Course topics: Stochastic simulation. This is an attempt
to start a course in stochastic simulation. Since neither of the
instructors are experts in this, the attempt
may be at times rocky. Nevertheless, we hope it will be beneficial.
There are a large number of places in science and engineering where probabilistic
simulation
is a powerful tool in evaluating expressions. Random walks are
used in economics and finance. Molecular dynamics are used in materials
science to simulate
the behavior of large systems of particles via high-dimensional stochastic
differential equations. While we won't be able to cover much of these
high-end problems,
we will attempt to introduce a number of concepts which may be of use
in a scientific or engineering career. While it would be beneficial
for the students to have
Math 361, we will be content with a certain amount of `mathematical
maturity'.
Grading policy: The grades will be entirely based on computer
projects. These will be assigned as the semester progresses.
We will assume that you can cope with Mathematica
and C and Java. We do not require expertise, only the ability
to get along. As we mentioned above, it is entirely likely that the
students will be more competent in programming than the instructors.
Note: the projects will only be gradeable if they can run on
the Math network (which has Mathematica, Java, and various forms of C).
We will sort all of this out as we go along.
Since the class is relatively small, our pedagogical goal will be
to together explore the subject.
Books: We have
Mathematica has great online documentation, so perhaps you don't need to buy that book. The C++ book is perhaps too compendious for our needs---there are undoubtedly pithier books.The Mathematica Book Mathematica 3.0 Standard Add-on Packages Java for Engineers and Scientists by Stephen Chapman (Prentice-Hall, 2000) The C++ Programming Language by Bjarne Stroustrup (Addison Wesley, 1997)
Tentative Course Outline