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

Math 165FS: Cryptography and Society (QS, STS)

Lillian Pierce, Nicholas J. and Theresa M. Leonardy Associate Professor of Mathematics

Introduction to topics in mathematical cryptography, and the role of cryptography within society, in both historic and modern contexts. Cryptographic systems studied will include: early historical ciphers; the Enigma machines of WWII; modern public channel cryptography. Students will learn: to encode/decode using each system; to quantify the complexity, strength, and weaknesses of each system; to use elementary techniques from combinatorics, graph theory, abstract algebra, and number theory; about the role cryptography plays in human society. Open only to students in the FOCUS program.

Sociology 179FS: Visualizing Society (SS, QS)

Kieran Healy, Associate Professor of Sociology

This class will teach you how to use modern, widely-used tools to create insightful, beautiful, reproducible visualizations of social science data. We will also put the theory and practice of visualization into context throughout the semester. By that I mean that we will think about different ways of looking at social science data, about where data comes from in the first place, and the implications of choosing to represent it in different ways.

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

Lynn Smith-Lovin, Robert L. Wilson Professor of 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

Lillian Pierce
Lillian Pierce
  • Nicholas J. and Theresa M. Leonardy Associate Professor of Mathematics
Office: 
117 Physics Building
Campus Box: 
90320

pierce@math.duke.edu