Research

The Department maintains a vibrant research culture in pure and applied mathematics, fostering interdisciplinary collaboration, student research engagement, and scholarship with both theoretical and real-world impact. As an R1 institution, faculty pursue interdisciplinary research and teaching partnerships across the University, drawing on expertise in mathematical biology, probability and stochastic processes, complex dynamical systems, discrete mathematics, mathematics education, scientific computing, and machine learning and artificial intelligence. Faculty research spans a broad range of areas and evolves in response to emerging scientific and societal challenges.

The active research groups listed below represent key areas of faculty expertise and research activity. Faculty members are actively engaged in these areas and are currently welcoming graduate students to join their groups and contribute to ongoing research and collaborative projects.

---

Biomathematics and Difference Equations

Biomathematics studies biological systems through mathematical modeling and analysis, using differential and difference equations, probability, machine learning, and artificial intelligence to understand and predict phenomena such as population dynamics, disease spread, ecosystem interactions, and cellular processes. Difference equations provide a natural framework for modeling biological processes that evolve in discrete time, complementing continuous models and enabling analytical, computational, and data-driven investigations across the life sciences.

---

Complex Dynamical Systems

Complex Dynamics studies how simple rules repeated over time can create intricate patterns, fractals, and chaotic behavior. Research in this area uses mathematical analysis and computation to understand stability, predict long-term behavior, and uncover order in seemingly random systems.

---

Discrete Mathematics

Discrete Mathematics studies networks, graphs, combinatorics, and optimization. Research combines mathematical theory and algorithms to solve problems in communication networks, scheduling, resource allocation, cryptography, and data science, helping make efficient decisions in complex systems.

---

Machine learning and Artificial Intelligence

Machine Learning and Artificial Intelligence develop mathematical and computational methods for extracting insights from data and building predictive models. Research focuses on statistics, optimization, neural networks, and AI algorithms, with applications in scientific computing, healthcare, image analysis, natural language processing, and data-driven decision-making.

---

Mathematics Education

Mathematics Education focuses on improving how mathematics is taught and learned at all levels. Research develops innovative curricula, studies effective teaching strategies, and explores pedagogy to help students build a deeper understanding of mathematical concepts.

---

Scientific Computing and Numerical Linear Algebra

Scientific Computing and Numerical Linear Algebra focus on developing and analyzing algorithms to solve mathematical problems on computers. Research emphasizes efficient computation, matrix methods, and numerical stability, with applications in scientific modeling, data analysis, and large-scale simulations across science and engineering.

---

Probability and Stochastic Processes

Probability and Stochastic Processes provide the mathematical framework for understanding randomness. They study how to measure likelihood, model evolving random systems, and make predictions under uncertainty, with applications in finance, ecology, biology, and decision-making.