Introduction to :
Mathematical Modeling
Math 252/ 254
 

Random number distribution

1. Radioactive decay/ carbon dating
2. Malthusian growth
3. Logistic equation
   1. Differential Form
   2. Discrete Form/bifurcation and chaos
      (stock market analogy)
   3. Predation effects/catastrophe theory
   4. Time-delay effects/periodicity
   5. Epidemic modeling (AIDS Epidemic)

1. Radioactive cascade system/ computational instability*
2. Ecology models
   1. Competitive Hunters Model
   2. Predator-prey model
   3. Linear stability analysis

1. Probabilistic models
2. Random-number generators
3. Applications/projects*   

1. Stochastic matrices, stationary distributions
2. Probabilistic forecasting

1. Optimization/ a detailed business application
2. Simplex method
   1. Convex sets
   2. Solution of linear systems: Gauss elimination

Student-Written Software

Trinity Science Symposium Projects

• Predator/Prey Trajectories [P. LaBella, N. Ryan, C. Sternal]**
• Monte Carlo Horse Race [C. Gigl]
• NBA Draft Using Monte Carlo Simulation [J. Sweeney] **
• Electron Spin Using Monte Carlo Technique [P. Almquist]
• Integration Using Monte Carlo Simulation [R. Young]
• Flocking Applet [B. Jackson and J. Kavanaugh]
• Computational Instability [I. Presnyakoff, T.Klasik]*
• Roulette [K.Ward and J. Furnari]
• Linear Inequality Solver [S. Susslin]
• Baseball Trajectory [B. Feld, D. Gyllstrom, D. Oh]
• Random Number Generation [M. Kobilarov]*
• Richardson's Arms Race Model [A. Williams]**
• Predator/Prey Simulation [A. Schurr]**
• Bingo [A. Benjamin]
• Buffon's Needle [A. Issacson]
• Voter Problem [A. Morelli]
• Blood Alcohol Content Project [C. Klein]
• Chaotic Population Growth [T. Klasik]
• Random Walk [D. Whitley]
• Easter Island Population Trajectories [T. Klasik]

*Some programs may run only with Internet Explorer

** Some programs may run only on Windows

©2004 Philip S. Brown, Jr. Mathematics Department Trinity College