Basic Information

Something You Would Hope Wouldn't Need To Be Said, But It Does

• A Pathway to Equitable Math Instruction Dismantling Racism in Mathematics Instruction (not that I am perfect at it. Please tell me ways that I can improve, if you have time and energy)
• the Online Undergraduate Resource Fair for the Advancement in Academia of Marginalized Mathematicians. You're a part of OURFA²M² now!
• Hidden Norms webinars : Navigating Obstructive Rules in the Mathematical Sciences

A Sense of Belonging

Parenting

General Description

Course Catalog Entry

Prerequisites

Follow-up courses: Math 325 Differential Equations, Math 418 Modeling with Linear Algebra, Math 419W Introduction to Stochastic Mathematical Modeling, Math 425 Math for Scientists, Math 436 Numerical Analysis

The U of M has two related courses: Math 462, "Mathematical Modeling", and Math 463, "Mathematical Modeling in Biology". However, these focus on differential equation models, while this class focuses on regression, operations research, and dynamical systems.

Class Meetings

Block#	Date 2022	day	unit	topics	Bonus Excel Material after class	HW assigned	HW due	Python goals
1	1/10	Mon	general modeling	intro; math model examples; a math model has; graph sketching		M1		
2	1/12	Wed	general modeling	bloom's taxonomy; CCSS-M standards for mathematical practice; malaria nets--start simple; evacuation; modeling cycle	text-to-columns	M2	M1	import csv file
	1/17	Mon		MLK Jr. Day - No Classes; Campus-wide Celebration! Think about math/stats and civil rights.				
3	1/19	Wed	general modeling	real modeling cycle; oper tact strat; airline problems; concept maps; intro to excel (graphing, label axes, title, autofill, control-shift-down)	left/mid/right and =DATE	M3	M2	matplotlib
4	1/24	Mon	regression	linear regression: houses, predictions, residuals, graph residuals!	vlookup	R1, R2	M3	statsmodels.OLS or sklearn.linear_model.LinearRegression
5	1/26	Wed	regression	R^2; school district data; correlation/causation; ecological fallacy; common resid graphs; basic procedure; LSRL math model; averaging before regression?	marked scatterplots	R3	R1	Matrix of scatterplots: https://colab.research.google.com/drive/1QRhh8InP7jq3ygfZfkOo7vBoZkTtG8oG
6	1/31	Mon	regression	Pre-Lab at home: 4-function pre-quiz; in-class: answers; exponential fits, compound interest	sparklines		R3 before class, R2	R2 solution key in Python--ask me for link
7	2/2	Wed	regression	yeast; logplots; power fit	Pivot Tables	R4		logarithms and linear regression
8	2/7	Mon	regression	log-of-log, model selection, occam's razor, multivariate regression school data	parallel axis plots	R5	R4	multiple regression; r4 solution key in Python; r6 demo https://colab.research.google.com/drive/1eJGi9k7HIWmtLvnXlStOxKZNSnL_X3uS
9	2/9	Wed	regression	heat index; polynom; sines	LiveRegression		R5	numpy.polyfit or statsmodels.OLS
10	2/14	Mon	regression	falstad.com java fourier app; waves and trends		R6		FFT? voiceprint?
11	2/16	Wed	regression	Quiz on R5; Logistic; overfitting/crossvalidation; Machine Learning overview	generating random numbers	R7, R8, R9	R6	generating random numbers; scipy.optimize.curve_fit;  sklearn.linear_model.LogisticRegression ; r7 demo https://colab.research.google.com/drive/1g_UsVwZAGnnUEqc_0A46y4E9cg1FSmlH
12	2/21	Mon	optimization	LP toys, wyndor (no sensitivity analysis), knapsack, swimmers		O1	R7	scipy.optimize.linprog vs PuLP
13	2/23	Wed	optimization	shift scheduling; network flow		O2	R9	
14	3/7	Mon	optimization	Networks			O1	
15	3/9	Wed	optimization	MCNF node-node; ramen; brief fast-food intro; sensitivity analysis on wyndor; feas region; fundamental theorem of LP		O3, M4	O2	
16	3/14	Mon	optimization	example papers: dinosaur and relay; NLP: manufacturing, electricity	Pasting into Word/PPT: live or dead copies?		O3, M4	scipy.optimize.minimize
17	3/16	Wed	optimization	concavity			proposal 1	
18	3/21	Mon	optimization	airport		O4		
19	3/23	Wed	optimization	shotspotter		O5		
20	3/28	Mon	dynsys	Dynamical Systems; PID; credit card, repeated dosing			O4, O5	for-loop
21	3/30	Wed	projects	Project Presentations			report 1; presentation 1	
22	4/4	Mon	projects	Project Presentations		M6		
23	4/6	Wed	dynsys	limited population growth; quiz		D1	M6 (yes, before M5.)	
24	4/11	Mon	dynsys	pagerank; leslie; SIR; pred/prey;oilspill		D2	D1	
	4/13	Wed	dynsys	multiple initial conditions; equilibria; delta plots; phase-plane plots; fitting limited-pop growth		D3	proposal2	
25	4/18	Mon	dynsys	observation noise, process noise			D2	
26	4/20	Wed	dynsys	repeated dosing? accel/vel/pos? chaos? splines? PERT/CPM? wrapup; M5 & M6 discussion; presentations		D4, M5	D3	
27	4/25	Mon	projects	1:30-3:00 Presentations during "final exam" slot; AN HOUR EARLY!			report 2; presentation 2	
28	4/27			no class; other classes having finals.			D4, M5	

