Friday April 12
12:30 - 2:30 p.m. - Project NExT Workshop: Leveraging Teaching for Research
Delzell 109
2 - 2:50 p.m. - Registration
Patterson Hall 132
2:50 - 3:00 p.m. - Welcome and logistics
Catalin Georgescu, chair, University of South Dakota
Patterson Hall 117
3:00 - 3:20 p.m. - Investigating the Relationship Between Maternal and Congenital Syphilis
Kaleesta Waysman, undergraduate student, University of South Dakota
Syphilis is on the rise in the United States. The bacterium that causes syphilis can be passed from pregnant woman to fetus, causing malformations in the newborn. I will explain the SIR model I created to represent the infection and identify steady states and trends in the disease. The information from this model and further calculations has the potential to strengthen or encourage modification to the CDC's existing public control policies for syphilis and congenital syphilis.
3:20 - 3:40 p.m. - Implementing Lecture-Based Tutoring in Optimization Modeling Courses
Fabio Vitor, faculty, University of Nebraska Omaha
Lecture-based tutoring is an active learning method where the instructor selects a student and asks them a question. If the student cannot properly answer the question, the instructor tutors them to an appropriate answer. By asking each student in the class several questions during the semester, the instructor is aware of all students’ progress on learning outcomes. This talk will discuss the implementation of lecture-based tutoring to teach optimization modeling. Optimization modeling is frequently taught in operations research courses where the goal is to construct mathematical models to optimize systems with scarce resources. Some common classes of optimization models include linear, integer, and nonlinear programming.
3:40 - 4 p.m - "Academia vs. Industry: a (slightly unorthodox) comparison"
Dora Velcsov, faculty, University of Nebraska Omaha
In my career I had the chance to explore professions and activities that have some intersection, yet they require completely different types of training and knowledge. Although not a comprehensive list, the following are part of the common denominator: abundant logic, a scientific mind, many numbers, concept manipulation, interesting patterns, tenacity, and inevitably, computer work. Oh, and communication skills (I almost forgot!) The professions and experiences I’ve had the luck to be part of are: mathematics teaching, research, and service; telecommunication engineering and forecasting; financial data analytics; and health coaching. Quite a nice combo! The contrast of these professions and their distinct environments is remarkable, and the real-world experience is priceless. I am very grateful to have been a part of totally different professions that have allowed me to acquire diverse skills and to experience interesting thinking and behavior patterns. In this talk I’d like to share my reflections and comparisons of various aspects of academia and industry that go beyond the obvious differences between teaching and, say, a computer job. I hope this will help students understand that the choice of a profession goes beyond course work and exams. On the other hand, I hope this will help faculty view their choice of academia in a different light. Note: there won’t be any formulas in this talk! Sad, but true.
4 - 4:20 p.m. - Extended WEI Framework and the Convergence of α-Schemes with Source Terms for Conservation Laws
Nan Jiang, faculty, University of South Dakota
A class of highly effective finite difference methods, α-schemes, for hyperbolic conservation laws was constructed by S. Osher and S. Chakravarthy in the mid-80's. Nonetheless, the question of the entropy convergence of these schemes has been open for a long time. Fortunately, for m=2, I was able to show the entropy convergence of the semi-discrete α-schemes with or without source terms [Jiang, 2012] and of the homogeneous fully-discrete α-schemes [Jiang, 2014]. In this talk, we will address the convergence issues of the non-homogeneous case. By relying on an extended Yang's WEI (wave-wise entropy inequality, 1995) framework [Jiang, 2019], the α-scheme with source term, when m=2, indeed possesses of entropy convergence [Jiang, 2023].
4:20 - 4:40 p.m. - Break
4:40 - 5:40 p.m. - Pattern Avoidance in Restricted Permutations
Opel Jones, Researcher, John Hopkins University Applied Physics Laboratory
In 1974 Dumont found two types of permutations are counted by the same sequence. The first type is a permutation in which each even entry is followed by a smaller entry, and each odd entry is followed by a larger entry, or ends the permutation. The second type is a permutation wherein if an entry is a deficiency, it must be even, and if an entry is an exceedance or a fixed point, it must be odd. These are now known as Dumont permutations of the first and second kinds. In this talk we will discuss several enumerations of restricted Dumont permutations, that is Dumont permutations avoiding certain patterns. We will also briefly discuss their proofs which involve methods using induction, block decomposition, Dyck paths, and generating functions. We will conclude with a conjecture that the patterns 2143 and 3421are indeed Wilf-equivalent on Dumont permutations of the first kind.
