Basic Information

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

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.

Instructor information

Office Hours and other help

 
Mon/Wed
 10:00-11:00 Office Hours
 11:00-12:15 Math 319, PH 521
 12:30- 1:45 Stat 360-0, PH 305
  1:45- 2:45 Office Hours
  2:45- 3:15 (Wed) faculty research meeting
Tue/Thu
 11:30-12:30 Office Hours
 12:30- 1:45 Stat 360-1, PH 305
  1:45- 2:45 Office Hours 
  4:30- 5:30 Office Hours
  5:30- 6:45 Math 560, PH 503
Fri:
	no schedule--I'm often on campus, though.
	I have various meetings to go to.
	Send e-mail to make an appointment.

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. You are expected 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
• *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!)
• *Queueing Methods: for Services and Manufacturing by Randolph W. Hall
• 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
• Tools for Thinking: Modelling in Management Science, 3rd edition, by Michael Pidd
• http://www.cscs.umich.edu/complexadaptivesystems/
• An Introduction to Game-Theoretic Modelling, Second Edition, Mike Mesterton-Gibbons
  
• 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
  
• Modelling in Healthcare; The Complex Systems Modelling Group; (CSMG), The IRMACS Center, Simon Fraser University
• Mathematical Methods in Immunology; Jerome K. Percus
• Quantitative Methods in Health Care Management: Techniques and Applications, by Yasar A. Ozcan (EMU library)
• Mathematical Modeling for the Life Sciences, by Jacques Istas
• Patient Flow: Reducing Delay in Healthcare Delivery, edited by Randolph W. Hall (EMU Library, incl. electronic copy)
• Mathematical and Experimental Modeling of Physical and Biological Processes by Banks and Tran
• 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), January 19 - 23, 2017. 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)

Outline/schedule

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

In the unfortunate event of a 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.

Standard University Policies