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Department of Mathematics

Upcoming Events

Branwen Purdy at her stall during OMSI meet-a-scientist day.

Branwen Purdy prepares hands-on activities for kids at the OMSI Meet-A-Scientist Day in Portland, to share hands-on learning experiences about her research in topological data analysis.

Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.

Access our archive of events

Mathematical and Computational Aspects of Nonlinear Heat Conduction Models with Generalized Constitutive Laws

Kidder 274
Ph.D. Defense

Speaker: Madison Phelps

This dissertation is dedicated to the selected mathematical and computational challenges for nonlinear partial differential equation models of heat conduction. In particular, we illustrate the mathematical structure and develop robust computational techniques for a class of problems with generalized constitutive laws. The models we consider describe heat conduction with phase transitions in partially frozen to unfrozen soils for which the generalized constitutive laws may be expressed as multi-valued graphs. We show that these generalized constitutive laws can be framed in a single-valued monotone relationship in an appropriate product space. The solutions to these models may feature limited regularity or even discontinuities across the phase change interface and must be posed in the sense of distributions; we develop these formulations in detail. This framework also leads naturally to a new family of analytical solutions. However, the approximation of these solutions present… Read more.

A Comparative Analysis of Mathematical Knowledge for Teaching in Ghana’s Objective-Based and Standards-Based SHS Mathematics Curricula

Zoom
M.S. Presentation

Speaker: Philip Danso

Curriculum reform in mathematics education often seeks to improve students’ conceptual understanding, problem-solving abilities, and readiness for real-world application. In Ghana, the transition from the objective-based Senior High School (SHS) mathematics curriculum to the standards-based curriculum represents a significant shift in instructional expectations and learning goals. This study investigates these two curricula through the framework of Mathematical Knowledge for Teaching (MKT) in order to identify the types of teacher knowledge embedded within each and to examine how these have evolved over time. Using qualitative document analysis, the study codes both curriculum documents based on the MKT domains proposed by Ball, Thames, and Phelps (2008). The analysis focuses on key instructional components, including objectives, learning outcomes, and pedagogical guidance, to determine how each curriculum positions the role of the teacher in facilitating mathematical learning.… Read more.

A Stage-Structured Eco-Evolutionary Model with Pulsed Dynamics

Kidder 274
M.S. Presentation

Speaker: Abigail Adjei

Insecticide application is a major method of pest control in agriculture. Motivated by this, we develop a stage-structured mathematical model for population dynamics coupled with genetic evolution, in which the population is divided into developmental stages and the frequency of a resistant allele is tracked within each stage over time. Using this model, we study how repeated insecticide applications influence resistance evolution in pest populations. The baseline model combines continuous population dynamics, describing recruitment, maturation, and mortality, with allele-frequency dynamics for the resistant allele and discrete pulse updates representing repeated insecticide exposure. We establish basic qualitative properties of the model, including existence and uniqueness of solutions, positivity and invariance of the biologically relevant region, and we characterize how pulse events affect resistant-allele frequencies. The model is then extended to incorporate fitness trade-offs… Read more.