Properties of powers of ideals, including associated primes and depths. In particular, recent work has been focused on monomial ideals, which are then represented as graphs, simplicial complexes, or matrices (often unimodular) depending on the situation. Algebraic questions are then answered using these structures.
Dr. Acosta's research deals with equations and polynomials with special properties over finite fields. She has worked on the characterization of polynomials in two variables with minimal value set, matrix equations of the form Xn=B, and other related problems.
Dr. Bishop’s research interests are in two main areas: research on mathematics classroom discourse and research investigating children's mathematical thinking. She uses both qualitative and quantitative approaches to identify patterns in teacher-student and student-student discourse to better understand how discourse influences mathematics learning and the development of positive mathematics identities. She is currently working on an NSF CAREER grant focused on middle grades mathematics discourse and recently finished an NSF grant exploring K-12 students' conceptions of integers.
Dr. Sorto's research focuses on the preparation of teachers in the area of Statistics, the impact of professional development, and comparative studies in Latin-America and Africa. In particular, she is interested in developing instruments to measure content knowledge for teaching, teaching quality and analyzing its effect on student achievement. The National Science Foundation (NSF) recently awarded her a CAREER research grant to investigate the Mathematics instruction of English language learners in the state of Texas.
Dr. Strickland's current research focuses on the role of discourse in classrooms, particularly how teachers respond to students' mathematical thinking. Other areas of interest include preparing future teachers, mathematics majors learning to prove as they transition to upper level coursework, as well as everyone learning more geometry.
Dr. Sun has interests in statistical genetics and bioinformatics and has published more than 20 peer-reviewed research articles in high-impact journals. Dr. Sun's research focuses on addressing challenging genetic and epigenetic questions using statistical and computational methods. She has collaborated with biomedical researchers from different research groups in Canada and the United States on projects related to complex diseases (e.g., cancer and arthritis). She has also been developing statistical methodologies and software packages for genomic problems using Bayesian methods, hidden Markov models, Markov Chain Monte Carlo algorithms, and linear models.
Her research interests include students’ mathematical thinking and cognition, research in undergraduate mathematics education (RUME), the impact of mathematical modeling tasks on students’ mathematical thinking, and how mathematical reasoning supports STEM education. She is currently studying how individuals learn to use mathematics as a representational system and the role teacher questioning may have in helping individuals coordinate their mathematical and non-mathematical knowledge.
Her research interests focus on two primary areas: student understanding and activity in advanced mathematics, and supporting teachers in promoting high-level reasoning in their classrooms. Dr. Melhuish is currently co-PI on a DRK-12 grant looking at the efficacy of a sustained PD model at the 3rd-5th grade level. Her secondary project is the development of models of student thinking in abstract algebra and design and maintenance of the Group Theory Concept Assessment, a measure meant to reflect student thinking in this area.
Dr. Wang’s research interests fall under the broad heading of numerical methods and scientific computing for problems in science and engineering governed by partial differential equations. Her research is interdisciplinary and addresses modeling and computation of applied problems in science and engineering. She has devised new finite element methods and established the corresponding convergence analysis for (1) linear hyperbolic equations, (2) elliptic Cauchy problems, (3) second order elliptic equations in nondivergence form, (4) Maxwell's equation, (5) linear elasticity and elastic interface problems, (6) div-curl systems, and (7) biharmonic equations.
Her research interests include areas of teaching and learning that foster productive struggle and investigation of professional teacher noticing of student thinking at pre-service and in-service levels. She is co-author of the Math Explorations curriculum, a Texas Mathworks middle school textbook series state adopted in Texas and the Mathworks Junior Summer Math Camp curriculum. She provides professional development to support curriculum implementation. She is the Mathworks research coordinator, overseeing Mathworks related research about summer math camps, teacher training, curriculum, and classroom interactions with faculty and doctoral students in mathematics and mathematics education.