FIDUCIAL DISTRIBUTION TO ESTIMATE THE PARAMETERS OF LOGNORMAL DISTRIBUTION FOR COMPLETE, CENSORED OR ZERO INFLATED DATA

Abstract: Fiducial inference was introduced in the first half of the 20th century by Fisher (1935). While the method originally fell out of favor due to nonexactness issues in multivariate cases, the method has garnered renewed interest in the last decade. Fiducial inference attempts to find a middle ground between the frequentist and Bayesian perspectives. The fiducial argument allows one to fit a posterior-like distribution on a target parameter θ in a way that is entirely data-driven and does not rely on a sometimes-arbitrary prior selection. While the strengths and limitations of generalized fiducial inference (GFI) continue to be explored, its usefulness has already been illustrated in numerous practical applications. This talk will be focusing on implementation of fiducial distributions to estimate different parameters of lognormal distribution based on complete, censored or zero-inflated data. Practical examples will demonstrate that the fiducial methods are accurate and practically exact even for small samples.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Biography: Md Sazib Hasan is an Assistant Professor of Mathematics in the Department of Mathematics at Utah Tech University. He has been teaching at UT since 2019. He received his PhD. in Statistics from University of Louisiana at Lafayette in 2019. His doctoral dissertation was in fiducial inference for Lognormal distribution which primarily applied to real-world issues in environmental sciences and pollution studies.

His research interest lies in small sample problems, statistical inference, and statistical learning. Hasan is a Project-NExT fellow and demonstrates a keen interest in undergraduate research, evidenced by his mentorship resulting in twenty-four student presentations across local, regional, and national conferences. Currently, he is serving as a First Vice Chair at the MAA Intermountain Section.

Contact: MdSazib.Hasan@utahtech.edu

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UNCERTAINTY QUANTIFICATION FOR ECOLOGICAL DYNAMICS: MODELING HETEROGENEOUS ICE ALGAL BLOOMS

Abstract: When parameterizing dynamical systems models of biological processes, we often use summary statistics (e.g., the mean) reported in experimental or observational studies. However, these summary statistics are abstractions, concealing variation occurring over space, time, or among individuals. Further, we know that the behavior of a nonlinear model using mean parameter values will differ from the mean model behavior if the parameter is instead treated as a random variable. Algae growing within polar sea ice provides an example of a system where extreme local heterogeneity in environmental conditions results in local heterogeneity in algal growth rates. Ignoring this and using a fixed, mean growth parameter to approximate regional dynamics can result in incorrect predictions of bloom timing and magnitude. Instead, algal growth rates at a given location should be treated as a random variable capturing the known heterogeneity. In this talk, I will provide an introduction to generalized polynomial chaos methods as an elegant, computationally efficient method for incorporating heterogeneous growth rates into standard algal bloom models, resulting in improved predictions of bloom dynamics. This method is broadly applicable for any system where local heterogeneity needs to be accounted for when considering aggregate dynamics over larger scales.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Biography: Dr. Jody Reimer is an Assistant Professor at the University of Utah in both the Department of Mathematics and the School of Biological Sciences. She received her PhD in 2019 from the University of Alberta, Canada, working with Mark Lewis and Andrew Derocher, and an MSc as a Rhodes scholar at the University of Oxford, working with Philip Maini and Michael Bonsall. Her research interests include population dynamics, uncertainty quantification, integrating models and data, and optimal control theory. Much of her work is motivated by the biology of polar regions--from polar bears to ice algae--and, more recently, by the ecology of the Great Salt Lake.

Contact: jody.reimer@utah.edu

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Graph Coloring

Abstract: A proper coloring of a graph is an assignment of colors to the vertices of the graph such that no two adjacent vertices receive the same color. Graph coloring is a classical subject in Graph Theory which contains many challenging problems. The famous Four-Color Theorem which stood as an unsolved problem for over a century says that every planar graph has a proper 4-coloring. Graph coloring has also numerous applications to real world problems such as scheduling and timetabling. In this talk, I will discuss some graph coloring results, problems and applications.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Biography: Dr. Aysel Erey is an assistant professor in the Department Mathematics and Statistics at Utah State University. She received her Ph.D. from Dalhousie University in Canada. Her research interests are in the area of Graph Theory.

