Math 319: Math Modeling

Fall Semester 2006

Basic Information

Note: this syllabus is temporary, and may change up to the first day of class.
This version posted on: 2006-08-31

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.

Prerequisites

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 12:00 noon - 12:50 in Pray-Harrold 321
"Final Exam" schedule: Fri, Dec. 15, 11:30-1:00
CRN 15067, 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
andrew.ross@emich.edu
http://people.emich.edu/aross15/
(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

Mon, Wed: 1:10-2:10pm
Tue, Thu: 11:00am-noon and 5:00-5:30pm

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 220. Please give them a call at 734-487-0983 to find out their hours.

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. 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 either the WebCT or eCollege system. As of now, it is unclear which one we will use. Either way, 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:

Outline/schedule

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

Attendance

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

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 TurnItIn.com 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 into roughly 75 percent for the written paper and actual work, and 25 percent for the presentation (subject to change). 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.

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 www.emich.edu/sjs.

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.