Class meetings will be mostly interactive lectures, with some time to work on problems in class, and some time to go over problems from the homework. You should bring a laptop to most class sessions, since I couldn't get a computer lab for us. If you don't have a laptop, buddy up with someone who does.

Instructor information

Office Hours and other help

 
Mon/Wed:
	2:00-3:15 Math 319
	then, haphazardly scheduled Zoom office hours. Email for an appointment.
Tue/Thu:
	haphazardly scheduled Zoom office hours. Email for an appointment.
	 
Fri:
	No official office hours, but I'm available for Zoom appointments.
	
	11:00-12:00 department colloquium (once a month)
	12:30-2:30 department meeting (once a month)
	

I am also happy to make appointments if you cannot come to the general office hours. Please send me e-mail to arrange an appointment.

The Mathematics Student Services Center (or "Math Lab") is also here to help you, in Pray-Harrold 411 Their hours are posted here. Please give them a call at 734-487-0983 or just drop by.

A good place to study, if the Math Lab doesn't suit you, is the Math Den, Pray-Harrold room 501.

Many assignments in this course will be in the form of papers, which I want to be well written. Please consult with The Writing Center for help in tuning up your writing.

Teaching philosophy, interests

I am a very applied mathematician. Applied, applied, applied. Not pure. Impure. I try to focus on real-world problems, rather than artificial drill problems (though I do recognize the need for some drill). My classes spend much more time on formulating problems (going from the real world to math notation and back) than on proving theorems. If you want the theoretical basis for anything we are discussing, please ask!

My general math interests are in Industrial Engineering and Operations Research (IEOR). In particular, I do research in applied probability and queueing theory, the mathematics of predicting how long it takes to wait in line for service. You can learn more about this in Math 319 and 419 when I teach them. I also enjoy teaching about cost-minimizing/profit-maximizing methods called Non-Linear Programming (NLP) in Math 560.

(not-absolutely-)Required materials

Most students do well in this course without a textbook. For those who feel the need to have one just in case, I suggest finding "A First Course in Mathematical Modeling", any edition, by Giordano, Weir, and Fox, in a library or the Math Den (PH 501).

A lot of our work will be done on computers, specifically in Excel or other spreadsheet software (except Apple Numbers). If you had been waiting for a good reason to buy a laptop, this is it.

Spreadsheets other than Excel (such as OpenOffice/LibreOffice, Google Docs, etc.) work reasonably well for most things in the class, but some things really don't work well without name-brand Excel. Fortunately, it's available free to EMU students (as of Fall 2016). Email me to ask for details.

Course Web Pages

I will post data files, homework assignment files, etc. on my home page.

We will use an on-line gradebook (via EMU Canvas) to keep track of grades. It is a good idea to keep an eye on your scores using the system, and get extra help if your scores indicate the need. Nearly everything will be submitted via the various dropboxes inside EMU Canvas. The rule is: if it's not in a dropbox, it doesn't exist (for grading purposes).

