Summer Ventures in Science and Mathematics

Summer Ventures in Science and Mathematics
Mathematical Modeling

This course will be an introduction to the mathematical modeling of systems in nature. Electronic data acquisition and computer analysis of experiments may be incorporated. Specific topics shall include an introduction to mathematical model building, exploring simple hands-on and simulated experiments using microcomputers mathematical software. Students will have the opportunity to develop and analyze mathematical models of real world continuous and discrete processes.
Class Photo

Lecture Materials

Mathematical Modeling Intro PPT, PDF

Modeling Motion in VPython PPT, PDF

Simple Motion of Balls
Mass on a Spring
- spring.py
- springmass.py
gravity.py - satellite motion
plotex.py - uses Graph Plotting
from Modeling Motion
- couposc.py
- cbounc.py => pool.py
- fountain.py needs universe.py
- readdata.py needs data.txt
sir.py - SIR epidemics model with data plotting
balls.py - using lists
Random Number generation
- plotrand.py - plotting a random sequence of numbers
- montecarlo.py - Using Monte Carlo method to compute pi
- perc.py - Simlutaing 2D percolation model of forest fires
- catest.py - 1D simple cellular automata as strings
Nonlinear Pendulum
- pend.py - setup
- pend2.py - add plots
- pend3.py - class example
baseball.py - motion of baseball under drag and magnus forces, needs rkf4.py
basket.py - simple game with sliders
testballs.py - use of frame to create golfball
LotkaVolterra.py - predator-prey model using SciPy, NumPy and Matplotlib
see Lotka-Volterra tutorial
Execultables - for display purposes

motioninbox.exe	bounce.exe	bounces2.exe
spring.exe	springmass.exe	gravity.exe
pool.exe	sir.exe	plotrand.exe
montecarlo.exe	perc.exe	LotkaVolterra.exe

Rendering Images
- Download povexport-2005-12-06.zip
- Download POV-Ray
- Example povex.py
- Screen Capture PILex.py - needs PIL
Rubki's Cube and variations from http://www.dougmair.blogspot.com/
- pyCube.py - original code
- Rubik.py - used to give points needed for other programs
- Rubik2.py - code for demonstrating program control of rotations
- strlabel.py, typetext.py - code for accepting keyboard text
- Rubik1.py - 2x2x2 version with buttons
- rubik keyboard.py - 2x2x2 version with keyboard input
- Rubik3.py - 3x3x3 version with buttons
- Rubik3c.py - Added menu for patterns and scramble cube
- Rubik4.py - Two 3x3x3 cubes with controls
- Rubik5.py - Two 3x3x3 cubes with partial subgroup table
- Rubik5b.py - Two 3x3x3 cubes with subgroup table - tentative

Introduction to Python
Fourier Analysis
Fractals and Chaos
- Fractal Curves
- Fractal Dimensions
- Cobweb Diagrams 1, 2
- The Chaos Game
- Iterated Function Systems
- Julia Set Fractal, Generator
- Xaos
- Fractint - and older Fractal program
- The Fractal Microscope - online fractal viewer
- YouTube Fractals, Newton and Bach, Fractal Zoom Mandelbrot Corner
- Fractal Music FMusic, Hearing the Mandelbrot Set
- Chaos in the Solar System
Video Analysis
- Tracker Open Source, Uses QuickTime Movies
- DataPoint
Epidemic Models
- The SIR Model for the Spread in Disease
- Mathematical Modeling of Epidemics
- HIV/AIDS: How Mathematics Has Saved Lives
- SIR Model of Epidemics I, II
- SIR.mws
- Computing the SIR Model: Fractal dimension leads to vaccination strategies
- Avian Flu Worksheets - birds.mws, birds2.mws, birds3.mws, birds4.mws
Other Packages
- NumPy
- SciPy
- Matplotlib
- SymPy
- PyLab
World On a String
- Problem stated

Documents

Line, Slope and Intercept in Excel
Population Models - CCP
Population Models Lab
CountryPopModels.xls (Courtesy NSF NC-PIMS grant)
Uganda (High, Medium, Low variance),
Liberia, Nigeria, Rwanda, Sierra Leona, Somalia, Sudan
Game Theory, Population Models, And the Fish That Got Away
Card Shuffling Models
VPython Reference Sheet (DOC) New

Applets

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