Instructor: John Holte

Office: Olin 307
Office hours: MF 2:30-3:20, TR 10:30-11:20, W 11:30-12:20; and when my office door is open.
Telephone: x7465
E-mail: holte@gac.edu
Homepage: http://www.gac.edu/~holte/

Course web site

http://www.gac.edu/~holte/courses/mcs341/fall04/

Bookmark this page.

Textbook

Mathematical Statistics with Applications 6/e, Dennis D. Wackerly, William Mendenhall III, and Richard L. Scheaffer, Duxbury, 2002.

Class meetings

10:30-11:20 Monday, Wednesday, and Friday
Classroom: Olin 219
Regular attendance, both physical and mental, is required.

MCS 341 Syllabus--Fall 2004

Dates	Chapter	Topics	Exams
Sept. 8-27	1, 2	Statistics & probability	Exam 1 M 9/27
Sept. 29-Oct. 18	3	Discrete random variables	Exam 2 M 10/18
Oct. 20-Nov. 5	4	Continuous random variables	Exam 3 F 11/5
Nov. 8-24	5	Multivariate probability distributions	Exam 4 W 11/24
Nov. 29-Dec. 15	6 7	Functions of random variables Sampling distributions, Central Limit Theorem Wrap-up and review	Final exam M 12/20, 1:00-3:00

This is a tentative syllabus. Changes may be made during the semester.

Homework rules

Students are encouraged to discuss course topics with one another. On assigned work, though, you are expected to do the work on your own. Your discussion with other students should be confined to matters related to understanding the problems and general approaches to doing problems, and you should acknowledge those who help you in this way. You should not collaborate on problem solutions unless directed otherwise.

• Acknowledge your sources (people and texts).
• In nontrivial problems, show how you get your answers.
• Turn in neat, well-written solutions, not messy first drafts. Trim "fringes." Staple multiple-page submissions.
• Do not copy collaborative solutions; write up solutions in your own words.
• Turn in homework on time. Each class day late reduces the possible points by 33%.
• Do extra credit problems entirely on your own.

Exams

There will be four unit exams and one comprehensive final examination.
Your final exam score will count as two unit exam scores, effectively making a total of six unit exam scores. The worst unit exam score will then be thrown out.
Sometimes a unit exam may be a take-home examination due on the class day following the day it is given out. See the syllabus for the exam schedule.

Make-up policy

Make-up exams will not be given except for medical or family emergency reasons. Students who will be absent from an exam for a school-sponsored event should arrange with me in advance to have an exam sent along with the coach.
If you miss a class for any reason, you are still responsible for learning what was covered in class and for getting any homework that is due turned in on time.
The standard way for making up an absence is to turn in a handwritten report on the material and examples that were covered in class.
Late homework will be penalized as stated under Homework rules.
If there is a compelling reason for granting an extension, you must negotiate the arrangements with me.

Your grade will be based on the following, assuming satisfactory attendance and participation in class. Absences that are not made up may reduce your score by as much as 2.5 percentage points per day.
 

Percent	Work
25%	Problem assignments
5%	In-class work & maybe quizzes
70%	Best 5 of 6 exam scores (4 unit exams and final exam counted as two scores)

Participation and performance factors may modify your grade.

You are expected to contribute to a classroom atmosphere that encourages learning and is marked by respect for your fellow learners. This involves, in part, faithful attendance, preparation, and participation, including attendance in the classes before and after each break. I may take into account exceptional effort and/or a trend of improvement throughout the semester. I appreciate students who are more interested in points of mathematics than in points of grading.