Supplementary Materials

• Mathematical Modeling: A Comprehensive Introduction, Gerhard Dangelmayr and Michael Kirby, a free e-text!
• Optimization Modeling with Spreadsheets, Second Edition by Kenneth R. Baker, 2011 (EMU library has electronic access)
• An Introduction to Linear Programming, Stephen J. Miller, 2007 (free on the web)
• An Introduction to Statistical Learning, with Applications in R by James, Witten, Hastie and Tibshirani (Springer, 2013) (free on the web)
• Practical Optimization by John Chinneck (free on the web)
• Invitation to Dynamical Systems, Edward R. Scheinerman (free on the web)
• Elementary Mathematical Modeling: A Dynamic Approach/ Sandefur, James
• *Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics by Robert B. Banks, and its sequel:
• *Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics by Robert B. Banks
• Race car vehicle dynamics by William F. Milliken, Douglas L. Milliken
• Going Faster: Mastering the Art of Race Driving by Carl Lopez
• Logistics Systems Analysis by Carlos Daganzo
• The nature of mathematical modeling by Neil Gershenfeld
• Mathematical and Experimental Modeling of Physical and Biological Processes by Banks and Tran
• *Small is Profitable by Amory B. Lovins, et al.
• Statistical Orbit Determination by Tapley and Schultz
• Street-Fighting Mathematics (free online book!)
• Applied Mathematical Programming by Bradley, Hax, and Magnanti (Addison-Wesley, 1977) (free online book! A bit old, though).
• Beasley's O.R. Notes (free!)
• Quantitative Methods in Health Care Management: Techniques and Applications, by Yasar A. Ozcan (EMU library)
• Patient Flow: Reducing Delay in Healthcare Delivery, edited by Randolph W. Hall (EMU Library, incl. electronic copy)
• *Queueing Methods: for Services and Manufacturing by Randolph W. Hall
• Mathematical Modeling for the Life Sciences, by Jacques Istas
• Turning Numbers into Knowledge: Mastering the Art of Problem Solving by Jonathan G. Koomey (EMU library, incl. electronic copy)
• *The Active Modeler: Mathematical Modeling with Microsoft Excel by Erich Neuwirth
• * Mathematical Modeling With Excel by Brian Albright
• Dynamic Modeling and Control of Engineering Systems, 3rd edition, Kulakowski, Gardner, and Shearer
• Guerilla data analysis using Microsoft Excel
• *Modeling for Insight: A Master Class for Business Analysts by Powell and Batt
• Management Science: The Art of Modeling with Spreadsheets by Powell and Baker
• http://www.cscs.umich.edu/complexadaptivesystems/
• Methods of Operations Research (1951) by Morse and Kimball--especially for military applications
• Military operations research (1997) By N. K. Jaiswal
• Applied operations research (1988) By Ronald William Shephard--especially for military applications
• Mathematics and Sports edited by Joseph A. Gallian
• Excel for scientists and engineers : numerical methods / E. Joseph Billo.
• Guerilla data analysis using Microsoft Excel / Jelen, Bill
  Nonlinear regression:
• Handbook of nonlinear regression models / David A. Ratkowsky
• Nonlinear regression modeling : a unified practical approach / David A. Ratkowsky.
• Nonlinear regression / G.A.F. Seber and C.J. Wild.
• Applied logistic regression By David W. Hosmer, Stanley Lemeshow

• Interfaces
• Mathematical and Computer Modelling
• Journal of Quantitative Analysis in Sports
• Journal on Spreadsheets in Education
• INFORMS Transactions on Education

• Microsoft Excel, or other spreadsheet software like Gnumeric or OpenOffice or Google Docs
• Python or R is used for only a few people's projects--most people don't use them.
• Mathematica, Maple, or Matlab/Octave/Scilab are even more rarely used in this class.

Course Content

Course Goals

Our primary goal is to teach you to be a good (or great!) math modeler. To be a good modeler, you need:

• Good habits and procedures, just like a scientist, and
• Knowledge of common math models.

• Get enough people together to form a few teams for the Math Contest in Modeling (MCM), usually in February. Also see these resources for the MCM. I participated in this 3 times as an undergrad and had a lot of fun. Recent EMU teams have done well!
• Give future teachers some great ideas to show your kids how high-power math is used in the real world. You may enjoy reading Meaningful Math.
• Give computer-science students lots of interesting things to program. You may like reading this blog entry about math for programmers.
• Teach you how to communicate your math models by writing math papers and giving math presentations.

