VHCC Governor's School 2000
Mathematical Modeling
Instructional Goals: To complement the traditional presentation of
topics in mathematics and science through the second year of the typical undergraduate
curriculum. To achieve a synthesis of mathematical, theoretical and experimental
knowledge and technique in the sciences. To provide unlimited challenge to students.
Student Goals: (to be completed by students)
Contents
"Old Problems": Problems related
to first test. Subject matter includes rates and related graphing techniques,
sequences, modeling by stochastic matrices, random walks, neural nets, frequency
distributions and standard deviation, and associated notational conventions.
"New Problems": Problems which
build upon and synthesize the concepts and techniques of the "old problems", as
well as problems concerning cellular automata, numerical solutions of differential
equations and some systems thereof, logistic maps, logistic population models, genetic
algorithms and more.
"Experiments": Reports of hands-on
experiments which demonstrate the topics explored through the problems, and which use the
concepts and techniques of the problems in their analysis.
"Computer Experiments":
Experiments based either on computer programs which employ randomized parameters to
simulate some aspect of reality, or on varied parameters within calculation structures
designed and executed using a spreadsheet or computer algebra program.
"Thought Experiments":
Generally conceptual questions requiring a knowledge of a central mathematical concept
(e.g., proportionality) in order to arrive at useful speculations.
"Notes on Questions": Short notes
on questions posed to authors by peers, written by the authors, or posed to the
instructors, written by the individuals receiving the explanations.
"Articles on Questions":
Longer responses to the types of questions described above.
"Articles": Articles on various topics
which emerge from our investigations.
Miscellaneous Pages: Pages that were
accidentally mislabeled by author, or for some other reason were not included under the
appropriate heading.
Billiard Ball Simulation Samples:
Time Interval Samples
Free Path Samples
x and y kinetic energy Samples
Velocity Samples