APPM 7400 - Fall 2009: Foundations and Applications of Probability Theory

APPM 7400 - Section 006 - Foundations and Applications of Probability Theory
Department of Applied Mathematics

University of Colorado - Boulder

Fall 2009

Lecturer: Manuel Lladser
E-mail*: just like your CU e-mail but with my last name before the @
Office: ECOT 232
Lecture: MWF 10-10:50am @ ECCR 116
Lecturer's office hours: M 1-1:45pm ; T 9-9:45am ; W 4-4:45pm ; R 11-11:45am

*:Use as Subject the sentence APPM 7400/Fall 2009:, followed by 0-3 keywords describing the main content of the e-mail.
E-mails that do not follow the previous guideline will not be acknowledged!

Current Information:

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Course Schedule

DEC/17: Final grades have been submitted. The course is closed! Have a good break!
DEC/11: The answerkey for exam #3 is posted
DEC/08: Recall that today there will be additional office hours from 11:30am-12:30pm
DEC/07: The answerkey for quiz #3 is posted
OCT/28: The answerkey for exam #2 is posted
OCT/26: The answerkey for quiz #2 is posted
SEP/23: The answerkey for exam #1 is posted
SEP/21: The room for exam #1 will be ECCR 131
SEP/11: The answerkey for quiz #1 is posted
AUG/24: Welcome to class!
Please check this webpage often for updates

Course Information:

Description: The main purpose of this course is to expose you to a wide variety of topics in probability theory while leaving you with strong foundations in its measure theoretical aspects. Measure theory is a useful and powerful tool of real analysis that aims to make a precise yet general sense of the concept of integration. In this course, probability and measure theory will be developed in parallel as needed. More specifically, the course will include the following topics: 1. In terms of probability theory, we will discuss about independence of random variables, various types of convergence of random variables (weak, point-wise, convergence in distribution), the Law of Large Numbers, the Central Limit Theorem (one- and multi-dimensional), conditional probabilities and conditional expectations, martingales, Markov processes, and one-dimensional Brownian motion. 2. In terms of measure theory, we will see how the above topics fit in the context of sigma-algebras and measures, measurable functions, integrals with respect to a measure, convergence theorems for integrals, product spaces and product measures, and Radon-Nikodym derivatives.

By the end of this course you will have a much deeper understanding of probability theory and a wider scope of its applications in various fields. This course should be of particular interest to anyone (especially mathematicians and applied mathematicians, economists and engineers) who want or need to have more advanced understanding of contemporary probability or statistics.

Pre-requisites: (1) An understanding of probability theory at an introductory level (e.g. APPM 3570) or at the level of the textbook: A First Course in Probability Theory by S. Ross, and (2) an undergraduate real analysis course (e.g. MATH 4310).
Textbook: There will be no textbooks for this class. Lectures will be based in the following textbooks: Probability and Measure (P. Billingsley), Convergence in Measure and Distribution (P. Billingsley), Probability: Theory and Examples (R. Durrett), A Modern Approach to Probability Theory (B. Fristedt and L. Gray), A User’s Guide to Measure Theoretical Probability (D. Pollard), Probability with Martingales (D. Williams), and Probability Theory (S. R. S. Varadhan).
Blue books: Each student is responsible to bring an unused blue book at the beginning of each exam. Please do not write anything (including any personal information) in the bluebooks you bring because they will be randomly assigned right before each exam.

Homework/Quizzes/Exams: Weekly practice problems will be assigned during lecture. Homework will not be graded, however, it will help you have a better grasp of the material covered in lecture. There will be a total of 5 quizzes (on random dates), and 3 exams (see course schedule for dates and times). Quizzes will have a duration of 20 minutes and will only include material and homework discussed up to a week in advance. Unless very exceptional situations, no make-up quizzes or exams will be allowed. Furthermore, no early exams will be allowed.

Illness: If you become sick during an examination please bring a note from your doctor verifying your illness. Your doctor's note should clearly specify the time frame (start and ending date) during which you were unable to comply with your school obligations. Your course grade will then be determined by the rest of your course work.

Final grade policy: Each quiz is worth 20 points and each exam is worth 100 points. The two lowest quizzes will be replaced by the average quiz score. The lowest exam will be replaced by the average exam score. Approximate final grade lines will be based on a 10%-curve-letter grade system: A is guarantee with a 90% or better final grade, a B for those with 80% or better, a C with 70% or better, and a D with 60% or better. To pass this course you must obtain 50% or better of the final grade. Any adjustments to this scale will be in the students' favor.

Addendum to Syllabus:

Special Accomodations: If you qualify for accommodations because of a disability, please submit to me a letter from Disability Services in a timely manner so that your needs may be addressed. Disability Services (located in Willard 322, phone: 303-492-8671) determines accommodations based on documented disabilities. For more information please visit www.colorado.edu/disabilityservices.
Religious Observance: If you have a religious observance that may conflict with some of the course examinations, please let me know by writing or e-mail as soon as possible. An early notice of at least two weeks in advance is preferred to make the appropriate arrangements. Be aware that no accomodations will be addressed without having made them explicit in advance. Additional information can be found at www.colorado.edu/policies/fac_relig.html.
Envisioning/Promoting Diversity: The University of Colorado at Boulder is committed to build a campus community in which diversity is a fundamental value regardless of race, culture, religion, politics, sexual orientation, gender variance, and nationalities. If you would like to know more about the various resources available to minority students in campus or about the University of Colorado diversity policies, please visit www.Colorado.edu/cu-diversity for more information. Additional information can be found at www.colorado.edu/policies/classbehavior.html, www.colorado.edu/policies/discrimination.html, and at www.colorado.edu/studentaffairs/judicialaffairs/code.html#student_code. Any student, staff or faculty member who believes s/he has been the subject of discrimination or harassment based upon race, color, national origin, sex, age, disability, religion, sexual orientation, or veteran status should contact the Office of Discrimination and Harassment (phone: 303-492-2127) or the Office of Judicial Affairs (phone:303-492-5550). The referenced policies and the campus resources available to assist individuals regarding discrimination or harassment can be obtained at http://www.colorado.edu/odh
Academic Honesty: Students are encourage to work in groups and discuss problems with each other, however, all work turned in must be of your own. Violation of the CU Student Honor Code or the College of Engineering Academic Honesty Advising Guidelines will result in a final grade of F in this course. Please visit www.colorado.edu/academics/honorcode, www.colorado.edu/policies/honor.html and www.colorado.edu/engineering/ar_ugradadvising.html for more information.