Electronic Coursepack for Math 319

Prof. Andrew Ross

Misc. stuff

• The Real Modeling Cycle
• As Many Math Models as I could Think Of
• Applications of Differential Equations
• Types of Publication; how trustworthy is each type?

Log plots

• Data for practicing log plots
• A Log-Log plot of body mass vs. flying velocity
• The electromagnetic spectrum on a log scale
• Height on a log scale
• Depth on a log scale

Regression

• Single-variable data examples
• Averaging and Regression
• Multivariate data examples
• Sum of Two Sine Waves
• Harmonic Analyzer (also here, and its opposite the harmonic synthesizer, and check out tide predicting machines)
• falstad.com applets, and the Fourier one in particular.
• PHeT wave applet
• Overfitting, Jackknife, and LOOCV (leave-one-out-cross-validation) example spreadsheet
• Regression extras: sum of absolute values, etc.
• Thoughts on regression: sample size needed, etc.
• Math Placement data for logistic regression
• logistic regression solver (original)
• logistic regression solver (backup)
• California electric data, 2001
• EMU electric data, 2006
• Weather data, 2004 2005 2006
• monthly-enplanements.jpg
• Pennsylvania school district data (see here and here for more PA school data; let me know if you find a similar site for Michigan)

Splines

• Old-Fashioned Splines
• Why Smoothed Lines in Excel can be bad, and the .xls source file.

Queues

• How hard is it to solve various type of queues?
  Some sample paths of various types of queues:
• M/M/1
• M/M/50
• M/D/1
• M/D/50
  Real data:
• Israeli bank call center, more data at here.
• EMU computer labs

Graph Theory

• A paper on social networking (ahem) in high schools, as published and manuscript form (better graphs)

Linear and Nonlinear Programming

• Solver intro
• Wendy's nutrition information
• McDonald's nutrition information
• Rubio's nutrition information
• NLP: Airport location, Shotspotter
• Minimum Cost Network Flow worksheet
• Optimizing Lumber Saws
• Optimizing Archimedes Screws for pumping water

Population models

• Wolf/Moose article and graphic and data sheet
• hare-lynx.dat
• The Logistic Curve is tanh

The Mathematical Contest in Modeling

My three entries from 1994, 1995, and 1996: mcm/