Student Outcomes

• (General modeling skills):
  • categorize problems into operational/tactical/strategic categories,
  • identify nearby problems in the oper./tact./strat. hierarchy,
  • evaluate models by constructing simple test cases,
  • conduct cross-validation when needed,
  • select the most important variables to start modeling with,
• (Empirical modeling skills):
  • use ordinary, semilog, and loglog plots to evaluate relationships in data sets,
  • perform linear regression in software,
  • interpret the correlation coefficient,
  • perform transformations before regression as appropriate,
  • perform multiple variable linear regression in software,
  • fit sine/cosine functions to data using multiple linear regression (simplified Fourier),
  • fit a function to data using nonlinear regression,
  • decide when to use logistic regression (logit), and interpret the results
• (Communication skills):
  • write a technical report,
  • differentiate between literature of varying quality, e.g. peer-reviewed vs. working paper vs. white paper vs. web site,
  • design appropriate figures to communicate models and results,
• (Optimization skills):
  • Formulate non-linear programs (NLP) as appropriate,
  • solve NLP using software,
  • describe the (im)possibility of multiple optimal solutions (convexity/concavity)
  • formulate linear programs (LP) as appropriate,
  • solve LP using software,
  • describe the nature of LP solutions,
  • identify common LP models: network flow, diet/blending, inventory, assignment, (minimax ?)
  • formulate Integer programs (IP) as appropriate,
  • identify common IP models: knapsack, scheduling, (fixed charge ?)
• (Dynamical Systems skills):
  • use Dynamical Systems to model:
    • single-variable, incl. financial models (credit cards, mortgages),
    • single-variable limited population growth/ carrying capacity
    • two-population: predator/prey, competition, cooperation
    • age-structured populations (Leslie models)
    • Markov-chain models
  • Fit model parameters to data,
  • Describe equilibrium behavior,
  • Implement and interpret x=time plots, phase-plane plots, and delta-a_n versus a_n plots
• (Other models):
  • (?) describe basic Queueing models,
  • describe the Traveling Salesperson problem (TSP)
  • (?) describe project-scheduling models (PERT)
  • (?) describe dynamic-programming models (DP)

This course was originally organized around the Giordano modeling textbook, though it is not required for the course. Here we show which chapters from that book we cover, in roughly the order we will cover them. A star (*) denotes full coverage, a plus (+) denotes partial coverage, and no symbol denotes no coverage. For example, DTMCs (as cool as they are) will be covered in Math 419 rather than 319.

Ch  2:+ proportionality, similarity
Ch  3:* model fitting, least-squares
Ch  4:+ experimental modeling, high-order polynom, low-order polynom, splines
Ch  5:+ simulation
Ch  6:  Discrete Time Markov Chains (DTMCs)
Ch  8:+ modeling using graph theory
Ch  7:+ Linear Programming (LP), one-dim. line search
		(and add Integer Programming?)
Ch 13:* Non-Linear Programming (NLP), inventory
Ch  9:+ dimensional analysis and similitude
Ch 10:  graphs of functions as models
Ch  1:* difference equations, dynamical systems
Ch 11:+ one-dim ODEs
Ch 12:+ systems of ODEs

Grading Policies

Attendance

Regular attendance is strongly recommended. Since there is no formal textbook, missing class means you will miss a lot! If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you.

My lectures and discussions mostly use the document camera, along with demonstrations in Excel and other mathematical software. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.

Homework

Homework will be assigned about once per class meeting, though some assignments are short. It will sometimes be a small problem set designed to help you understand the behavior of math models. Other times, it will involve writing up a little paper on an assigned topic. All homework should be typed unless noted.

Homework papers should be submitted on-line, where they might be checked by TurnItIn or a similar service. This is partly to help keep you honest, and partly to help you learn acceptable ways to cite the work of others. A side benefit is that sometimes TurnItIn finds papers relevant to your work that you would not have found otherwise!

Exams

There will be no exams, unless the class demonstrates an unwillingness to be motivated any other way.

