Math 319: Math Modeling

Fall Semester 2007

Basic Information

Note: this syllabus is temporary, and may change up to the first day of class.
This version posted on: 2007-09-05

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

Class Meetings

Mon, Wed, Fri 1:00pm - 1:50 in Pray-Harrold 421
"Final Exam" schedule: Mon, Dec. 17, 1:00-2:30pm
CRN 14434, 3 credit hours.

Class meetings will be mostly interactive lectures, with some time to work on problems in class, and some time to discuss homework.

Instructor information

Professor Andrew Ross
Pray-Harrold 515b
(734) 487-1064, 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

Office Hours: tentatively

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.

I am definitely unavailable during the times I teach other classes:

The Mathematics Student Services Center (or "Math Lab") is also here to help you, in Pray-Harrold 220. Their hours for Fall 2007 are:

Please give them a call at 734-487-0983 or just drop by.

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.

(not-absolutely-)Required materials

Our suggested textbook is "A First Course in Mathematical Modeling, 3rd Edition" by Giordano, Weir, and Fox, published by Thomson:Brooks/Cole, ISBN 0-534-38428-5. It is not absolutely required, though. A quick survey of last year's class found that those who didn't buy it felt okay with their decision. Amazon link

The textbook should be available at all the usual bookstores on and around campus. The library has a page about class textbooks that includes bookstore addresses, and also information about the student government's Bookswap.

Course Web Page

We will use the WebCT system 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.

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. 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:


Here we show which chapters from the book we will probably cover. 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  1:* difference equations, dynamical systems
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  7:+ Linear Programming (LP), one-dim. line search
		(and add Integer Programming?)
Ch  8:+ dimensional analysis and similitude
Ch  9:  graphs of functions as models
Ch 10:+ one-dim ODEs
Ch 11:+ systems of ODEs
Ch 12:* Non-Linear Programming (NLP), inventory
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 chalkboard, 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 a week. 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.

Homework papers should be submitted on-line, where they will be checked by 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.

Overall Grades

No scores will be dropped, unless a valid medical excuse with evidence is given. In the unfortunate event of a medical need, the appropriate grade or grades will 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: Once final scores are computed, a curve will be applied.

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:


Date	Category	ComputerLab?	Description
05-Sep	modeling		First Day of Class
07-Sep	modeling		What Is a Math Model?
10-Sep	modeling		Modeling Procedures; oper/tact/strat; rental car gas problem
12-Sep	modeling		more modeling, Graph/Net terminology, writing tips, publication types
14-Sep	other	Yes	Excel intro, incl. plotting
17-Sep	DS		Dynamical Systems
19-Sep	DS		Rent-to-own, drug dosing, transient/equilibrium
21-Sep	DS	Yes	equilibrium, stability, Newton's Law of Cooling, Limited Growth
24-Sep	DS		multivariate dynamical systems, 2-state DTMC
26-Sep	DS		multivariate equilibrium, 3-state DTMC
28-Sep	fitting	Yes	Exploratory Data Analysis (EDA), plotting in Excel
01-Oct	fitting		model fitting, Linear Regression
03-Oct	fitting		Correl. Coeff.
05-Oct	fitting	Yes	Semilog and Log-Log
08-Oct	fitting		time-of-day/week/year modeling
10-Oct	fitting		Multiple Linear Regression, polynomial regression, non-linear regression
12-Oct	fitting	Yes	Lagrange Polynomials, Splines
15-Oct	stochastics		Simulation (Ch 5)
17-Oct	stochastics		Queueing
19-Oct	stochastics		Queueing
22-Oct	LP		Linear Programming (Ch 7)
24-Oct	LP		LP: feasible, infeasible, optimal; transportation, assignment
26-Oct	LP	Yes	LP in Excel
29-Oct	LP		LP techniques: piecewise linear, etc.
31-Oct	other		writing/presentations/flex-time
02-Nov	presentations		projects due;Project Presentations
05-Nov	presentations		Project Presentations
07-Nov	presentations		Project Presentations
09-Nov	IP		Integer Programming: basic, and sneaky;
12-Nov	IP		IP: Fixed-Charge
14-Nov	IP		more IP
16-Nov	IP	Yes	finished IP
19-Nov	other		Graph applications (TSP, Min Spanning Tree, PERT)
21-Nov			no class (Thanksgiving break)
23-Nov			no class (Thanksgiving break)
26-Nov	NLP		Non-Linear Programming (Ch 12): economies/diseconomies of scale
28-Nov	NLP		unconstrained NLP: L2 facility location, regression
30-Nov	NLP	Yes	protein folding movie, minimize concave down -> many local minima, solution is jumpy
03-Dec	NLP		NLP loose ends
05-Dec	other		Dimensional Analysis (Ch 8)
07-Dec	DE		Differential Equations (Ch 10-11)
10-Dec	DE		Differential Equations
12-Dec	other		course overview; last day of class
14-Dec			no class--other classes having finals
17-Dec	presentations		projects due;Final Presentations

Standard University Policies

Religious Holy Days

I support students' right to observe religious holidays without penalty. To the best of my ability, I will schedule exams to not conflict with major religions' holidays. Students are to provide advance notice to the instructor in order to make up work, including examinations that they miss as a result of their absence from class due to observance of religious holidays. If satisfactory arrangements cannot be made, the student may appeal to the head of the department.

Academic Honesty

Academic dishonesty, including all forms of cheating and/or plagiarism, will not be tolerated in this class. 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 Judicial Services 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’re doing would be considered academic dishonesty, consult with the instructor.

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 Judicial Services (SJS) for discipline. Examples of inappropriate classroom conduct include repeatedly arriving late to class, using a cellular telephone, or talking while others are speaking. You may access the Code online at

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 Access Services Office (ASO) in room 203 King Hall. You may contact ASO by telephone at (734) 487-2470. Students with disabilities are encouraged to register with ASO 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, 229 King Hall 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 OIS at 487-3116, not your instructor. Also, see the EMU SEVIS page.