Electronic Coursepack for Math 319

Prof. Andrew Ross

Modeling Methods, etc.

• An Important Thing To Do In Math 319 (and in life!)
• The Real Modeling Cycle
• 5 Reasons to Teach Mathematical Modeling, by Rachel Levy (mostly about K-12 classes)
• a list of reasons to do math models
• Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape Bautista, Wilkerson-Jerde, Tobin, and Brizuela
• Textbooks offer some opportunities to practice modeling, but we can do more for students to experience where mathematics and science meet. Dan Meyer
• As Many Math Models as I could Think Of One Day--there are lots more out there, of course!
• KD Nuggets, a web site about data mining/machine learning/data science that you should read through.
• Types of Publication; how trustworthy is each type?
• Modeling Misconceptions
• Homework M1: get-to-know-you questions, and reading
• Homework M2: sketching input/output graphs
• Homework M3: strategic, tactical, and operational decisions
• Homework M4: reading sample class projects
; see the assignment in Canvas for links to the files you need.
• Homework M5: concept map of the entire course
• Homework M6: Doing Good, Ethics, and so much more
• Bloom's Taxonomy
• Revised Bloom's Taxonomy
• Next Generation Science Standards increases emphasis on modeling
• more on NGSS and modeling
• Cognitive Instruction in Mathematical Modeling, or CIMM,aimed at lower grades to get them ready for high school.
• Ladder of Abstraction in driverless-car models
• similar ladder of abstraction in projectile motion
• Ethics and OR: Operationalising discourse ethics

Regression

• Single-variable data for regression
• Homework R1: concept map of basic linear regression
• Homework R2: technical report on US population growth
• Homework R3: four-function starter exercise (from Sheldon Gordon)
• Homework R4: transformations and regression
• Homework R5: full four-function summary table
• Homework R6: multi-variable regression
• Homework R7: Logistic regression
• Homework R8: choose-your-own Logistic regression (optional)
• Homework R9: concept map of whole regression unit
• Log plots
  • largest data set you've analyzed
  • Khan Academy
  • resistors
  • The electromagnetic spectrum on a log scale
  • Height on a log scale
  • Depth on a log scale
  • Another log-scale graph
  • A Log-Log plot of body mass vs. flying velocity
• Excel statistical plots: dotplots, histogram, Cumulative Relative Frequency, empirical CDF and CCDF, and QQ plot
• Averaging and Regression
• Excel sheet to do other regressions: sum of absolute residuals, minimize maximum residual, and orthogonal regression
• Links to videos about setting up and using Excel add-ins: Data Analysis and Solver
• OOo_STAT, an add-in for OpenOffice that does statistics stuff like multiple regression
• Multivariate data examples
• City data regression article in NYT
• Excel multivariable regression, updates live, includes many residual plots
• 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.

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• Realistic 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
• 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

• Introduction to Queueing Theory

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
• How hard is it to solve various type of queues?

Graph Theory

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

Optimization: Linear and Nonlinear Programming

• Solver intro, version 14(trimmed)
• EMU Library, look for "Optimization modeling with spreadsheets, second edition" by Kenneth R. Baker
• Homework O1: concept map of basic Linear Programming
• Homework O2: practice formulating LPs as in class
• Homework O3: fast-food diet problem
• Homework O4: various optimizations
• Homework O5: concept map of whole optimization unit
• Desmos graphing calculator, good for showing LP feasible regions and iso lines
• J E Beasley's intro to LP formulation
• more LP formulation from JE Beasley
• LP matrix visualizations, also see Punk Rock OR about it.
• Wendy's nutrition information
• Tiny diet problems
• McDonald's nutrition information
• Rubio's nutrition information
• Defense Lawyer: Crows Do Not Sell Drugs, but the court ruled that distance should be measured as the crow flies
• contour plot for simple car-manufacturing problem
• contour plot for simple electric-power generation problem
• NLP: Airport location, Shotspotter
• Minimum Cost Network Flow worksheetA
• Nonlinear least-squares data fitting in Excel spreadsheets, an article in Nature Protocols
• Optimizing Archimedes Screws for pumping water
• Seedable random number generator for Excel
(if you're using Solver, you probably don't want live-updating random numbers, so use these instead.)
• Free spreadsheet VRP solver

Dynamical Systems

• Introduction to Dynamical Systems slides
• A few applications of Differential Equations
• Dynamical Systems overview worksheets/quizzes
• Homework D1: Dynamical systems, 1-variable, concept map
• Homework D2: 1-variable dynamical systems exercises
• Homework D3: Dynamical systems, multi-variable, concept map
• Homework D4: multi-variable dynamical systems exercises
• Wolf/Moose article and graphic and data sheet
• hare-lynx.dat
• The Logistic Curve is tanh
• Interactive Exploration of a Dynamical System
• Leslie matrix model
• Pharmacokinetics: can math save overdose patients?
• Economic mobility (see page 6)
• differential equations (PDEs) for how animals get their stripes: page1, about Turing's work, Morphogenesis, Morphogenesis
• differential equations for the economy: Phillips model like in this paper: Phillips model, and some MONIAC hydraulic computer links: paper1, paper2, reddit
• SageModeler, software from CODAP / Concord for modeling dynamical systems for middle-school and high-school students. Future teachers, take a look!

Excel Stuff

• EMU Enrollment data for practice making pivot tables
• Seedable random number generator for Excel
(if you're using Solver, you probably don't want live-updating random numbers, so use these instead.)
• http://faculty.tuck.dartmouth.edu/serp/ Spreadsheet Engineering Research Project
• https://ir.library.oregonstate.edu/xmlui/handle/1957/9324?show=full College student novice spreadsheet reasoning and errors by Hoag, James A. This taxonomy was revised by Rajalingham (2005) and later by Pursar and Chadwick (2006) but the reasoning categories have remained the same.
• http://www.eusprig.org/conference-abstracts.htm
• Pursar and Chadwick 2006 http://arxiv.org/ftp/arxiv/papers/0803/0803.0167.pdf
• http://arxiv.org/ftp/arxiv/papers/0805/0805.4224.pdf CLASSIFICATION OF SPREADSHEET ERRORS Kamalasen Rajalingham, David R. Chadwick & Brian Knight University of Greenwich, United Kingdom Email: k.rajalingham@gre.ac.uk Fax: 020 8331 8665
• http://panko.shidler.hawaii.edu/SSR/HICSS33/HICSS33-Rajal-SoftEngr.pdf Quality Control in Spreadsheets: A Software Engineering-Based Approach to Spreadsheet Development Kamalasen Rajalingham, David Chadwick, Brian Knight, Dilwyn Edwards

  The Mathematical Contest in Modeling

  • A grand table of MCM problems
  • My three entries from 1994, 1995, and 1996: mcm/