This course will introduce students to Bayesian data analysis, including modeling and computation. We will begin with a description of the components of a Bayesian model and analysis (including the likelihood, prior, posterior, conjugacy and credible intervals). We will then develop Bayesian approaches to models such as regression models, hierarchical models and ANOVA. Computing topics include Markov chain Monte Carlo methods. The course will have students carry out analyses using statistical programming languages and software packages.

Introduction to computational techniques used in science and industry. Topics selected from root-finding, interpolation, data fitting, linear systems, numerical integration, numerical solution of differential equations, and error analysis. Prerequisites: MATH 233 and 235, or consent of instructor, and knowledge of a scientific programming language.

We learn how to build, use, and critique mathematical models. In modeling we translate scientific questions into mathematical language, and thereby we aim to explain the scientific phenomena under investigation. Models can be simple or very complex, easy to understand or extremely difficult to analyze. We introduce some classic models from different branches of science that serve as prototypes for all models. Student groups will be formed to investigate a modeling problem themselves and each group will report its findings to the class in a final presentation.

Calculus of several variables, Jacobians, implicit functions, inverse functions; multiple integrals, line and surface integrals, divergence theorem, Stokes' theorem.

This is an Honors level introductory linear algebra course. The course will cover abstract vector spaces over arbitrary fields and linear transformations between them. In addition to standard discussion of characteristic polynomials, eigenvalues and eigenvectors, orthogonality, and inner product spaces, the course would also discuss some applications of linear algebra to problems from the other sciences and engineering, and include a discussion of the importance of numerical solutions of large systems of equations.

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals, and a complete coverage of Vector Analysis, including the theorems of Green, Stokes, and Gauss. There will be some emphasis on the underlying theory, numerous applications will be included, and some attention will be paid to history. Active student participation will be encouraged. A 50-minute discussion meeting will be included in this course.

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals, and a complete coverage of Vector Analysis, including the theorems of Green, Stokes, and Gauss. There will be some emphasis on the underlying theory, numerous applications will be included, and some attention will be paid to history. Active student participation will be encouraged. A 50-minute discussion meeting will be included in this course.

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals, and a complete coverage of Vector Analysis, including the theorems of Green, Stokes, and Gauss. There will be some emphasis on the underlying theory, numerous applications will be included, and some attention will be paid to history. Active student participation will be encouraged. A 50-minute discussion meeting will be included in this course.

Techniques of calculus in two and three dimensions. Vectors, partial derivatives, multiple integrals, line integrals, and a complete coverage of Vector Analysis, including the theorems of Green, Stokes, and Gauss. There will be some emphasis on the underlying theory, numerous applications will be included, and some attention will be paid to history. Active student participation will be encouraged. A 50-minute discussion meeting will be included in this course.