Global Arc

This course is an introduction to probability and statistical methods, and covers topics in probability, random variables, sampling, descriptive statistics, probability distributions, estimation and hypotheses testing, introduction to the regression model. The course emphasizes the practice, and students will learn how to perform data analysis using modern computational tools.

This course is an introduction to mathematical modeling in physical and social sciences. Topics covered include modeling via simple first and second order differential equations, fitting experimental data, optimization and an introduction to modeling probabilistic events. One substantial goal of the course is to learn MATLAB through homework, weekly group projects and an individual final project. Equal emphasis will be put on practical implementations of the models through MATLAB scripts and on theoretical underpinnings of the models.

An exploration of some of the mathematical ideas behind important modern applications, from banking and computing to listening to music. Intended for students who have not had college-level mathematics and are not planning to major in a mathematically based field. The course is organized in independent two-week modules focusing on particular applications, such as bar codes, CD-players, population models, and space flight. The emphasis is on ideas and mathematical reasoning, not on sophisticated mathematical techniques. Two 90-minute classes, one computer laboratory.

An introduction to differential equations, covering both applications and fundamental theory. Basic second-order differential equations (including the wave, heat, and Poisson equations); separation of variables and solution by Fourier series and Fourier integrals; boundary value problem and Green's function; variational methods; normal mode analysis and perturbation methods; nonlinear first order (Hamilton-Jacobi) equations and method of characteristics; reaction-diffusion equations. Application of these equations and methods to finance and control. Prerequisites: MAT 102, 103, and 202. Two 90-minute lectures.