The following introductory courses are recommended by the faculty associated with the Biomathematics Initiative at W&M.
Calculus I & II for Life Sciences
MATH 131 & 132. (GER 1) Fall & Spring (4). Calculus with a focus on biological applications, e.g., models of population dynamics, ecology, physiology, genetics, neurology, and epidemiology.
Introduction to Mathematical Biology
MATH 345. Fall (3) Prerequisite: MATH 112 or 132 or consent of instructor.
An introduction to developing, simulating, and analyzing models to answer biological questions. Mathematical topics may include matrix models, non-linear difference and differential equations, and stochastic models. Biological topics may include ecology, epidemiology, evolution, molecular biology, and physiology.
Cellular Biophysics and Modeling
APSC/BIO 351. Fall (3) Smith and Del Negro. Prerequisite: MATH 112 or 113, BIOL 203, or consent of instructor.
An introduction to simulation and modeling of dynamic phenomena in cell biology and neuroscience. Topics covered will include the biophysics of excitable membranes, the gating of voltage- and ligand-gated ion channels, intracellular calcium signaling, and electrical bursting in neurons.
Matrix Models in Population Biology
BIO 404. Spring (3) Dalgleish.
Matrix population models are widely used in evolutionary biology, population ecology, conservation biology, and wildlife management. This course introduces students to the concepts, methods, and applications of matrix model analyses in biology.
APSC 450. Fall (3) Smith and Del Negro. Prerequisite: APSC 351 or consent of instructor.
Computational function of hippocampus, thalamus, basal ganglia, visual cortex, and central pattern generators of hindbrain and spinal cord emphasizing how experiment and theory comple- ment each other in systems neuroscience. Relevant mathematical modeling and computer simulation techniques will be taught.
APSC 455. Fall (3) Shaw. Prerequisite: MATH 302 or equivalent.
An introduction to population dynamics and bifurcation theory. Classic population models including the logistic map, predator-prey systems, and epidemic models will be used to motivate dynamics concepts such as stability analysis, bifurcations, chaos, and Lyapunov exponents.
Random Walks In Biology
APSC 456. Spring (3) Shaw. Prerequisite: MATH 131 or equivalent and BIOL 221.
This course introduces random processes in biological systems. It focuses on how biological processes are inherently stochastic and driven by a combination of energetic and entropic factors. Topics include diffusion, cell motility, molecular motors, ion channels, and extinction in populations.
Newtworks In Biology
BIO 460-05. Spring (3) LaMar.
This course will give an introduction to the structure and function of networks in biological systems, including gene regulatory networks, protein-protein interaction networks, neuronal networks, and ecological networks. Most of the material will come from the primary literature focusing on how network theory has been used in biological research. Note: Students will be expected to give one or more oral presentations and complete one or more major writing assignments. Fulfills the major writing requirement in biology.
APSC 751. Spring (3) Smith.
Computational and mathematical aspects of cellular and systems physiology emphasizing stochastic and spatial modeling applied to biochemical dynamics, genetic regulatory networks, cell signal transduction, and neuroscience. Interested undergraduates may register for Independent Study in Applied Science (APSC 403-10) and receive credit toward the Applied Science Computational and Mathematical Biology minor.
Other recommended courses:
Computational Problem Solving
CSCI 141. Fall and Spring (4) D. Noonan. Corequisite: CSCI 141L.
An introduction to computational problem solving, including basic programming and algorithms. Programming assignments will emphasize the solution of problems taken from the natural sciences, the social sciences, and business.
MATH 221. Fall and Spring (3,3) Prerequisite: MATH 112 or MATH 132.
Linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues, orthogonality. Optional topics include least squares problems, matrix factorization, applications. A computer lab using the software package Matlab may accompany the class.
Introduction to Multivariable Calculus
MATH 212. Fall and Spring (3,3) Prerequisite: MATH 112 or MATH 132.
Functions of several variables, surfaces in three-space, vectors, techniques of partial differentiation and multiple integration with applications. MAPLE or Matlab will be used in this course.
Multivariable Calculus for Science and Mathematics
MATH 213. Fall and Spring (4,4) Prerequisite: MATH 112 or MATH 132.
Covers all Math 212 material plus other vector calculus topics (including Gauss’ and Stokes’ theorems). Students may not receive credit for both Math 212 and MATH 213. Math 213 may replace Math 212 as a prerequisite and is particularly recommended for science and mathematics students.
Practical Computing for Scientists
PHYS 256. Fall (3) Mikhailov. Prerequisite: MATH 112.
This course will focus on breaking scientific problems into algorithmic pieces that can be solved using computational methods in MATLAB. Root finding, linear and non-linear equations, numerical modeling, optimization, random processes, graphical data presentation and fitting, scientific documentation preparation.
Ordinary Differential Equations
MATH 302. Fall and Spring (3,3) Prerequisite: MATH 211 and Math 212 or 213 or consent of instructor.
First-order separable, linear, and nonlinear differential equations. First-order systems and forced second-order linear equations. Systems of linear equations and linearization. Numerical methods, bifurcations, and qualitative analysis. Applications to biology, chemistry, economics, physics, and social sciences.
APSC 312. Spring (3) Hinders. Prerequisites: PHYS 101/102 or PHYS 107/108.
Introduction to the modern clinical non-invasive diagnostic imaging techniques. The course will cover the physical, mathematical and computational principles of x-ray, ultrasound, radionuclide and magnetic resonance imaging techniques.
Introduction to Laser Biomedicine
APSC 327. Spring (3) Luepke. Prerequisites: Junior standing or consent of instructor.
The course will build a foundation for understanding the use of lasers in biology and medicine. There will be particular emphasis on laser beam interactions with human tissue for diagnosis, therapy, and surgery, with additional attention to optical coherence tomography, two-photon microscopy, fluorescent imaging, optical tweezers, and refractive surgery.