# MATP 4600/DSES 4750

## Syllabus

### Instructor: Dr. Peter R. Kramer

• #### Office Hours:  Wednesdays 2-3 PM and Fridays 4-5 PM

Resources

Course Objectives

Learning Strategy

Honesty

Schedule

Resources

• Probability and Statistics, Morris H. DeGroot and Mark J. Schervish, Third Edition, Addison Wesley, 2002.  A serious and comprehensive textbook on probability and statistics, oriented toward an engineering mindset. If you are unsure about which textbook to choose for this course, I would recommend this one. Moreover, this book should also serve you well for the Mathematical Statistics class in the spring.
• Introduction to Probability, Dimitri P. Bertsekas and John N. Tsitsiklis, Athena Scientific, 2002. A lively "lecture note" presentation of the subject of probability that should appeal to strong students interested in mathematics and physics. The book focuses more on interesting aspects and ways of thinking about probability rather than following a standard, detailed textbook approach.
• Introduction to Probability and Mathematical Statistics, Lee J. Bain and Max Engelhardt, Second Edition, Duxbury,1992. This was the text used for the probability and statistics classes last year. It has a more concise conceptual treatment than deGroot & Schervish, but many more simple examples. However, I have not heard good reviews from students about this book.
• Probability for Risk Management, Matthew J. Hassett and Donald Stewart, ACTEX Publications, 1999. A development of probability oriented toward actuaries which also serves as a relatively easy introduction for those who may find deGroot and Schervish too demanding.
• WebCT (Blackboard Learning System) will be used for some aspects of course management.  You can get started by going to http://rpilms.rpi.edu and consulting the document describing the use of WebCT/Blackboard in this class.
• Maple may be used for some parts of the course.  By my understanding, this is accessible to all Rensselaer students.  If you would like to learn more about Maple, you may find the department's Maple Resources page of use.

Course Objectives

• To learn and use various mathematical techniques which are generally useful in probabilistic analysis and reasoning
• To gain experience with setting up, analyzing, and interpreting the results of probabilistic models in applied settings in science and industry

• Homework:  25%
• Midterm #1:  20%
• Midterm #2:  25%
• Final exam:  30%

Your course grade can be enhanced by active and substantive contribution to discussions in class and on the WebCT site.   You can be awarded as much as 5 percentage points on your final grade for exceptionally insightful and thoughtful input and questions

Late homework will be penalized 10 points (out of 100) per working day.  Once I post solutions to the homework (which could be as soon as the class after the assignment was due), no more homeworks will be accepted for credit.  If you have need for an extension on your homework, you should ask me in advance of the due date.  Homework is due at 2 PM on the due date specified on the calendar; submissions later in the class or day will be penalized 5 points.

Takehome components of exams are due at 2 PM on the due date specified on the calendar.  I will accept submissions until 4 PM with a 10 point penalty, but nothing later than that without an excellent excuse.

• A:  90% +
• B:  80-89%
• C:   70-79%
• D:  50-69%
• F:    0-50%

Graduate students are graded in the same way for scores of 70% and above, but they will receive a grade of F for scores between 0-69%.

If you miss an exam, you will only be permitted to make up the exam if you obtain an explanatory note from the Dean of Students indicating that you had a valid excuse (such as serious illness).  In any event, you must contact me within 24 hours of a missed exam with at least a preliminary explanation if you wish to make it up.  Unexcused absences (including "forgetting" about the exam) will result in a 0 score for that exam.

You may only appeal scores on exams based on factual criteria (a correct answer was marked wrong, or scores were added incorrectly).  Any such legitimate appeals will only be accepted within one week of the date on which the graded exam was returned to the class.  I will not entertain quibbles about how many points of partial credit you think you should have been given on some problem.  Students making frivolous appeals will be given one warning, after which further nuisance appeals will be penalized by as many points as the student was frivolously arguing.

Learning Strategy
I will direct the class according to the following learning strategy:
• Students preview the sections of their textbook pertaining to the material to be covered in class before the class.  It is not necessary to have a thorough understanding of the section after a first reading, but knowing the basic facts and content should help in following the class discussion.  In particular, I do not plan on spending much time in class on simply stating facts and definitions which students can more easily read in a nicely typeset textbook (as opposed to my childlike scrawls).  Rather, I will assume students have at least looked over the section enough to have encountered new definitions and classifications, so that I can spend the class time explaining more about the "how" and "why" of the material rather than the "what."
• Students attend class as much as possible, and obtain class notes from a friend when they are unable to attend.  The material covered in class is intended to supplement, and not simply restate, the material in the textbook.   Moreover, the class discussion will emphasize those aspects of the material which I find most important (and are therefore most likely to appear on the exams).
• Students work either alone or with a small group of colleagues to solve the homework problems. A pair of students may submit a single set of homework solutions with both students receiving the same grade for that assignment. While collaboration is encouraged to stimulate learning and understanding, each student is responsible for understanding any solution submitted under his or her name. If the assigned homework problems are too difficult, students should work out some of the simpler problems from the related sections of their textbooks until they have gained enough confidence and skill to tackle the assigned problems. Students may in particular want to work on those problems for which answers appear in the back of the book so they can check their work and understanding.   If students do not feel sufficiently confident with the material through self-study or consultation with colleagues, they should seek further assistance from the professor during his office hours.
• Students review for exams by checking that they are familiar with the material from the classes and textbook sections to be covered, can still do the homework problems from the relevant sections, and by taking one or more practice exams until they are satisfied with their performance.

Honesty
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 homework problems.  You are strongly encouraged to work with a partner on homework, and may turn in one solution set per pair.  While you may 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 and explain your calculations clearly and coherently to achieve most of the credit..  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.  Please believe that I 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.  Don't let your partner or your friends do your thinking for you!
• You may under no circumstance 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, except for one single (8.5 by 11 inch) sheet of notes in your own handwriting.
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.  In addition, I will report all instances of academic dishonesty to the Dean of Students.

Schedule
• The dates for topical coverage are approximate.  The exam dates are tentative for the moment, but will be fixed in the first week or two.

 Dates Topics August 28 Conceptual Foundations of Probability August 31--September 11 Counting and Combinatorial Techniques No class on September 4 September 14 Conditional Probability, Independent Events, and Bayes' Rule September 18--21 Discrete Random Variable Theory September 25--28 Binomial Distribution Model and Generating Functions October 2 Other Discrete Probability Model Examples October 5 Exam 1 in class October 10--19 Continuous Random Variable Theory Monday, October 9 class moved to Tuesday, October 10 October 23-26 Continuous Probability Model Examples October 30--November 2 Joint Probability Distributions November 6--16 Characterizations of Relations between Random Variables Exam 2, Monday, November 13 in class November 20--30 Functional Relationships between Random Variables No class November 23 December 4--7 Probability Limit Theorems December 14 Final exam, 6:30-9:30 PM

Date Last Revised: 09/06/06