Dr. Timothy Lucas is an associate professor of mathematics at Pepperdine University. He earned his PhD in mathematics at Duke University in 2006. In his research, Dr. Lucas collaborates with undergraduates to construct and analyze mathematical models of biological processes. This includes a discrete-time population model of chaparral vegetation response to frequent wildfires and an agent-based model that incorporates plant growth and competition for resources. He has also used discrete-time population models and agent-based models to predict whether California newt populations can persist given severe drought and the invasion of non-native crayfish. Dr. Lucas has also researched how using iPads in the classroom transforms the learning space and facilitates social interaction. Inspired by that work, he developed two mobile apps for visualizing solutions to ordinary and partial differential equations called Slopes and Waves.
- PhD, Mathematics, Duke University, 2006
- MA, Mathematics, Duke University, 2001
- AB, Mathematics, Occidental College, 2000, With Honors
- Krista L. Lucas and Timothy A. Lucas. Using Slopes to enhance learning in ordinary differential equations. PRIMUS, 32:90–105, 2021.
- William R. Milligan, Marjorie T. Jones, Lee B. Kats, Courtney L. Davis, and Timothy A. Lucas. Predicting the effects of manual crayfish removal on California newt persistence in Santa Monica Mountain streams. Ecological Modelling, 352:139-151, 2017.
- Marjorie T. Jones, William R. Milligan, Lee B. Kats, Thomas L. Vandergon, Rodney L. Honeycutt, Robert N. Fisher, Courtney L. Davis, and Timothy A. Lucas. A discrete stage-structured model of newt population dynamics during a period of drought. Journal of Theoretical Biology, 414:245-253, 2017.
- Timothy A. Lucas, Reanna A. Doña, Wancen Jiang, Garrett C. Johns, Dayna J. Mann, Cassandra N. Seubert, Noah B.C. Webster, Charlotte H. Willens, and Stephen D. Davis. An individual-based model of chaparral vegetation response to frequent wildfires. Theoretical Ecology, 10:217-233, 2017.
- Junyuan Lin and Timothy A. Lucas. A particle swarm optimization model of emergency airplane evacuations with emotion. Networks and Heterogeneous Media, 10(3):631-646, 2015.
- Timothy A. Lucas, Garrett Johns, Wancen Jiang, and Lucie Yang. A population model of chaparral vegetation response to frequent wildfires. Bulletin of Mathematical Biology, 75(12):2324-2345, 2013.
- Brian Fisher, Timothy A. Lucas, and Araksi Galstyan. The role of iPads in constructing collaborative learning spaces. Technology, Knowledge and Learning, 18(3):165-178, 2013.
- Timothy A. Lucas. Numerical solutions of an immunology model using reaction-diffusion equations with stochastic source terms. SIAM J. Numer. Anal., 49(6), 2011
- Timothy A. Lucas and Joseph Spivey. A transition course from advanced placement to college calculus. PRIMUS, 21(5):417-433, 2011
- Timothy A. Lucas. Operator splitting for an immunology model using reaction-diffusion equations with stochastic source terms. SIAM J. Numer. Anal., 46(4), 2008
- Faheem Mitha, Timothy A. Lucas, Feng Feng, Thomas B. Kepler, and Cliburn Chan. The multiscale systems immunology project: Software for cell-based immunological simulation. Source Code for Biology and Medicine, 3(6), 2008
- Frank R. Seaver Professor of Natural Science
- L.P. and Barbara Smith Award for Teaching Excellence, Duke University Mathematics Department, August 2004
- MAA Project NExT Fellow, 2008-2009
- Phi Beta Kappa Honor Society
- Member: Mathematical Association of America, Pi Mu Epsilon, Society for Industrial and Applied Mathematics
- Mathematical Ecology
- Mathematical Biology
- Educational App Development
- Numerical Analysis
- Partial Differential Equations
- Stochastic Differential Equations
- Calculus I, II and III
- Calculus for Business and Economics
- Probability, Linear Systems, and Multivariable Optimization
- Linear Algebra
- Differential Equations
- Partial Differential Equations
- Complex Variables
- Mathematical Statistics