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 are:
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.
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.
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. 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), inventorySome 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 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!
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:
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 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
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.