Math 679 is a graduate level mathematics course whose purpose is to prove Mazur's theorem (link is external). Mazur's theorem is a well-known and important result, however it is not often taught in classroom settings. The course is divided into three parts: elliptic curves and abelian varieties, moduli of elliptic curves, and proof of Mazur’s theorem.
This is an intermediate algorithms course with an emphasis on teaching techniques for the design and analysis of efficient algorithms, emphasizing methods of application. Topics include divide-and-conquer, randomization, dynamic programming, greedy algorithms, incremental improvement, complexity, and cryptography.
This course develops and applies scaling laws and the methods of continuum and statistical mechanics to biomechanical phenomena over a range of length scales, from molecular to cellular to tissue or organ level.
This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).
Projections of commercial airline flight schedules worldwide. Describe characteristics of each flight such as: departure and arrival airports, flight times, carrier, fares, capacity, and more. Projections are made at the beginning of every time period (month or year) and project the schedules for that time period until the next update is received. Data from 1979-March 1987 are available monthly. Data from 1987 onward are available annually.
