Tuesday and Thursday
3:30-5:45 in Academic Hall 211
Instructor: David Barsky Telephone: 750-4201 (with voice mail) E-mail: djbarsky@csusm.edu URL: http://www.csusm.edu/public/DJBarskyWebs/mainpage.html Office: Craven Hall, Room 6231 Office Hours: To Be AnnouncedRequired Text: An Introduction to Mathematical Modelling, by Fowkes and Mahony
Recommended: One or two floppy diskettes formatted for Macintosh computers.
Prerequisite: MATH 360, 462, 500 and 540 or consent of instructor. Students can automatically gain my consent by either
(i) being a graduate student in the Master's program in Mathematics at CSUSM, or
(ii) (for undergraduates taking this course in place of Math 490, Senior Seminar) having completed 12 units of Mathematics courses numbered 350 or higher.
I. Catalog Description. Mathematical modeling with emphasis on models used in the social, life, and management sciences and their role in explaining and predicting real world phenomena. Combines theoretical ideas with hands-on laboratory experience.
II. Expanded Description. I intend to widen the focus in this course to also include models having their basis in the physical sciences and engineering, as well as models from the social, life, and management sciences. We will learn how to apply mathematics in this course in a number of real-world situations. These applications should be quite unlike those in any other course where one first learns a specific technique and then sets off in search of problems that lend themselves to that particular method. (Such an artificial set of applications can be found in any calculus book in the section on related rates problems that follows the section on implicit differentiation.) In a true modeling situation, you are not tipped off to the mathematical techniques that might prove most fruitful by the location of the problem in a text.
Our course will have three interwoven strands; but there is a great deal of freedom and flexibility within each of these. (It is my hope that there will be considerable student input into the choice of models that we explore, but that means that you have to come and tell me about your particular interests.)
Throughout this course we will make use of whatever technology seems most appropriate to the problem at hand. This might include the Computer Algebra System (CAS) Maple [the course text includes a modest amount of material on Maple] or the statistical software package Minitab. There are occasion when a simple spreadsheet (like Excel) might be well-suited for our purposes. You should bring your Macintosh-formatted diskette with you to class so that you can save any computer work that you do.
III. Course Goals. In short, this will be a course on modeling, not "meta-modeling." That is, rather than trying to develop a general theory of modeling (the forest), we will immerse ourselves in studying many particular models (the trees). The basic goal is for you to develop the (confidence in your) ability to take a vaguely stated problem, turn into a precise mathematical model, analyze that model to make a prediction or to explain some phenomenon, and successfully communicate your findings.
IV. Grades. Your grade will be based on:
Homework 25% Class Participation 15%, Class Project Written Reports 15% MCM Oral Reports 25% Final Modeling Project(s) 20%V. Homework. Homework, and its due date, will be posted on the whiteboard at class meetings. The initial policy will be that homework is due three lectures after it is assigned (but this may be changed if it becomes necessary). This should allow you several opportunities to come to my office hours for assistance if you are having difficulty with the assignments. Late homework will generally not be accepted. If you have to miss a lecture (see Section VI for comments on the importance of attending each class), you should make arrangements to have your homework placed under my door no later than 5:45 p.m. of the day on which it is due; it is your responsibility to get the next homework assignment - you may call me at my office or check the class web site (see Section XIII). In all of my syllabi, I have a sentence which reads "The importance of homework cannot be overstressed: one only learns mathematics by doing it!" That is especially true in this course, as the problems are the course.
As the 2500 word All-University Writing Requirement will be satisfied in part through the homework, your homework assignments will be graded for both the correctness of your solutions and the level of your exposition. I encourage you to regularly consult the course text and any other mathematics books that you own for examples of good mathematical writing. You will be working together with your classmates on a number of projects during the class. I encourage you to also meet together outside of class to work on the homework, but I will ask that you meet two conditions:
I want to warn you that not all of the homework will be graded; typically only a few representative problems will be examined. This makes it extremely important that you do all of the homework in each set - so that you don't find yourself in the unfortunate situation of having done most of the problems, but not the ones that were graded. Even if this does happen to you once or twice, you should still have an excellent homework grade if you are following the material (if not, get help - see Section XI) and handing in every homework assignment.
I will occasionally be asking students to rewrite their solutions in a form suitable for distribution to the rest of the class.
VI. Class Participation. It is my intent to use the "laboratory' period largely (but not exclusively) for exploring various modeling problems. I will be asking you to work together on these in groups. As I expect the class to have low enrollment, it is important that everyone attend every class in order for this aspect of the course to work -- I will keep track of attendance. It (almost) goes without saying that in the part of the class set aside for this group work, I expect you to be doing that and not, say, going over the homework problems that might be due that day.