Projects

Instead of a mid-term and a final exam, you will do a mid-term and a final project. Your results will be reported in a paper and a presentation to the class. You may work by yourself or in a team of 2 people, but no groups larger than 2 will be allowed. You may switch project partners at your will. Your project grades will each be split something like this:

• 10 pct: proposal
• 80 pct: work and written report
• 10 pct: presentation

On average, students should spend a total of about 30 minutes in office hours discussing the project. Plan for this in advance!

Overall Grades

No scores will be dropped, unless a valid excuse with evidence (as needed) is given. In the unfortunate event of a medical need, the appropriate grade or grades might be dropped entirely, rather than giving a make-up, at the instructor's discretion. You are highly encouraged to still complete the relevant assignments and consult with me during office hours to ensure you know the material.

• 50 percent for all the homework together,
• 20 percent for the mid-term project, and
• 30 percent for the final project.

• 92.0 and above : A
• 88.0 to 92.0: A-
• 84.0 to 88.0: B+
• 80.0 to 84.0: B
• 76.0 to 80.0: B-
• 72.0 to 76.0: C+, etc.

General Caveat

Advice from Other Math Modeling Students

• * work in groups * start the first day assignment is given * don't take too many credits w/ this class * ask a lot of questions * utilize Dr. Ross
• Do go to his office hours more than you normally would; if you have a question ask don't wait.
• See Prof. Ross in office hours and don't be afraid to email him. He is usually very helpful and approachable.
• Plan on visiting Prof. Ross during office hours in order to do well in the class. You will learn a lot in the end, but be ready to work.
• [prof ross:] add a note to the syllabus stating something to the effect of, "This class will not be like other math classes. Instead of straight-up problems or proofs, the biggest amount of work will be setting up the models, exercises, etc. and in analysing what your results mean. It will not be the mathematical work done to obtain the results that is the tricky part." But word the note better.
• attend the office hours Prof Ross is really good at explaining & helping out with the homework
• WORK TOGETHER!
• Take notes during the computer lab days and send yourself the excel sheets.
• Go to class. The computer lab days help even if you know excel well.
• Go to class. Go to office hours and pick project that you're energized about and interested in even if they're harder. It will make this math class the best one you've ever taken.
• Don't drop the class! It sounds impossible in the beginning, but stick with it.
• Don't procrastinate.
• Take differential equations close to this class, it will make more sense!
• Start projects ASAP.
• Ask questions!!! The professor will guide you along the way like Yoda.
• Talking to anyone about your projects or the homework, be it Prof. Ross or other students, is a really, really good idea.
• Never be afraid to ask for help.
• If project falls through, have backups.

Land Acknowledgement

University Writing Center

Standard University Policies

Food Pantry

Resources

EMU COVID Policies, etc.

In addition to the articulated course specific policies and expectation, students are responsible for understanding all applicable university guidelines, policies, and procedures. The EMU Student Handbook is the primary resource provided to students to ensure that they have access to all university policies, support resources, and student's rights and responsibilities. Changes may be made to the EMU Student Handbook whenever necessary, and shall be effective immediately, and/or as of the date on which a policy is formally adopted, and/or the date specified in the amendment. Electing not to access the link provided below does not absolve a student of responsibility. For questions about any university policy, procedure, practice, or resources, please contact the Office of the Ombuds: 248 Student Center, 734.487.0074, emu_ombuds@emich.edu, or visit the website at www.emich.edu/ombuds. CLICK HERE to access the University Course Policies

Refusals to comply with COVID mitigation requirements are a disruption of the classroom learning environment. This includes examples such as refusing to wear a face mask, maintain appropriate distancing, or otherwise comply with the University' COVID-19 policies. Steps that instructors may take in the event of a classroom disruption include:

Make reasonable efforts to resolve the classroom disruption within the classroom. This includes reminding the student that they must wear a face mask, class will not begin and instructors are not permitted to conduct a class session until they do so. Failure to comply with University policy will subject the student to disciplinary action.

If the behavior persists and the student does not comply with the policy, the instructor has the right to (and with masking violations SHOULD) discontinue the class session and immediately report the behavior to their department head/school director who will contact the Office of Wellness and Community Responsibility.

If the situation escalates and an instructor feels an immediate threat to themselves or others, they may contact DPS (911 or 734-487-1222) for support.

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