# Math 4510: Introduction to Probability Theory

 Instructor: Sean O'Rourke Office: Math 325 Office Hours: W: 3:00 pm - 4:00 pm, F: 1:00 pm - 2:00 pm, and by appointment. E-mail: Lectures: MWF: 2:00 pm - 2:50 pm in STAD 140 Webpage: http://math.colorado.edu/~seor3821/teaching/4510.17f/

## Text

We will be using A First Course in Probability (9th Edition) by S. Ross. In addition, you may find Janko Gravner's lecture notes helpful; these notes were created for a similar course taught at UC Davis.

## Course Description

In this course, we will study axioms, combinatorial analysis, independence and conditional probability, discrete and absolutely continuous distributions, expectation and distribution of functions of random variables, laws of large numbers, central limit theorems, and simple Markov chains. This is more or less the first 8 chapters of the text.

• Homework: 25%
• Midterm 1 (Oct. 6): 20%
• Midterm 2 (Nov. 15): 20%
• Final exam: 35%

## Homework

Every week you will have a written homework assignment, which will give you an opportunity to use the concepts, definitions, theorems and techniques we have learned. These will be posted on the course website. Late homework will not be accepted.

Homework should be legible, have your name on it, and be stapled in order to ensure that you get credit. A goal of this course is for you to improve your ability to write clear, precise mathematical arguments; the homework (and the exams) will be graded accordingly.

I encourage you to discuss the homework problems with your classmates, tutors, or me (or any other resources you find helpful). However, the Honor Code requires that the solution you turn in must be in your own words and reflect your own understanding.

## Homework Assignments

• Homework #1 (due 9/8):
• Chapter 1 problems: 1, 3, 5, 8, 10, 14, 18, 21, 22, 26
• Chapter 1 theoretical problems: 4, 11, 12(a)
• Homework #2 (due 9/15):
• Chapter 1 problems: 31, 33
• Chapter 1 theoretical problems: 21
• Chapter 2 problems: 1, 2, 3, 5, 6, 8
• Chapter 2 theoretical problems: 7
• Homework #3 (due 9/22):
• Chapter 2 problems: 12, 15, 18, 19, 23, 28, 32, 35, 36, 41, 47
• Chapter 2 theoretical problems: 13
• Homework #4 (due 9/29):
• Chapter 3 problems: 1, 8, 10, 17, 20, 23, 28, 33, 35, 44
• Chapter 3 theoretical problems: 2, 5
• Homework #5 (due 10/6):
• Chapter 3 problems: 53, 58(a), 62, 67, 91
• Chapter 4 problems: 2, 5
• Homework #6 (due 10/20):
• Chapter 4 problems: 13, 17, 19, 21, 25, 35, 37, 38, 40, 41, 57
• Chapter 4 theoretical problems: 7, 8
• Homework #7 (due 10/27):
• Chapter 4 problems: 60, 71, 75, 78, 83
• Chapter 4 theoretical problems: 27, 29
• Chapter 5 problems: 1, 3, 6, 8
• Homework #8 (due 11/10):
• Chapter 5 problems: 10, 11, 14, 15, 18, 19, 24, 26, 27, 32, 33, 38
• Chapter 5 theoretical problems: 5, 7, 9
• Homework #9 (due 12/1):
• Chapter 5 problems: 37, 39, 40
• Chapter 5 theoretical problems: 15, 31
• Chapter 6 problems: 1, 2, 3, 4
• Homework #10 (due 12/8):
• Chapter 6 problems: 7, 8, 15, 20, 22, 23, 26, 27
• Chapter 6 theoretical problems: 5, 6
• Homework #11 (this homework will not be turned in for credit):
• Chapter 7 problems: 1, 4, 6, 16, 33, 38, 40
• Chapter 7 theoretical problems: 19, 41

## Course policies

### Student classroom and course-related behavior

Students and faculty each have responsibility for maintaining an appropriate learning environment. Those who fail to adhere to such behavioral standards may be subject to discipline. Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Class rosters are provided to the instructor with the student's legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records. For more information, see the policies on classroom behavior and the Student Code of Conduct.

### Students with disabilities

If you qualify for accommodations because of a disability, please submit your accommodation letter from Disability Services to your faculty member in a timely manner so that your needs can be addressed. Disability Services determines accommodations based on documented disabilities in the academic environment. Information on requesting accommodations is located on the Disability Services website (www.colorado.edu/disabilityservices/students). Contact Disability Services at 303-492-8671 or dsinfo@colorado.edu for further assistance. If you have a temporary medical condition or injury, see Temporary Medical Conditions under the Students tab on the Disability Services website and discuss your needs with your professor.

### Religious obligations

Campus policy regarding religious observances requires that faculty make every effort to deal reasonably and fairly with all students who, because of religious obligations, have conflicts with scheduled exams, assignments or required attendance.

If a religious observance conflicts with a scheduled exam or other course activity, please let me know during the first two weeks of the semester so that we can make alternate arrangements.

### Statement on discrimination and harassment

The University of Colorado Boulder (CU Boulder) is committed to maintaining a positive learning, working, and living environment. CU Boulder will not tolerate acts of sexual misconduct, discrimination, harassment or related retaliation against or by any employee or student. CU's Sexual Misconduct Policy prohibits sexual assault, sexual exploitation, sexual harassment, intimate partner abuse (dating or domestic violence), stalking or related retaliation. CU Boulder's Discrimination and Harassment Policy prohibits discrimination, harassment or related retaliation based on race, color, national origin, sex, pregnancy, age, disability, creed, religion, sexual orientation, gender identity, gender expression, veteran status, political affiliation or political philosophy. Individuals who believe they have been subject to misconduct under either policy should contact the Office of Institutional Equity and Compliance (OIEC) at 303-492-2127. Information about the OIEC, the above referenced policies, and the campus resources available to assist individuals regarding sexual misconduct, discrimination, harassment or related retaliation can be found at the OIEC website.