Math 319: Math Modeling

Prof. Andrew Ross

Fall 2015

Basic Information

Note: this syllabus is temporary, and may change up to the first day of class.
This version posted on: 2015-09-04

General Description

Math Modeling is the art of taking a real-world problem and stating it in mathematical terms. It often involves making simplifying assumptions. In our class, we get in the habit of doing all the parts of the math modeling cycle: modeling, solving, checking, and guessing. Often, a large part of the problem is even deciding which problem to solve. For example, should you find the best schedule for your staff at one location, or consider opening new locations? Should you start with a theoretical model then match it to data, or just model the data directly? We will also consider a lot of common mathematical models, and explore their properties.

Course Catalog Entry

The modeling process; model building and evaluation, techniques of modeling; model fitting and models requiring optimization; empirical model construction---experimental models, dimensional analysis, simulation models, dynamic models; use of derivatives in the modeling process, single and multivariable dynamic models.


Math 120 and Math 122.
Some experience using Excel, VBA, Mathematica, Maple, or Matlab will also be VERY helpful, but it is not strictly a prerequisite.

Follow-up courses: Math 325 Differential Equations, Math 418 Modeling with Linear Algebra, Math 419 Advanced Math Modeling (stochastics), 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

Section 0, CRN 11379: Tue/Thu 12:30-1:45 in Pray-Harrold 502
Brief schedule overview: 3 credit hours.
Detailed schedule:
Prof. Andrew Ross Math 319, CRN 11379; Tue/Thu 12:30-1:45, PH 502
Block# Date 2015 day unit topics HW assigned HW due
1 9/8 Tue general modeling intro; math model examples; a math model has; graph sketching M1
2 9/10 Thu general modeling bloom's taxonomy; CCSS-M standards for mathematical practice; malaria nets--start simple; evacuation; modeling cycle M2 M1
3 9/15 Tue general modeling real modeling cycle; oper tact strat; airline problems; concept maps; intro to excel (graphing, label axes, title, autofill, control-shift-down) M3 M2
4 9/17 Thu regression linear regression: houses, predictions, residuals, graph residuals! R1, R2 M3
5 9/22 Tue regression R^2; school district data; correlation/causation; ecological fallacy; common resid graphs; basic procedure; LSRL math model; averaging before regression? R3 R1
6 9/24 Thu regression Pre-Lab at home: 4-function pre-quiz; in-class: answers; exponential fits, compound interest R3 before class, R2
7 9/29 Tue regression yeast; logplots; power fit R4
8 10/1 Thu regression log-of-log, model selection, occam's razor, multivariate regression school data R5 R4
9 10/6 Tue regression heat index; polynom; sines R5
10 10/8 Thu regression java fourier app; averaging and regression; waves and trends R6
11 10/13 Tue regression Quiz on R5; Logistic; overfitting/crossvalidation; Machine Learning overview R7, R8, R9 R6
12 10/15 Thu optimization LP toys, wyndor (no sensitivity analysis), knapsack, swimmers O1 R7
13 10/20 Tue optimization shift scheduling; network flow O2 R9
14 10/22 Thu optimization Networks O1
15 10/27 Tue optimization MCNF node-node; ramen; brief fast-food intro; sensitivity analysis on wyndor; feas region; fundamental theorem of LP O3, M4 O2
16 10/29 Thu optimization example papers: dinosaur and relay; NLP: manufacturing, electricity O3, M4
17 11/3 Tue optimization concavity proposal 1
18 11/5 Thu optimization airport O4
19 11/10 Tue optimization shotspotter O5
20 11/12 Thu dynsys Dynamical Systems; PID; credit card, repeated dosing O4, O5
21 11/17 Tue projects Project Presentations project 1
22 11/19 Thu projects Project Presentations
23 11/24 Tue limited population growth; quiz D1
24 11/26 Thu Thanksgiving
25 12/1 Tue dynsys pagerank; leslie; SIR; pred/prey;oilspill D2 D1
26 12/3 Thu dynsys multiple initial conditions; equilibria; delta plots; phase-plane plots; fitting limited-pop growth D3 proposal2
27 12/8 Tue dynsys observation noise, process noise D2
28 12/10 Thu dynsys repeated dosing? accel/vel/pos? chaos? splines? PERT/CPM? D4, M5, M6 D3
29 12/15 Tue presentations presentations; M5 & M6 discussion project 2, D4, M5, M6

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.

I expect that you will work on Math 319 for 6 to 9 hours per week outside of class during a regular (Fall or Winter) semester, and 2.5 times that during a Summer semester (6-week session)

Instructor information

Professor Andrew Ross
Pray-Harrold 515m
(734) 487-1658, but I strongly prefer e-mail instead of phone contact.
Math department main office: Pray-Harrold 515, (734) 487-1444

Office Hours and other help

Here is my complete schedule.
 10:00-11:00 (Wed) grad student meeting
 11:00-12:00 (Wed) research meeting
 12:00- 1:00 meeting
  1:00- 2:00 Office Hours
  2:00- 3:15 UNIV 101, PH 503
  3:15- 4:00 Office Hours
  9:00- 9:30 Office Hours
  9:30-10:45 Math 110, PH 305
 10:45-12:30 Office Hours and lunch
 12:30-1:45 Math 319, PH 502
  1:45-2:00 office hours/transition between classes
  2:00-3:15 Math 360, PH 324
  3:15-4:00 Office Hours
  No official office hours, but I'm often on campus.
  E-mail me to make an appointment, or drop by.