6 - 7:30 p.m. - Reception at CeeCee's, Downtown Vermillion
7:30 - 8:30 p.m. - Executive Meeting at CeeCee's
Saturday April 13
8 - 8:30 a.m. - Registration
Patterson Hall 117
8:30 - 8:50 a.m. - An Analysis of Initial Perceptions of Mathematics in a First-Year College Course
Thomas Spoehr & Emman Osamau, graduate students, University of Nebraska Omaha
First-year college mathematics courses serve a wide population of students with various mathematical backgrounds and experiences. These experiences shape the way students view themselves as mathematical learners and their mindsets toward mathematics. We report our findings on student reflections written in Fall 2023 by students in a college algebra course. These findings relate to students’ mathematical mindsets, their life events prior to beginning college algebra, and past mathematical experiences. Our work sheds light on students’ dispositions towards mathematics at the start of a first-year mathematics course and provides valuable insights for math faculty.
8:50 a.m. - 9:10 a.m. - Topologizing the Prime Spectrum of a Frame
Ramiro Lafeuente-Rodriquez, faculty, University of South Dakota
We consider a lattice with certain natural characteristics and construct a topology by using the prime elements of the lattice. We briefly go over some properties of this topology and finally, we discuss some further research.
9:10 - 9:30 a.m. - Musical Systems with Z_n Cayley Graphs
Gabriel Picioroaga, faculty, University of South Dakota
We apply ideas from group theory to study and interpret known concepts from Western music. We show that chords, the circle of fifths, scales and certain aspects of the first species of counterpoint are encoded in the Cayley graph of the group Z_12, generated by 3 and 4. Using Z_12 as a model, we extend the above music concepts to a particular class of groups Z_n, which displays geometric and algebraic features similar to Z_12. Using Maple software, we implement these new constructions and show how to experiment with them musically. We will also present the construction of two cigar-box guitars, one with the standard temperate tuning in Z_12 and another with tuning and chords in Z_15 with respect to generators 3 and 5.
9:30 - 10 a.m. - Break
10 - 10:20 a.m. - Proof by Blobs
Keith Gallagher, faculty, University of Nebraska Omaha
The Nature and Uses of Generic Examples in Undergraduate Topology Expert mathematicians use examples and visual representations as part of their informal mathematics reasoning when constructing proofs. In contrast, the ways undergraduates reason and work toward creating proofs is an open area of investigation, particularly in advanced mathematics. Furthermore, research on students’ reasoning in topology is largely unexplored. We present a case study of an undergraduate taking a first course in general topology and her use of generic examples in argumentation prior to producing formal proofs and counterexamples. We discuss patterns that emerged in her use of generic examples when proving true statements and disproving false claims. We compare and contrast this student’s generic examples with other generic examples in the literature from other content areas within mathematics, and we argue that generic examples are not one-size-fits-all but rather must be fit-for-purpose. Our results suggest that generic examples may be particularly useful for students writing proofs when they may not have access to specific examples.
10:20 - 10:40 a.m. - Dieting, Optimization, and Linear Algebra
Fabio Vitor, faculty, University of Nebraska Omaha
We are all going on a diet! This talk will discuss the successful implementation of an optimization project into an applied linear algebra course. In this project, students model an optimization problem to determine their daily diet. Their model determines the amount of different foods they should consume to either maximize weight loss or muscle gain. Some constraints include the maximum amount of calories, protein, carbohydrates, fat, fiber, and sodium they can ingest daily. The project also requires students to solve their model using the simplex method, which optimally solves linear programs. The primary goal of this project is to help students visualize several of the concepts learned throughout the semester such as solving systems of linear equations, linear independence, basis, and rank of a matrix into a real-world application. Another goal of this project is to educate students about optimization and operations research, and the importance of making better decisions when it comes to food.
10:40 - 11 a.m. - Have Exams Changed Over the Years?
Mark Sand, College of Saint Mary
I was lucky enough to find three exams from the 1930s. These will be discussed, along with some of the history behind them, the mathematics needed to solve the problems, and comparison with modern exams.
11 a.m. - 12 p.m. - Business Meeting
