Brooks Emerick

This course is an upper level math class focusing on discrete and continuous probability, combinatorial analysis, random variables, random vectors, density and distribution functions, moment generating functions, and particular probability distributions including the binomial, hyper-geometric, gamma, and normal.  The weak and strong law of large numbers is discussed and the proof of the Central Limit Theorem is covered.  The figure to the left illustrates the Central Limit Theorem.

MATH 228 is a proof-based course in linear algebra, covering systems of linear equations, matrices, determinants, finite dimensional vector spaces, and linear transformations.  The least-squares problem and eigenvalues/eigenvectors are typically covered towards the end of the class.  Although there is a computational component to the class, a stronger focus is put on developing well written proofs, which may include the properties of matrix algebra, set containment, linear independence, and properties of vector spaces and subspaces.  The figure to the left shows the intersection of three planes in three dimensional space, i.e. a 3x3 linear system with a unique solution.

This course is a computational workshop designed to introduce the student to Matlab, a powerful scientific computing software package. The workshop will focus on visual learning based on graphical displays of scientific data and simulation results from a variety of mathematical subject areas, such as calculus, differential equations, statistics, linear algebra, and numerical analysis. No prior computer language skills are required as basic programming tools such as loops, conditional operators, and debugging techniques will be developed as needed. The workshop prepares the student for future courses in applied mathematics as well as courses in other disciplines where scientific computing is essential.  The figure to the left is a fractal map called the Julia set generated by Matlab with additional lighting/smoothing features enabled.  Figure credit goes to Mariam Avagyan.

This course is a typical first calculus class designed for mathematics, natural science, and computer science majors.  The course introduces important functions and graphs, the concept of limits and continuity, derivatives and their applications, and anti-derivatives with a brief introduction to the fundamental theorem of calculus.  The figure to the left demonstrates Newton's Method for approximating roots of functions.