• Mathematics Applied to Deterministic Problems in the Natural Sciences, SIAM 1988.  Optional textbook available at bookstore.
• Class reserves available online and at Folsom Library.  See Readings on the WebCT site for current reading list.
• Maple and MATLAB may be used for some parts of the course.  You will not be expected to program in either of these packages, and will be given specific instructions for how to use them for the particular purposes of the course.  You are welcome to use mathematical computing packages such as these to assist you in your homework, subject to any explicit restrictions I may state on particular assignments.  Be careful that you are learning the concepts and techniques  though; you will not have access to a computer or calculator during exams!
• WebCT will be used for some aspects of course management.  You can get started by going to http://www.rpi.edu/web/webct/ and consulting the document describing the use of WebCT in this class.

Course Objectives

• To learn and use various mathematical techniques often helpful in applications
• To gain familiarity with the general mathematical modeling process
• To gain facility in mathematical approaches to problems in the sciences and social sciences

• You will be responsible on homework and exams for all material covered in class, and there will be quite a bit you won't find in the course readings.  It would therefore behoove you to attend the classes, and if you miss class, I suggest getting notes from a friend.
• If you are absent for a midterm of final, you must let me know as soon as possible, and certainly within 24 hours after the exam.  If I excuse your absence because of a very good reason (like a serious illness), you can take a make-up oral examination.  If your absence is unexcused, you get a zero for that exam and there will be no opportunity for a make-up.  "Forgetting" that a midterm has been scheduled will not be excused.

• OPTION:  Term project in lieu of homeworkst.  Under this option, you will submit progress reports on your project on dates that homework are due, submit a written report by December 5, and deliver a 15-20 minute oral presentation of your work to the class during the last few class meetings.  While your project grade will be based primarily on your final written and oral presentations, your progress reports will also be graded and incorporated into your project grade.  You can propose your own topic for a project, perhaps after consulting my list of suggestions, the books that will be placed on reserve, or the World Wide Web for ideas.  In any event, if you want to explore this option, please contact me.  You may work on final projects individually or in teams of two, but more will be expected from pairs than from individuals. WARNING:  Even though you will be excused from formal submission of homework while you are working on your term project, you are still responsible for mastering the course material so that you will perform well on examinations.  You must earn at least a B on the midterms to reamin eligible for this project option.

• If you do not do a term project, your course grade will be weighted as follows:
• Homework:  30%
• Midterm #1:  20%
• Midterm #2:  20%
• Final exam:  30%
• If you elect to do a term project, your course grade will be weighted as follows:
• Term project:  30%
• Midterm #1:  20%
• Midterm #2:  20%
• Final exam:  30%

A:  90% +

B:  80-89%

C:   70-79%

D:  50-69%

F:    0-50%

Evaluating student performance is an important part of the service provided by Rensselaer, and for it to be meaningful, it must be based on fair and honest representations.  Acts which violate this trust undermine the educational process.
The general rules governing academic honesty in this course are those found in the Rensselaer Handbook of Student Rights and Responsibilities, with the following clarifications:
• Unless otherwise indicated, you may cooperate in small groups  in and outside of class on the solution of problems.  You are strongly encouraged to work with a partner on homework, and may turn in one solution set per pair.  While you can work together in groups larger than 2, each homework submitted should be written essentially independently once the ideas are hashed out.   Generally speaking, you should show your work.  It is not permissible for one pair to simply copy the solutions of another pair, even if they are working together.  If there is evidence for such copying, all people involved will be penalized 10 points for the first such infraction, 20 points for the second, 30 points for the third, and so on in arithmetic progression.  Remember, I have a Ph. D. and am able to detect trivial attempts to conceal a copying operation.  The worst penalty for not making your own independent and serious effort on the homework is, of course, a disappointing performance on the exams.  Several people fell into this trap last year, so be warned!  Don't let your partner or your friends do your thinking for you!
• You may under no circumstances collaborate on examinations or misrepresent another person's work as your own on examinations.
• You may not bring books, notes, or electronic instruments to examinations outside of those explicitly permitted, and you may not write on or alter examination materials that you submit for regrading.
Students who violate the spirit or letter of these rules are subject to penalties according to the principles outlined in the Rensselaer Handbook, in addition to receiving a zero on any work on which cheating has taken place.

• Dates are approximate, but the topics are pretty firm.  There may be some changes if I discover some interesting new material during the course of the semester.
  

 

Session/ Date	Topics
1. 08/26	Introduction
2. 08/29-09/09	Self-similarity and Dimensional analysis (physics, engineering, animals)
3. 09/12-09/19	Regular perturbation theory (projectiles, mechanics)
4. 09/23-10/07	Singular perturbation theory (oscillators, genetic drift)
5. 10/03	Midterm 1
6. 10/10-10/17	Population Modeling (enzymes, war, epidemics)
7. 10/24-10/31	Random modelling (Card shuffling, tournament scheduling)
8. 11/04-11/11	Diffusion phenomena (Brownian motion, air pollution)
9. 11/07	Midterm 2
10. 11/14-11/25	Continuum Modeling (traffic)
11. 12/02-12/05	Case study:in mathematical modeling (Auctions)