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.

Another resource on campus is the Holman Success Center, formerly the Holman Learning Center.

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.

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

Here is a list of books that I have found interesting and related to math modeling. Perhaps some of them will strike your fancy, too. I own the ones that are starred (*) and can lend them to you. Others you will have to find at the library or on the usual Internet booksellers. Links are given to Amazon, but I do not specifically endorse them or any particular bookseller. Of course, if you like a book you can see what similar books the online bookseller recommends. Here are some journals that you might be interested in: Other Stuff:

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:

We have a few secondary goals, which may be more or less applicable to your personal situation:

Student Outcomes

By the end of the course, students will be able to: (optional topics that we might not get to are marked with a ?) Also compare this list of outcomes to the CUPM 2015 course guide for math modeling.


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
Some variations in this outline are to be expected.

Grading Policies


Regular attendance is strongly recommended. There will be material presented in class that is not in the textbook, yet will be very useful. Similarly, there are things in the textbook that are might not be covered in class, but are still very useful. 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 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!


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


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:

The final presentations will be made during the time slot reserved for the final exam.

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. You are highly encouraged to still complete the relevant assignments and consult with me during office hours to ensure you know the material.

Your final score will be computed as follows: Final percentage scores will be given letter grades as follows:

General Caveat

The instructor reserves the right to make changes to this syllabus throughout the semester. Notification will be given in class or by e-mail or both. If you miss class, it is your responsibility to find out about syllabus and schedule changes, especially the due dates and times of projects, assignments, or presentations.

Advice from Other Math Modeling Students

In the last two semesters, I've asked my math modeling students to give advice to you, future math modeling students, based on their experiences in my course. Here are some of the highlights:

Standard University Policies

Religious Holy Days

Current University policy recognizes the rights of students to observe religious holidays without penalty to the student. Students will provide advance notice to the instructor in order to make up work, including examinations, they miss as a result of their absence from class due to observance of religious holidays. If satisfactory arrangements cannot be made with the instructor, the student may appeal to the school director or head(s) of department(s) in which the course(s) is / are offered.

Academic Honesty

Academic dishonesty, including all forms of cheating, falsification, and/or plagiarism, will not be tolerated in this course. Penalties for an act of academic dishonesty may range from receiving a failing grade for a particular assignment to receiving a failing grade for the entire course. In addition, you may be referred to the Office of Student Conduct and Community Standards for discipline that can result in either a suspension or permanent dismissal. The Student Conduct Code contains detailed definitions of what constitutes academic dishonesty but if you are not sure about whether something you are doing would be considered academic dishonesty, consult with the course instructor. You may access the Code online at:

Classroom Behavior

Students are expected to abide by the Student Conduct Code and assist in creating an environment that is conducive to learning and protects the rights of all members of the University Community. Incivility and disruptive behavior will not be tolerated and may result in a request to leave class and referral to the Office of Student Conduct and Community Standards (SJS) for discipline. Examples of inappropriate classroom conduct include repeatedly arriving late to class, using a mobile/cellular phone while in the class session, or talking while others are speaking. You may access the Code online at

Those who use laptops during class should sit in the back row if possible, to avoid distracting others with what is on their screens.

Special Needs Accomodations

If you wish to be accommodated for your disability, EMU Board of Regents Policy 8.3 requires that you first register with the Disability Resource Center (DRC) in 240K EMU Student Center. You may contact DRC by telephone (734.487.2470). Students with disabilities are encouraged to register with the DRC promptly as you will only be accommodated from the date you register with them forward. No retroactive accommodations are possible.

Student and Exchange VISitors (SEVIS)

The Student Exchange Visitor Information System (SEVIS) requires F and J students to report the following to the Office of International Students 244 EMU Student Center within ten (10) days of the event: Prior permission from OIS is needed for the following: Failure to report may result in the termination of your SEVIS record and even arrest and deportation. If you have questions or concerns, contact the Office of International Students at 734.487.3116, not the course instructor.

The Family Educational Rights and Privacy Act (FERPA)

The Family Educational Rights and Privacy Act (FERPA) is a Federal law designated to protect the privacy of a student's education records and academic work. The law applies to all schools and universities which receive funds under an applicable program of the U.S. Department of Education and is applicable to students at EMU. All files, records, and academic work completed within this course are considered educational records and are protected under FERPA. It is your right, as a student in this course, to expect that any materials you submit in this course, as well as your name and other identifying information, will not be viewable by guests or other individuals permitted access to the course. The exception will be only when you have given explicit, written, signed consent. Verbal consent or email is insufficient.