Can We Bridge the Gap? Mathematics and the Life Sciences, Part 1–Calculus-Based Modules, Programs, Curricula

This editorial serves as an introduction to Part 1 of the Special Issue Mathematics and the Life Sciences–a collection of articles showcasing ideas, examples, pedagogical frameworks, and curricular materials aiming to bridge the stubbornly persistent gap at the undergraduate level between the mathematical and the life sciences. The special issue features authors from public and private institutions of diverse types, sizes, and geographic locations: community colleges, liberal arts colleges, and research-oriented universities. We hope this special issue will serve as a resource to faculty who seek to make changes to their own course(s) or initiate curriculum reforms at their own schools. Part 1 focuses on educational initiatives that are appropriate for Calculus classes or require calculus as a prerequisite. Part 2 of the special issue features course materials and programs based on discrete mathematics, computational approaches, and statistics. Part 2 also includes articles on internship programs and co-curricular opportunities

Can We Bridge the Gap? Mathematics and the Life Sciences: Part 2–Discrete Models, Statistics, Co-Curricular Opportunities

This editorial serves as an introduction to Part 2 of the Special Issue Mathematics and the Life Sciences–a collection of articles showcasing ideas, examples, pedagogical frameworks, and curricular materials aiming to bridge the stubbornly persistent gap at the undergraduate level between the mathematical and the life sciences. The special issue features authors from public and private institutions of diverse types, sizes, and geographic locations: community colleges, liberal arts colleges, and research-oriented universities. We hope this special issue will serve as a resource to faculty who seek to make changes to their own course(s) or initiate curriculum reforms at their own schools. This Part 2 special issue features course materials and programs based on discrete mathematics, computational approaches, and statistics. It also includes articles on internship programs and co-curricular opportunities. Part 1 focuses on educational initiatives that are appropriate for calculus classes or require calculus as a prerequisite

Age-Structured and Vaccination Models of Devil Facial Tumor Disease

Tasmanian devil populations have been devastated by devil facial tumor disease (DFTD) since its first appearance in 1996. The average lifespan of a devil has decreased from six years to three years. We present an age-structured model to represent how the disease has affected the age and breeding structures of the population. We show that with the recent increase in the breeding of juvenile devils, the overall devil population will increase but not nearly to pre-DFTD levels. The basic reproductive number may be increased with the influx of young breeding devils. In addition, our model shows that the release of nearly 100 captive-bred, vaccinated devils into infected, wild populations may help eliminate the disease and hence enable the population\u27s recovery. Specifically, we demonstrate that with this release of captive-bred, vaccinated devils the basic reproductive number is decreased to below one

Paying Our Dues: The Role of Professional Societies in the Evolution of Mathematical Biology Education.

Mathematical biology education provides key foundational underpinnings for the scholarly work of mathematical biology. Professional societies support such education efforts via funding, public speaking opportunities, Web presence, publishing, workshops, prizes, opportunities to discuss curriculum design, and support of mentorship and other means of sustained communication among communities of scholars. Such programs have been critical to the broad expansion of the range and visibility of research and educational activities in mathematical biology. We review these efforts, past and present, across multiple societies-the Society for Mathematical Biology (SMB), the Symposium on Biomathematics and Ecology Education and Research (BEER), the Mathematical Association of America (MAA), and the Society for Industrial and Applied Mathematics (SIAM). We then proceed to suggest ways that professional societies can serve as advocates and community builders for mathematical biologists at all levels, noting that education continues throughout a career and also emphasizing the value of educating new generations of students. Our suggestions include collecting and disseminating data related to biomath education; developing and maintaining mentoring systems and research communities; and providing incentives and visibility for educational efforts within mathematical biology

Hyperbolic Dehn surgery and convergence of Kleinian groups.

Let N be a compact three-manifold with boundary containing k tori. Assume that the interior of N is homeomorphic to H\sp3/G, where G is a nonelementary, torsion-free geometrically finite Kleinian group with the property that each parabolic element of G is conjugate into one of k rank two parabolic subgroups corresponding to the tori. We show that the interiors of most manifolds obtained from N by Dehn filling admit geometrically finite hyperbolic structures that are geometrically close to H\sp3/G. We use the above result to obtain a general recipe for constructing examples of convergent sequences of discrete, faithful representations of a group into PSL(2, C) whose algebraic limits are properly contained in their geometric limits.Ph.D.MathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/129966/2/9711945.pd

On impulsive integrated pest management models with stochastic effects

We extend existing impulsive differential equation models for integrated pest management (IPM) by including stage structure for both predator and prey as well as by adding stochastic elements in the birth rate of the prey. Based on our model, we propose an approach that incorporates various competing stochastic components. This approach enables us to select a model with optimally determined weights for maximum accuracy and precision in parameter estimation. This is significant in the case of integrated pest management because the proposed model accommodates varying unknown environmental and climatic conditions, which affect the resources needed for pest eradication

Almost alternating links

AbstractWe introduce the category of almost alternating links: nonalternating links which have a projection for which one crossing change yields an alternating projection. We extend this category to m-almost alternating links which require m crossing changes to yield an alternating projection. We show that all but five of the nonalternating knots up through eleven crossings and links up through ten crossing are almost alternating. We also prove that a prime almost alternating knot is either a hyperbolic knot or a torus knot. We then obtain a bound on the span of the bracket polynomial for m-almost alternating links and discuss applications