Academic honesty

• Page 31 of the Gustavus Adolphus College Academic Bulletin states in part: "The faculty of Gustavus Adolphus College expects all students to adhere to the highest standards of academic honesty... In all academic exercises, examinations, papers, and reports, students shall submit their own work. Footnotes or some other acceptable form of citation must accompany any use of another's words or ideas." The complete statement may be found at: http://www.gac.edu/oncampus/academics/general_catalog/current/acainfo.cfm.
• The following code will be written in full and signed on every examination and graded paper:
  "On my honor, I pledge that I have not given, received, or tolerated others' use of unauthorized aid in completing this work."
• "By enrolling classes at Gustavus, you have taken up membership in a worldwide community of scholars, and like any community, Academia has ethical standards to which you are expected to adhere. You are expected to learn and follow the principles of honesty and integrity that apply in academic life. Among those standards are that you faithfully represent your own work, acknowledge any borrowing from the work of others, avoid falsifying data or sources, be respectful of other scholars' efforts and not interfere with their access to resources (e.g., by misappropriating or damaging library materials), do a fair share of the work in group efforts, give others the benefit of your informed opinions and observations in discussion, and be respectful of others' values, knowledge, and feelings while developing your own.... Regrettably, serious and deliberate violations of ethics may incur serious penalties.... If you are in doubt about whether your work conforms to ethical standards, please inquire--you are, after all, a learner." --John Rezmerski, Advising and Registration Manual 1995-96, pp. 60-61.
• A first violation of the academic honesty policy will result in a zero grade on the paper in question and a report to the office of the Dean of the Faculty. A second case will result in a failing grade for the course.

Extra help

• I encourage you to see me during my office hours and at other times when my office door is open.
• If you have a disability that requires an accommodation, please see me privately as soon as possible.

MCS 341-342: Probability Theory and Mathematical Statistics

MCS 341 will concentrate on probability theory; MCS 342 will focus on mathematical statistics.

Probability theory is the branch of mathematics that deals with the concepts of chance and randomness.

Statistics is the science of collecting, organizing, analyzing, and interpreting numerical data. It makes heavy and essential use of mathematics and probability theory, but in practice it is not a proper subset of mathematics. The field of statistics may be divided into descriptive statistics and statistical inference. Statistical inference, drawing conclusions from sample data and assessing the quality of those conclusions, is the central focus of our textbook, and it relies heavily on probability theory.

Some statisticians and textbook writers treat probability theory as merely the handmaiden of statistics, but this perpective is myopic. Probability theory is much more. The study of probability theory also has great value as

• a subject in its own right
• an entree to vast areas of applied probability, including risk and insurance problems, mathematical modeling, and random processes, including time series (such as stock market prices), queueing theory (waiting lines), Markov processes, and much more
• a prerequisite for the the advanced study of statistical physics, quantum mechanics, and dynamical systems
• a new way to understand other areas of mathematics, such as number theory, cryptography, and combinatorics.

MCS 341: Probability Theory

• Probabilistic thinking
  According to the noted probabilist Leo Breiman, "Probability theory has a right and a left hand. On the right is the rigorous foundational work using the tools of measure theory. The left hand `thinks probabilistically,' reduces problems to gambling situations, coin-tossing, motions of a physical particle." The famous probabilist William Feller saw a three-way division: "Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation."

• A brief history
  In Western intellectual history, the current notion of probability was conspicuously absent until its sudden emergence in the middle of the 17th century. The correspondence between Pascal and Fermat in 1654, in which Pascal solved a couple of gambling problems, is often cited as marking the beginning of probability theory.

  Thereafter the study flourished. In just three years, Christian Huygens published the first textbook. During this classical period, mathematicians dealt primarily with problems involving finitely many equiprobable elementary events, as well as some continuous limiting cases and geometric probability. The study developed as "a chapter in applied mathematics," consisting largely of ad hoc methods. Probability then lacked coherence and a clear connection to the rest of mathematics and science.

  The early 20th century saw the transition from classical probability to modern probability. Richard von Mises and others developed the frequentist, or objective, concept of probability. Bruno de Finetti and others developed the notion of personal, or subjective, probability, and connected it with the classical Bayesian approach to conditional probability. In 1933 Andrei Kolmogorov, in his classic paper, Grundbegriffe de Wahrscheinlichkeitsrechnung, laid the axiomatic foundations for probability theory, providing the mathematical basis for the subject as it is developed today.