar Crest College
Sudoku has risen in popularity over the past few years. The rules are simple, yet the solutions are often less than trivial. Mathematically, these puzzles are interesting in their own right. This talk will use the idea of a Sudoku puzzle to define a new kind of n x n array. Further, we will aim to prove some necessary (and on occasion sufficient) conditions for the existence of these arrays. To that end, we define a Latin square of order n as an n x n array where every row and every column contain every symbol 1,2,...,n exactly once. We say (a,b) is an ordered factor pair of the integer n if n = a x b. An (a,b)-Sudoku Latin square is a Latin square where in addition to each row and column containing every symbol exactly once, each a x b rectangle also contains every symbol exactly once when the n x n array is tiled with a x b rectangles in the natural way. A factor pair Latin square of order n (denoted FPLS(n)) is an (a,b)-Sudoku Latin square for every factor pair (a,b) of n. This talk will mainly be concerned with the existence of such designs as well as related problems to such designs.
Tuesday, September 15, 2015 at 4:00 p.m. in Boehm Hall 261
"Unsolved! History's Greatest Ciphers"
Dr. Craig Bauer, York College
While developments in cryptanalysis have forced enciphering techniques to become more and more sophisticated, there remain scores of ciphers stretching back to antiquity that remain unsolved. These were created variously by professional cryptographers, amateurs, artists, killers, and victims. In some cases the identity of the author is also unknown. The talk covers many of these mysteries, along with some mathematics that provides a glimmer of hope for those seeking the solutions. These solutions could reveal the identity of a serial killer or spy, provide the exact location of buried treasure worth millions, expose a secret society, illuminate our understanding of ancient history, or even rewrite the history of science.
Thursday, September 10, 2015 at 4:00 p.m. in Lytle Hall 228
"Numerical ranges: from matrices to pretty pictures"
Dr. Patrick Rault, State University of New York at Geneseo
In Philadelphia there are coin machines which take two quarters and a penny and output a flattened penny with an impression of the Liberty Bell. Mathematical functions share this sort of property, and in this talk we will specifically be learning about dot products and matrix products. The Numerical Range is a map which uses these products to define a function, like the Liberty Bell coin machine, which inputs a matrix and outputs a two-dimensional picture in the complex plane. These pictures include ellipses, triangles, and some bizarre egg-shaped curves. We will discuss some number theoretic results by the speaker's students, as well as a deep integer invariant of these matrices which we call the Gau-Wu number.
Friday, April 10, 2015 at 6:15 p.m. in Boehm Hall 145
Eighth Annual Thomas Pirnot Lecture in Mathematics
"My Favorite Integer Sequences, or, Confessions of a Sequence Addict"
Neil J.A. Sloane, Ph.D., Founder of the On-Line Encyclopedia of Integer Sequences (OEIS) and President of the OEIS Foundation
The On-Line Encyclopedia of Integer Sequences (or OEIS, oeis.org) is a free web site that contains information about a quarter of a million sequences, and is often called one of the most useful mathematical sites on the Web. I will discuss some of my favorites, including the van Eck, Zizka, Fredkin, Quet, Kelly, Yellowstone, etc. sequences. There will be music, movies, and a number of unsolved problems. Warning: some of these may prevent you sleeping at night.
Thursday, January 29, 2015 at 3:00 p.m. in Lytle Hall 218
"Learning Communities: Theory, Models, Applications, etc."
Dr. Gil Clary, Dr. Gail Craig and Dr. Robert Ziegenfus
For the first colloquium of the semester, we will hear from a panel consisting of Dr. Gil Clary, Director of the Office of Assessment, Prof. Gail Craig, Director of TRiO Student Support Services, and Dr. Robert Ziegenfus from the Department of Geography on the topic of Learning Communities. Dr. Clary will lay the theoretical foundations of the concept of a learning community. Dr. Craig will follow by discussing how she runs a learning community in the Student Support Services Program. Finally, Dr. Ziegenfus will discuss different learning community models and pragmatics and challenges of implementing a learning community. This colloquium is being organized by the Department of Mathematics Retention Committee with the goal of enhancing the learning experience of our students. To that end, we welcome all faculty and students to attend and offer feedback.
Thursday, December 4, 2014 at 3:00 p.m. in Boehm Hall 260
"Glitzy Math: The Mathematics of Computer Graphics"
Dr. Tom Pirnot, Professor Emeritus of Mathematics, Kutztown University
Dr. Pirnot will give an introduction to the mathematics used to create the astonishing graphical objects seen in today's popular animated movies and video games. He will explain how relatively elementary mathematics such as algebra, geometry, linear algebra, and calculus can be used (billions of times!) to create, render, and view the amazing and beloved characters such as Buzz Lightyear from Toy Story to Anna from Frozen. Disclaimer: To be honest, he will not actually show you how to create a whole animated movie in one hour; he will just explain some of the interesting math behind the glitz.
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 parentheses ? 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"
Mr. Zachary Bales and Ms. Lauren Williams, Kutztown University '14
In this talk we will encourage students to participate in summer research programs. We will proceed chronologically through the steps of searching and applying for various summer research programs. We will also briefly discuss our acceptance and experiences into the Summer Institute for Training in Biostatistics (SIBS) at both the University of Pittsburgh and University of Iowa. We will emphasis that although Kutztown University of Pennsylvania is not as well-known as Ivy League schools, admission panels are looking for the diamonds in the rough. Our talk will conclude with tips and resources to alleviate any concerns about summer program research and applications processes and open up the discussion for questions.