VII. Class Project Written Reports. As explained in the preceding section, certain class periods will be devoted to trying to model various problems. The final step in these projects will be the submission of a short report explaining how you tried to model the given situation including what assumptions you made, and how you analyzed your model. Although there should be enough time in class to make significant progress on your model, there will not generally be enough time to write this report on your work. You will need to work with the other group members outside of class to prepare the report. I recommend that you agree to have one member of the group take the lead in this project and that you use a word processor or a mathematical typesetter so that it is easier to make revisions suggested by the other group members. I will make announcements giving one week notice before these reports are due. As the written reports will be used to satisfy part of the 2500 word All-University Writing Requirement, they will be graded for the level of your exposition as well as the innovation and appropriateness of your modeling assumptions, and the correctness of your analysis.
VIII. MCM Oral Reports. The Mathematical Contest in Modeling (MCM) is a nationwide undergraduate contest that has been run annually since 1995. Teams of up to 3 students receive a pair of open-ended problems at 12:01 a.m. on a Friday in late February or early March. They have until noon to choose which of these problems they will analyze; typically one of these problems is discrete or combinatorial in nature while the other is continuous or analytic. A typed solution to the selected problem is due by 11:59 p.m. on Monday. Over the intervening weekend the students may use computers, software packages, libraries, or any other inanimate sources. A few of the most outstanding submissions are published in THE UMAP JOURNAL, several volumes of which are in the CSUSM library: QA 11 .A1 U48.
One of the major strands of the course will consist of looking at these published student solutions. After consulting with the class to determine which problems are of the greatest interest, I will assign particular solutions to each member of the class. You will need to go to the library and make a copy of your article. Read the solution, and prepare an oral report that you will make on this to the rest of the class. I will set aside some time after all of the solution papers have been for us to discuss the different approaches (and the comments made by the problem posers, the contest judges and practitioners in the field from which the problem came) in an effort to see if we can improve on these solutions.
It is my hope that any undergraduates taking this course will consider serving on forming a CSUSM team for the 1998 MCM. Please let me know if you are interested in this, and I will check into registering a team.
IX. Final Modeling Project. In place of a final exam, there will be a final modeling project. I plan to assign individual projects to each student by November 25, the last class before the Thanksgiving Break. Completed modeling projects are due at 12:00 noon on Tuesday, December 16, which is the time reserved for the final exam. As this is yet another means through which we will exceed the 2500 word All-University Writing Requirement, your modeling projects will be graded in part on the clarity of your presentation.
X. Classroom Procedure. I strongly encourage your participation in the lectures. When I ask a question, please don't be afraid to answer it if you think that you can. You probably are right, and even if you aren't, I'm not going to ridicule you. Also, if you have a question (about mathematics) in lecture, please feel free to ask it as it occurs to you.
During the group work part of the course, don't be afraid to make suggestions. Often in the give-and-take where a group makes good progress toward solving a problem, each correct step is preceded by several others that are "not entirely successful."
When we're working with various computer packages, let me know if you're having difficulty working out the calculations on the computer, and I will try to help you (to the best of my ability); that's part of why I'm there.
XI. How To Get Help. You should come see me as soon as you realize that you need help. In addition to the several office hours a week that I will be running, you can also contact me by telephone or by e-mail (the number/address is on the first page of this syllabus). I also strongly encourage you to form study groups with your classmates.
XII. Resources. I will be placing several books on reserve at the CSUSM library over the course of the semester. These books may be checked out for one day. I strongly encourage you to browse through them. One text already on reserve is Mathematical Models and Their Analysis by Wan. As other books are placed on (and taken off of) reserve, I will update the supplementary reference page on my web site (see the next Section).
XIII. Internet. [Note there are no active links in this paragraph, but if you're already here, you don't need them anyway.] I will produce and maintain a Web page for this course. The URL is http://www.csusm.edu/public/DJBarskyWebs/570page.html. You can also reach it from the San Marcos home page (http://www.csusm.edu) by going to CSUSM CWIS (the whole thing) [near the top of the page], then to Faculty [under Personal Home Pages, near the bottom of the page], then to David Barsky [about the third screen down], and finally to MATH 570 Mathematical Modeling [about the second screen down]. My MATH 570 page will serve as a repository for official course announcements such as what books are currently on reserve, reading assignments, homework assignments, MCM assignments, and (perhaps) capsule summaries of the class lectures. During the one of the lab periods I will show you how to use Netscape Navigator to reach this site.
XIV. Important Dates. Mark these on your calendar.
First lecture, Add/Drop period begins Tuesday, September 2 Last day to add classes or drop with no record Monday, September 15 Last day to change grading option Monday, September 22 Last day to withdraw with a grade of W Monday, October 20 Thanksgiving Break - No class Thursday, November 27 Last class Thursday, December 11 Final Modeling Project Due 12:00 noon Tuesday, December 16XV. Our Contract. By enrolling in and attending this course, you are agreeing to conduct yourself with complete academic honesty at all times. In particular, you are promising to neither receive nor provide assistance on the final modeling projects, and that the solutions to all of the homework problems that you submit will be composed by yourself. This handout is a contract between you and me. My commitment is to teach the course as described in the preceding sections of this document. By remaining in this course, you affirm that you have read and understood this contract, and that you agree to it.
XVI. Welcome to Mathematical Modeling. - David Barsky
This page posted 9/6/97