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.

Challenge Problems:   Especially challenging problems.

"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