Contact: aysel.erey@usu.edu

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Sharing Lesson-Specific Instructional Knowledge

Abstract: Do you know instructors that teach well, where you would love to get into their heads about how they reason through their lessons? Or, do you have a lesson about an important mathematical idea that you have refined over time, and that you think would be valuable to other instructors? Questions like this prompted us to develop a written genre for sharing lesson-specific teaching knowledge in undergraduate mathematics. In this discussion I introduce a way to share the results of having carefully crafted and refined a lesson over time, which we (my coauthors) call Lesson Analysis Manuscripts (LAMs). LAMs can help us learn from each other, and incrementally improve undergraduate math teaching, through detailed accounts of specific lessons. Importantly, we emphasize sharing knowledge and skills that aren’t usually part of our teaching conversations, such as how to think through instructional choices, how to lead classroom discussions to support learning, and how to describe the student thinking in our classrooms.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Biography: Dr. Doug Corey is a professor of Mathematics Education at Brigham Young University. His research has focused on elements and characteristics of high-quality instruction; Japanese math instruction and teacher education; and sharing detailed, lesson-specific instructional knowledge through carefully crafted lesson plans. He is co-editor, with his colleague Steven Jones, of a recent book published by the MAA: Sharing and Storing Knowledge about Teaching Undergraduate Mathematics. The book introduces a written genre for college mathematics instructors to share lesson-specific knowledge, a genre they call Lesson Analysis. His real love is teaching math, and showing the power of math to make sense of the everyday world. He recently turned this love into a youtube channel called "MathTheWorld" which mathematically analyzes everyday situations.

Contact: corey@mathed.byu.edu

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MATHEMATICAL MODELS FOR INVESTIGATING THE DYNAMICS OF MOSQUITO-BORNE DISEASES AND CLIMATE EFFECTS

Abstract: In this talk, we will discuss two undergraduate research projects that use mathematical models to investigate the population ecology and transmission dynamics of mosquito-borne diseases, such as dengue and West Nile virus. Specifically, the talk will focus on the potential impact of successful biocontrol strategies, including the release of Wolbachia-infected mosquitoes and the control of larvae and adult mosquito populations, on mitigating the spread of these diseases. We will also highlight how incorporating local temperature data and the passive immunity of birds into models can aid in predicting disease transmission dynamics.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Bio: Dr. Vinodh Chellamuthu is an associate professor of mathematics at Utah Tech University in St. George, Utah. He received his MS in applied mathematics from Tulane University and PhD in mathematics from the University of Louisiana at Lafayette. He is firmly committed to promoting quality education for future scientists by creating opportunity channels for career development through research as a high impact teaching pedagogy. He has mentored several undergraduate research projects coming directly from business, industry, and government agencies. His work with students has been supported by MAA’s PIC Math and NREUP grants and funding from the Center for Undergraduate Research in Mathematics. In recognition of his success as a teacher-mentor, Dr. Chellamuthu has received the Early Career Mentoring Award from CUR, the Distinguished Teaching Award from the MAA’s Intermountain Section, and the Distinguished Teaching Award from Utah Tech University. Dr. Chellamuthu currently serves as a councilor on the Council on Undergraduate Research, Vice-Chair of Programs for BIG SIGMAA, Program Coordinator for UR SIGMAA, and past Chair for the MAA Intermountain Section.

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Mathematical Models of Evolution

Abstract: Mathematicians have often used probability to model evolutionary ideas. The complicated dynamics of how populations change over time inspire new and exciting mathematical systems and interactions. Despite the different settings of these models, many common themes can be observed in the dynamics and results. In this talk, we’ll discuss a few of these models, ranging from more historical setups to ongoing research.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Bio: Dr. Erin Beckman is an Assistant Professor at Utah State University. Before joining the faculty at USU, Erin did her graduate work at Duke University and her postdoc in Montreal, Quebec. Her research is in the field of probability, where she is interested in problems with applications in biology and connections to partial differential equations.

