Two Concurrent Sessions

Undergraduate Mini-courses

October 12, 2016
12:00 – 1:00: Registration/Check-in (in front of Promenade Rooms 101A-102B)
01:00 – 4:30: UG Mini-Course 1: Concave Monotone Mappings in Higher Dimensions (Promenade Room 102A)
01:00 – 4:30: UG Mini-Course 2: Mathematical Modeling in Ecology: Applications of Graph Theory (Promenade Room 102B)
02:50 – 3:15: Break (Promenade Room 101B)
04:30 – 5:30: Keynote Lecture: Scientific Computing in the Movies and Virtual Surgery, Joseph Teran (UCLA) (Promenade Room 102B)
05:30 – 7:00: Poster Session & Reception (Promenade Room 101B)

Undergraduate Mini-Course 1: Concave Monotone Mappings in Higher Dimensions
Taught by: Selenne Bañuelos (CSU Channel Islands)
Time: 1:00pm-4:30pm
Promenade 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.

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
Promenade 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?

Back to NSF Mathematics Institutes' Modern Math Workshop (at SACNAS)