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 K12 classes)
 a list of reasons to do math models
 Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
Bautista, WilkersonJerde, 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 Daythere 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: gettoknowyou questions, and reading
 Homework M2: sketching input/output graphs
 Homework M3: strategic, tactical, and operational decisions
 Homework M4: reading sample class projects
 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 driverlesscar models
 similar ladder of abstraction in projectile motion
 Ethics and OR: Operationalising discourse ethics
Regression
 Singlevariable data for regression
 Homework R1: concept map of basic linear regression
 Homework R2: technical report on US population growth
 Homework R3: fourfunction starter exercise (from Sheldon Gordon)
 Homework R4: transformations and regression
 Homework R5: full fourfunction summary table
 Homework R6: multivariable regression
 Homework R7: Logistic regression
 Homework R8: chooseyourown Logistic regression (optional)
 Homework R9: concept map of whole regression unit
 Log plots
 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 addins: Data Analysis and Solver
 OOo_STAT, an addin 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 (leaveoneoutcrossvalidation) 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
 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
Queues
Graph Theory
Optimization: Linear and Nonlinear Programming
 Solver intro, version 9
 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: fastfood 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 carmanufacturing problem
 contour plot for simple electricpower generation problem
 NLP: Airport location, Shotspotter
 Minimum Cost Network Flow worksheetA
 Nonlinear leastsquares 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 liveupdating random numbers, so use these instead.)
 Free spreadsheet VRP solver
Dynamical Systems
 Introduction to Dynamical Systems slides
 Applications of Differential Equations
 Dynamical Systems overview worksheets/quizzes
 Homework D1: Dynamical systems, 1variable, concept map
 Homework D2: 1variable dynamical systems exercises
 Homework D3: Dynamical systems, multivariable, concept map
 Homework D4: multivariable dynamical systems exercises
 Wolf/Moose article and
graphic and
data sheet
 harelynx.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
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 liveupdating 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/conferenceabstracts.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/HICSS33RajalSoftEngr.pdf
Quality Control in Spreadsheets:
A Software EngineeringBased Approach to Spreadsheet Development
Kamalasen Rajalingham, David Chadwick, Brian Knight, Dilwyn Edwards
The Mathematical Contest in Modeling