Spring 2025
Thursday, February 20th
Dr. Dick Forrester, Dickinson College
The First-Year Seminar Assignment Problem
At Dickinson College, all incoming first-year students enroll in a First-Year Seminar designed to introduce them to the rigors of college-level work through writing assignments, research projects, and classroom discussions. To match students with seminars that align with their interests, they rank their top six choices from a list of options. The college then assigns students to seminars with the dual objectives of honoring individual preferences while maintaining diversity within each seminar.
This talk will explore student-faculty research projects that have shaped the modeling techniques used in the assignment process. We will introduce key concepts in optimization modeling, multi-criteria optimization, and linearization approaches, highlighting how these methods balance competing priorities.
Noon
Tome 115
Pizza provided
Tuesday, March 18th
Dr. Grant Innerst, Shippensburg University
Approaching Minimum Chi-Square Estimation Through an Algebraic Geometric Lens
This work arises from the realization that statistical estimation problems often display a strong algebraic structure. In certain cases, we can leverage this structure to use powerful software from the algebraic community to find solutions that were previously unattainable. We focus on using tools from numerical algebraic geometry to solve estimation problems that fall into the class of minimum chi-square estimators.
Noon
Tome 115
Pizza provided
Thursday, April 10th
Mathematics & Computer Science Majors' Dinner
HUB Social Hall (or Rector Atrium)
6:00pm
Served meal by Dining Services
Tuesday, April 15th
Professor English and Professor Jackson
What does a rock falling into a hole have to do with iterated maps and chaos? Approaching first-semester physics problems in a creative way"
In PHYS 131, students are asked to find the depth of a chasm from the time it takes to hear the sound of a dropped boulder hitting the bottom. The standard solution involves a system of two equations with two unknowns, but it turns out that a recursive method will also give the right answer. We analyze this non-traditional approach using iterated maps and determine the conditions under which it converges to the correct solution. Interestingly, the iterative method fails to converge when the well depth is large enough for the rock to reach the speed of sound; instead, we get a series of period-doubling bifurcations very similar to what is seen in the logistic map. It turns out that other basic physics problems can also be solved in this way, as long as a mathematical condition is satisfied.
Noon
Tome 115
Pizza provided
Thursday, April 24th
Megan Triplett '25
Mathematics Honors Presentation - Finite and Countable Dynamical Systems
A dynamical system is a function f from a set X to itself. From a given starting element x in X, this function is then iterated — that is, we apply the function repeatedly to produce orbits x, f(x), f(f(x))=f2(x). It is possible for orbits to be periodic. In our investigations, X is either a finite set or a countably infinite set, and, in the countably infinite case, we focus on dynamical systems that exhibit behavior similar to finite dynamical systems. In particular, we illustrate that every orbit in a finite dynamical system is eventually periodic, and we outline conditions under which countably infinite dynamical systems exhibit the same property. To relate such dynamical systems to finite ones, we introduce bounds on the eventual behavior of countably infinite systems that depend on the function on which it is constructed. From there, we investigate a particular finite dynamical system on the natural numbers: sums of functions of digits, and we focus on finding a bound for such systems. We introduce a bound that is easier to compute than Stewart's tight bound C and tighter than Kiss's loose bound. Then, to discuss countable sets that need not be a subset of the natural numbers, we introduce discrete Lyapunov functions.
Noon
Tome 115
Pizza proivded
Wednesday, May 7th
Mathematics & Computer Science Year End Picnic
Tome Outdoor Classroom (Rain Location: Tome 115)
12:00pm
Hot dogs, hamburgers and veggie burgers grilled to perfection by our Math & CS faculty.