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
This talk will discuss a study on the beliefs that mathematics majors and mathematics majors pursuing secondary certification have regarding mathematics. In particular, the study looks at the influence of an introduction to proofs course and mathematics research on their beliefs. Teachers beliefs about the content that they teach play a role in how they present the material to their students. Knowing what those beliefs are and what affects them can inform the instruction of future teachers. Beliefs were measured using the Conceptions of Mathematics Inventory, which includes seven categories each with eight questions. Findings as well as ideas for future research will also be discussed.
Wednesday, March 26, 2013 at 3:30 p.m. in McFarland Student Union Building 250
Sixth Annual Thomas Pirnot Lecture in Mathematics
"Cantor and the Paradise He Gave Us"
Robert Vallin, Ph.D., Professor of Mathematics, Slippery Rock University of Pennsylvania
Thursday, February 28, 2013 at 3:00 p.m. in Lytle Hall 214
"Hopf Algebra Structure of Generalized Scissors Congruence Groups"
Jianqiang Zhao, Associate Professor of Mathematics, Eckerd College
Tuesday, February 19, 2013 at 3:00 p.m. in Lytle Hall 214
"Individual Based and Dynamic Energy Budget Models"
Baldvin Einarsson, University of California at Santa Barbara
Friday, February 15, 2013 at 3:00 p.m. in Lytle Hall 214
"Decomposing Graphs into Stars and Hyperstars "
D.P. Roberts, Assistant Professor of Mathematics, Illinois Wesleyan University
Tuesday, February 12, 2013 at 3:00 p.m. in Lytle Hall 214
"The Hopf Algebra of Sashes "
S.E. Law, North Carolina State University
Tuesday, February 5, 2013 at 3:00 p.m. in Lytle Hall 214
"Spying on Cages, Generalized Quadrangles and Moore!"
B.G. Kronenthal, University of Delaware
Thursday, November 1 2012 at 11:00 a.m. in Lytle Hall 228
"Blood, Sweat and Tears: the Cable-Trench Problem and some Applications"
Dr. Eric Landquist, Assistant Professor of Mathematics, Kutztown University of Pennsylvania
Thursday, October 18, 2012 at 3:30 p.m. in Lytle Hall 228
"Braids, Permutations and Games"
Dr. Jennifer Franko Vasquez, Assistant Professor of Mathematics, University of Scranton
Tuesday, March 27, 2012 at 5:00 p.m. in Boehm Hall 261
Fifth Annual Thomas Pirnot Lecture in Mathematics
"Adventures with The Moore Method as a Student and Teacher," a MILK Lecture
Dr. E. Lee May, Distinguished Professor of Mathematics, Salisbury University
Thursday, March 8, 2012 at 11:00 a.m. in Lytle Hall 228
"On the Collatz Conjecture," a MILK Lecture
Mr. Patrick Wiltrout, Kutztown University '11
Thursday, March 1, 2012 at 11:00 a.m. in Lytle Hall 228
"On Cardinality of Sets: What does `Big' or `Small' Really Mean?," a MILK Lecture
Mr. John Paul Jablonski, Kutztown University '13
Thursday, February 23, 2012 at 11:00 a.m. in Lytle Hall 228
"Research Experience for Undergraduates- Research Report," a MILK Lecture
Mr. Clinton Watton, Kutztown University '13
Thursday, February 16, 2012 at 11:00 a.m. in Lytle Hall 228
"From Finite Geometries to Translation Planes"
Dr. Craig Culbert, Assistant Professor of Mathematics, Kutztown University of Pennsylvania
Thursday, November 17, 2011 at 11:00 a.m. in Lytle Hall 228
"Aspects of Some Interesting Sets: A Primer"
Dr. Padraig McLoughlin, Associate Professor of Mathematics, Kutztown University of Pennsylvania
Tuesday, November 8, 2011 at 5:00 p.m. in Boehm Hall 260
"Thoughts on a Modified Moore Method Course in Undergraduate Analysis," a MILK Lecture
Dr. Alex Meadows, Assistant Professor of Mathematics, St. Mary's College of Maryland
Tuesday, November 8, 2011 at 11:00 a.m. in Lytle Hall 228
"Chomp, Chomp, Bechewy Chomp: Math and Games
Dr. Alex Meadows, Assistant Professor of Mathematics, St. Mary's College of Maryland
Thursday, October 20, 2011 at 11:00 a.m. in Lytle Hall 228
"Research Experience for Undergraduates- Research Report," a MILK Lecture
Ms. Ashley Dougherty, Kutztown University of Pennsylvania '12
Thursday, October 6, 2011 at 11:00 a.m. in Lytle Hall 228
"Using Math to Make Games fun"
Dr. Ryan Gantner, Assistant Professor of Mathematics, St. John Fisher College
Mathematics Inquiry Learning at Kutztown (MILK) Lectures are funded by the generous support of the Academy for Inquiry-Based Learning, The Educational Advancement Foundation, and Mr. Harry Lucas, Jr.