Undergraduate Mini-Course 1: Concave Monotone Mappings in Higher Dimensions
Taught by: Selenne Bañuelos (CSU Channel Islands)
Time: 1:00PM – 4:30PM (break 2:50PM-3:15PM)
Room: Promenade Series Room 102A (Long Beach Convention Center)
Abstract: In this session, we will motivate the discussion of concave monotone mappings in higher dimension in the context of population dynamics. Concave monotone mappings form the real line to itself receive much attention because of this application. One of the interests in studying these mappings in higher dimensions arises in analyzing multi-patch populations – populations of the same species in adjacent locations. We will take an inquiry-based learning approach to define concavity and monotonicity in higher dimensions. We will also show that these mappings form a semigroup under composition. The semigroup property allows us to discuss periodic mapping systems; in the context of population dynamics – populations that rise and fall over a predictable period of time. Finally, students will apply this knowledge and study the stability of a structured two-stage population model with migration.
Selenne Bañuelos is an Assistant Professor of Mathematics at CSU Channel Islands. She earned her PhD from the University of Southern California (USC) in 2013. During her graduate studies she was a founding member of the first Society for Advancement of Chicanos and Native Americans in Science (SACNAS) chapter at USC. Her work is in applied mathematics, more specifically, in biological mathematical models. Dr. Bañuelos is committed to increasing the access to higher education in STEM fields for women and underrepresented minorities.
Undergraduate Mini-Course 2: Mathematical Modeling in Ecology: Applications of Graph Theory
Taught by: Amanda Ruiz (University of San Diego) and Jennifer Prairie (University of San Diego)
Time: 1:00PM – 4:30PM (break 2:50PM-3:15PM)
Room: Promenade Series Room 102B (Long Beach Convention Center)
Abstract: The field of ecology addresses fundamental problems concerning how organisms interact with their environment. Two particularly interesting areas of study include population connectivity and food web dynamics, both of which involve ecological concepts that can be viewed through a mathematical lens. In this workshop, we will explore how applications of graph theory can help us gain insight into these complex interactions to address ecologically relevant problems. We will begin by providing a background in metapopulational and food web theory from an ecological perspective. We will then introduce the basics of graph theory. Finally, students will work in teams to integrate this knowledge and investigate specific questions at the interface of these two topics. For example, how can weighted graphs be used to evaluate the impact of subpopulation extinctions, and how can the effect of individual species on food web dynamics be determined with directed graphs?
Amanda Ruiz is Assistant Professor of Mathematics at the University of San Diego. She received her PhD from Binghamton University, where she started the Graduate Women’s Organization and served as president of the Binghamton University Parent’s Collective, a community of graduate students juggling school and children. After that, she was a teaching and research postdoctoral fellow at Harvey Mudd College. Amanda enjoys doing research in combinatorics. Previous research has been in enumerative combinatorics and matroid theory. She is committed to making mathematics more accessible for women and students of color and considers service in this area an integral part of her job as an educator and academic.
Jennifer Prairie is an Assistant Professor in Environmental and Ocean Sciences at the University of San Diego with research interests in the application of mathematical and computational techniques to address problems in marine ecology. She received her B.A. in Mathematics from Dartmouth College before attending graduate school at Scripps Institution of Oceanography where she got her Ph.D. in Biological Oceanography. After that, she was a postdoctoral scholar and visiting lecturer at the University of North Carolina where she taught several upper-division courses in the Mathematics Department, including Mathematical Modeling with Applications to Biology. At USD she teaches a range of courses in marine science including Introduction to Atmospheric and Ocean Sciences and Plankton Ecology. Dr. Prairie is committed to increasing engagement of students from diverse backgrounds in STEM as the co-director of the National Ocean Sciences Bowl and the faculty advisor of the Women in STEM club at USD.