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3D Printing and Mathematics Teaching

Abstract: The recent (2009) expiration of the fused deposition modeling (FDM) patent has led to a great expansion in the availability of 3D printing technology. Today, 3D printers can be found in libraries, universities, and homes. In my presentation, I will give a brief history and overview of the FDM process, outline the process of designing and creating an object using a 3D printer, and give a few ideas as to how 3D printed models could enhance mathematics teaching and learning.

This presentation will be both practical and historical and should be of interest to a wide audience.

Bio: Skyler Simmons is an assistant professor at Utah Valley University. His research focuses on periodic orbits featuring collisions in the Newtonian n-body problem. Outside of mathematics, he also enjoys playing the piano, computer programming, and (unsurprisingly) 3D printing.

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Why 𝜋/5 should be included among the special angles

Abstract:

Since the earliest development of trigonometry in the days of Ptolemy and continuing up to our day special angles have been used while learning and applying the subject. These angles include 90, 60, 45 and 30 degrees or in radian measure 𝜋/2, 𝜋/3, 𝜋/4, and 𝜋/6. There are many good pedagogical and practical reasons to study the trigonometric function values of these angles. But an astute student may note that 𝜋/5 seems to be missing its rightful place in this list. Historically the special angle 𝜋/5 played an important role in applications and has beautiful and surprising geometrical implications including the golden ratio. We will look at these applications and connections in a bid to restore 𝜋/5 to its historic position as a special angle.

This presentation will be both practical and historical and should be of interest to a wide audience.

Bio:

Dr. Troy Goodsell is a professor of Mathematics at Brigham Young University-Idaho where he has taught since 2001. Previously he held positions at McMurry University in Abilene Texas, Pittsburg State University in Pittsburg Kansas, and Brigham Young University in Provo Utah. He received his PhD. from Brigham Young University and did his undergraduate work at the University of Utah. The history of mathematics is his main area of interest, and he has given a number of talks on the subject at both MAA section meetings and at the national meetings. He is deeply interested in both the teaching of a wide variety of mathematics courses and in helping the students learn the history of the subject so as to understand the culture and society and individuals that brought the science of mathematics to us. When not doing mathematics, he enjoys spending time with his children and grandchildren and enjoys camping and many other outdoor activities.

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MOVING FROM MEMORY TO MINDFULNESS IN MATHEMATICS TEACHING AND LEaRNING

Abstract: Learn how the brain processes new information, how this processing is affected by stress, and how a focus on memory tasks can trigger stress for many students. Explore several strategies for shifting student focus from memory recall to mindful problem solving. Theories and strategies shared will connect to Dr. Bachman's most recent collaborations with a licensed clinical social worker trained in trauma therapy. The presentation will also integrate research into student images of doing mathematics using the Draw Yourself Doing Mathematics drawing prompt.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Dr. Rachel Bachman is an associate professor of mathematics education at Weber State University where she teaches mathematics courses for developing elementary and secondary teachers. Her work at WSU focuses on developing effective strategies for teaching and learning mathematics, and her research interests include creating learning sequences beginning from activities and hands-on materials, helping struggling students succeed in mathematics, understanding student views about mathematics, and the use of physical movement to learn mathematics.

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Rational Maps and Towers of Finite Fields

We can create sequences from rational maps by iterating a map via composition. As we vary the starting value, this may vary the behavior of the sequence. The sequence could loop back to the starting point, or have a long tail then have a repeating set of numbers, or it can continue unbounded. If we restrict our set of numbers to only live in finite fields, then all points either live on a cycle or live on a tail. So, the question we want to explore is how many points are there that live on a cycle? Does this number vary widely as we travel up a tower of finite fields? In general, this is a difficult question to answer since a random rational function behaves chaotically, but for certain special families we can explore and answer these questions.

This talk is appropriate for faculty, undergraduate students, and a more general audience.

Dr. Bianca Thompson is an assistant professor at Westminster College. She identifies as queer, Latina, and biracial and has traveled from one end of the country to the other for her education (Massachusetts to Hawai'i and back again). Her research falls in the intersection of discrete dynamical systems and number theory in the relatively young field of arithmetic dynamics. She wants to find more ways to create a classroom environment where students know they belong.

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