What If? Explaining the Past/Predicting the Future

Overview

When is the right time to bluff in poker and diplomacy? How does a dating site find our right match? What needs to be done in order to stop an infectious disease from becoming epidemic? This cluster, with faculty from sociology, anthropology, statistics, and mathematics, will teach students how to build and test models in the natural sciences and social sciences. By using these models to evaluate different "what if?" scenarios, we can then explain the past, predict the future, and make the world more comprehensible.

One example of how modeling has contributed to notable recent progress in biosciences is the completion of the Human Genome Project, which is the first step toward a molecular genetic understanding of the human organism. To synthesize the massive sets of loosely structured data generated and to draw knowledge from them, scientists have relied heavily on mathematical and statistical models. In the social sciences, models can test theories of economics by creating a population of agents that exchange commodities at prices they determine from local information. Alternatively, computer simulations may determine the outcome of social policies under different conditions. These are used in domestic, international and military operations to discover the envelope of possibilities resulting from being different "what if" scenarios.

By participating in this Focus cluster, students will learn how to formulate mathematical models that can be used to answer scientific questions. They will also learn a variety of techniques for studying the models, including mathematical analysis, computations, and simulations. The ability to identify essential features of a system that must be represented in a model, and then to properly interpret model outputs in the appropriate scientific context, is a valuable skill that will be useful in many fields.

Courses

Seminar: Math 161FS.01 — Mathematics: Introduction to Mathematical Modeling in Biology (R, STS, QS)

Anita Layton, Robert R. & Katherine B. Penn Professor of Mathematics and Professor of Biomedical Engineering

Introduction to techniques used in the construction, analysis, and evaluation of mathematical models. Modeling topics include: How fast will an infectious disease spread within a community? What fraction of a population need to be vaccinated in order to eradicate a disease, and what is the best vaccination policy? How stable is a given ecosystem? Students will learn how to frame a scientific quest ion in mathematical terms; how to study the model using mathematical tools and techniques; how to interpret model predictions in the appropriate scientific context.

Seminar: Statistics112FS.01 — Statistics: Better Living Through Data Science: Exploring, Modeling, Predicting, Understanding (STS, QS)

Mine Cetinkaya-Rundel, Assistant Professor of the Practice, Statistics

Combining tools and techniques from statistics, mathematics, computer science, and the social sciences, students in this course will learn to use data to understand natural phenomena, explore patterns, model outcomes, and make predictions. Case studies will include examples from election forecasts, movie reviews, and online dating match algorithms. Discussions around reproducibility, data sharing, data privacy will accompany these case studies. Students will gain experience in data wrangling and munging, exploratory data analysis, predictive modeling, and data visualization, and effective communication of results. The course will focus on the R statistical computing language. No computing background is necessary.

Seminar: Evolutionary Anthropology 212FS — Social Structures in an Evolutionary Framework (NS, STS)

Jenny Tung, Assistant Professor, Evolutionary Anthropology

Exploration of the intersection between social structure, social behavior, and evolution. Examines the role of social and historical factors in promoting evolutionary change and the evolutionary history of social structures themselves, with an emphasis on humans and other primates. Topics include: evolution in modern human societies, evolutionary demography, genetic signatures of social and cultural change, the genetics of socially relevant traits, and social environmental effects on health.

Seminar: Sociology 176FS — Mathematical Models of Self, Identity and Emotion (CI, R, SS)

Lynn Smith-Lovin, Professor, Sociology

We explore a mathematical model of how people attempt to maintain identities in institutional settings, and self-actualize their fundamental conceptions of themselves in moving from one setting to another.  In other words, we explore a model of why people do what they do: both in performing normal roles, responding to odd situations, and trying to feel good about themselves.  The class involves reading academic literature, doing presentations, collecting evidence about research questions that you have developed, and proposing new research that will contribute to this growing literature.  The goal is to teach you to think scientifically about everyday life: both the routine and the unexpected parts of that life.

Faculty Director

Anita Layton
Anita Layton
  • Robert R. & Katherine B. Penn Professor of Mathematics
  • Professor of Biomedical Engineering
Office: 
213 Physics Bldg
Campus Box: 
90320
Phone: 
(919) 660-6971

anita.layton@duke.edu