Teaching
My philosophy about teaching derives from my philosophy about
learning: it should be fun, but it requires hard work.
I do not believe in shortcuts;
a student who wants to skimp on coursework should seek a
different instructor.
I give at least one in-class exam in almost all courses I teach.
This is the only practical way that I know to make sure that
students actually have acquired the knowledge that
constitutes the intellectual content of the course.
Studying for an in-class exam is a good way
of getting the knowledge in the mind --- at least for a while
(but if not for a while, then never!).
Easy Pieces
I encourage students to develop a repertoire of ``easy pieces''.
An easy piece is an example that you can work through or
a proposition that you can state and prove without resort to
any notes or other references.
The idea of a set of easy pieces comes from primers for
beginning music students, and is known to a wider audience through
the movie Five Easy Pieces, or Feynman's book Six
Easy Pieces. A set of easy pieces is useful for the
student because the pieces serve as models of approaches to
problems. The pieces themselves can be anything, but probably
should be chosen with an eye to the importance and general
applicability of the example or proposition.
Here are some examples of useful easy pieces. Some are propositions that you
should be able to state and prove, some are methods that you should be
able to develop from scratch, and others are just problems that you should
be able to work without having to look up anything.
- The Cauchy-Schwartz inequality.
- The joint density of the i-th and j-th order statistics in a random sample
of size n from a population with given density function.
- Direct evaluation of the integral of the normal PDF over the full support.
(Obviously, it's 1, but can you directly evaluate it?)
- Monte Carlo evaluation (estimation) of the integral from 0 to infinity of
x^2cos(x)exp(-x).
- A central limit theorem.
(Choose whichever version you think is appropriate for your level of expertise.)
- The information inequality.
- Cochran's theorem.
(Again, there are various versions; choose one.)
- The Gauss-Markov theorem.
- Given 3 linearly independent vectors, produce a set of 3 orthonormal vectors.
(Do it correctly, but please don't call it ``modified'' Gram-Schmidt;
there is only one correct Gram-Schmidt method. Use it.)
- The acceptance/rejection method for random number generation.
How many should you have? 5? 10? 20? The more, the better.
Some courses I teach or have recently taught at George Mason University
Undergraduate Courses
Graduate Courses
Seminars
The seminars are open to all. Registration is not required,
but students can register for 1 hour
of credit if they wish.
Research
CSI 998
CSI 999