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 will be mostly interactive lectures, with some time to work on problems in class, and some time to discuss homework.
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 were:
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.
Most students do well in this course without a textbook. For those who feel the need to have one just in case, I suggest "A First Course in Mathematical Modeling", 3rd or 4th Edition, by Giordano, Weir, and Fox.
A lot of our work will be done on computers, specifically in Excel. If you had been waiting for a good reason to buy a laptop, this is it.
I will post data files, homework assignment files, etc. on my home 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.
Our primary goal is to teach you to be a good (or great!) math modeler. To be a good modeler, you need:
Here we show which chapters from the book we will probably 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 ODEsSome variations in this outline are to be expected.
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 every two weeks. 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 may 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!
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:
On average, students should spend a total of about 30 minutes in office hours discussing the project. Plan for this in advance!
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:
Date PC Lab? Category Description 03-Sep modeling First Day of Class 05-Sep modeling What Is a Math Model? 08-Sep modeling Modeling Procedures; oper/tact/strat; rental car gas problem 10-Sep modeling more modeling, Graph/Net terminology, writing tips, publication types 12-Sep Yes other Excel intro, incl. plotting 15-Sep Yes fitting Exploratory Data Analysis (EDA), plotting in Excel 17-Sep fitting model fitting, Linear Regression 19-Sep Yes fitting Correl. Coeff. 22-Sep fitting Semilog and Log-Log 24-Sep fitting time-of-day/week/year modeling 26-Sep Yes fitting Multiple Linear Regression, polynomial regression, non-linear regression 29-Sep fitting Lagrange Polynomials, Splines 01-Oct stochastics Simulation (Ch 5) 03-Oct Yes stochastics Queueing 06-Oct stochastics Queueing 08-Oct LP Linear Programming (Ch 7) 10-Oct Yes LP LP in Excel 13-Oct LP LP: feasible, infeasible, optimal; transportation, assignment 15-Oct IP Integer Programming: basic, and sneaky; 17-Oct Yes IP IP: Fixed-Charge 20-Oct NLP Non-Linear Programming (Ch 13): economies/diseconomies of scale 22-Oct NLP unconstrained NLP: L2 facility location, regression 24-Oct Yes NLP protein folding movie, minimize concave down gives many local minima, solution is jumpy 27-Oct NLP LP/IP/NLP loose ends 29-Oct other writing tips/presentation tips/flex-time 31-Oct presentations projects due;Project Presentations 03-Nov presentations Project Presentations 05-Nov presentations Project Presentations 07-Nov other Graph applications (TSP, Min Spanning Tree, PERT) 10-Nov DS Dynamical Systems 12-Nov DS Rent-to-own, drug dosing, transient/equilibrium 14-Nov Yes DS equilibrium, stability, Newton's Law of Cooling, Limited Growth 17-Nov DS multivariate dynamical systems, 2-state DTMC 19-Nov DS multivariate equilibrium, 3-state DTMC 21-Nov Yes DS lab day 24-Nov other Dimensional Analysis (Ch 8) 26-Nov no class (Thanksgiving break) 28-Nov no class (Thanksgiving break) 01-Dec DE Differential Equations (Ch 11+) 03-Dec DE Differential Equations 05-Dec Yes DE Differential Equations 08-Dec DE Differential Equations 10-Dec other course overview; last day of class 12-Dec no class--other classes having finals 15-Dec presentations projects due;Final Presentations
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 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.
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.
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.