Math 5310 Probability

FALL 2016

Department of Mathematical and Statistical Sciences

University of Colorado Denver

Instructor: Burt SimonCourse dates/times: MW 3:30-4:45

Office: AB1 4209Course location: King Center 205

Office Hours: MW 10:00-12:00 or by apt.Text: Introduction to Probability

Phone: 303 315 1710 by Bertsekas and Tsitsiklis

Website:

Email:

Welcome! Probability is a fascinating and very useful mathematical theory. Math 5310 is a standard introduction to probability theory, with additional material on elementary stochastic processes. By successfully completing this course you will be ready to take courses in mathematical statistics, probabilistic modeling, stochastic processes, financial engineering, actuarial science, and various engineering fields. Please check the class web page regularly, which can be linked to from my page at math.ucdenver.edu/~bsimon. The class web page will have the weekly assignments, announcements, exam solutions, etc. I encourage students to participate in class by asking questions and answering (rhetorical) questions that I ask during class.

Course Overview: The course covers axioms of probability, combinatorial probability, conditional probability, random variables (discrete, continuous, and multivariate), Expected value (mean, moments, variance, covariance, etc.), limit theorems (laws of large numbers, Central Limit Theorem), Poisson processes and Markov chains.

Course Goals and Learning Objectives:

  1. Overall Learning Objectives: By successfully completing this course, students will be familiar with all the basic concepts of probability theory listed in the Course Overview, and will understand how they tie together. Students will be able to calculate probabilities, expected values, etc., and understand how probability applies to problems in science and engineering.
  2. Learning Outcomes:
  • Problem Solving: Students will learn to solve problems involving uncertainty that are posed as generic probability calculations, and as real-world applications of probability theory.
  • Creative Thinking: Students will learn to distill a probability problem from a description where it may not be obvious how probability theory applies
  • Critical Thinking: It is easy to misapply probability theory, so students will learn to apply the theory correctly.
  1. Major Topics: axioms of probability, combinatorial probability, conditional probability, random variables (discrete, continuous, and multivariate), Expected value (mean, moments, variance, covariance, etc.), limit theorems (laws of large numbers, Central Limit Theorem), Poisson process, Markov chains.
  2. Rationale: Probability is required as a prerequisite for many upper division math courses, like statistics, probabilistic modeling, stochastic processes; and is useful in business, engineering, and other technical fields.

Course Prerequisites: Math 2421 (calc. II)

Course Credits: 3 credit hours

Required Texts and Materials: Introduction to Probability 2nd ed., Bertsekas and Tsitsiklis

Assignments: I will assign homework problems (approximately) weekly. Typically the assignment will be posted on the class web page on Monday, and will be due the following Monday. The purpose of the homework each week is to practice the material covered in class that week. Working collectively on the homework assignments is encouraged!

Homework sets will be discussed in class the day they are due. There will (often) be a quiz based on the homework problems after the discussion.

Basis for Final Grade: Your final grade will be based on your quiz scores, 2 midterm exam scores, and final exam score (approximately 1/3 each). Intangibles, such as class participation, can increase your grade.

Grade Dissemination: I will try to grade quizzes and exams before the next class. If you sense a mistake in my grading, please send me an email, or come to my office hours to discuss.

Course Policies

  1. Attendance: I will not take attendance, but students are expected to attend every class. You will be responsible for material I cover in class, whether or not it is in the textbook. Class participation is one of the important “intangibles” that can impact your grade.
  2. Try to give me as much lead time as possible if you know something will force you to miss a quiz or midterm. There is no way to reschedule the final exam.
  3. Extra Credit Policy: There is no “extra credit” in general, but students can try to raise their grades by being attentive (and participating constructively) in class, and demonstrating competence in my office hours.
  4. Grades of “Incomplete”: I must follow university procedures on “incompletes”, i.e., they are only given in situations where unexpected emergencies prevent students from completing the course and the remaining work can be easily finished the following semester. Incomplete work must be finished the next semester or the grade automatically turns into an F.
  5. Group Work Policy: Students are encouraged to collaborate on homework sets. Of course, no collaboration is allowed on quizzes and exams, as that is considered cheating.
  6. Announcements: I will use the class web page for all communication that is meant for the whole class. Please check the page regularly. Private communication is best done by email. I will typically respond within a day.
  7. Laptops, Cell Phones, etc.: You are free to use your devices as you see fit during class. (No disruptive phone calls or texting, of course.) The rules during exams will be announced prior to the tests. Usually my exams are open-book, open-notes, and electronic devices (calculators, computers, etc.) are allowed for certain things.
  8. Civility: Students are expected to be quiet and attentive during class, although raising your hand to ask a question or make a comment is welcomed and encouraged.
  • Dishonesty: Students are expected to understand intuitively what proper ethical conduct means in the context of a college mathematics course. If you are caught cheating you could fail the class or (at least) have your grade lowered, so don’t even try it.

Tentative Course Schedule

Class datesMaterial Covered Description

August 22, 24Sections 1.1 – 1.3Foundations

August 29, 31Sections 1.4 - 1.6Foundations, Combinatorics

Sept 7Sections 2.1 – 2.3Discrete rv’s

September 12, 14Sections 2.4 – 2.7Discrete rv’s

September 19, 21Sections 3.1 – 3.4General rv’s

September 26, 28Review and Midterm#1Exam on 9/28

October 3, 5 Sections 3.5 – 3.6Conditioning

October 10, 12Sections 4.1 – 4.3Covariance

October 17, 19Sections 4.4 - 4.5Sums of rv’s

October 24, 26Review and Midterm#2Exam on 10/26

Oct 31, Nov 2Sections 5.1 – 5.5Limit theorems

November 7, 9Sections 6.1 – 6.2Poisson process

November 14, 16Sections 7.1 – 7.3 Markov chains

November 21 - 25Fall Break

November 28, 30Sections 7.4 – 7.5Markov chains

December 5, 7Catch up and Review

December 12 or 14Final Exam (date of exam to be announced)