Using Mathematica in an undergraduate Biophysics course enables students to model stochastic processes and analyze real and simulated data

The stochastic processes that govern the quantized nature of transmitter action at a chemical synapse were elaborated more than a half-century ago, yet it is a significant challenge for undergraduate students to grasp the statistical aspects required to understand these processes. Other examples, like understanding the details of lateral diffusion of membrane receptors, require a deep familiarity with free and confined random walks.

In order to teach and enable students to utilize these statistical concepts and analyze real and simulated data, I use Mathematica (Wolfram Inc.) extensively in my Biophysics course (PHYS 366). Mathematica has a tremendous set of functions that are ideally suited for introducing and implementing these ideas. It becomes relatively easy to introduce binomial and Poisson distributions (as well as many other distributions) and to introduce and implement simple random walk processes. Functions such as Wiener processes and Ornstein-Uhlenbeck processes enable the student to grasp and analyze data representing Brownian motion with drift as well as confined walks. Of course, Mathematica is also an outstanding tool that enables students to find analytical solutions to differential equations (e,g., the diffusion equation). Mathematica is used extensively for all my course material (e,g., ideal gas, entropy). Examples of classroom notes (with syllabus), problem sets and examinations will demonstrate the unique and powerful benefits of this approach.