MATH 350: Probability

1. MATH 350: Probability Fall 2017 Syllabus & Class Policies

2. Course topics • Introduction to Probability; Discrete and Continuous Distributions; Simulations • Combinatorics • Conditional Probability • Basic distributions and Densities • Expected Value; Variance; Moments • Sums of Random Variables • Law of Large Numbers • Central Limit Theorem • Generating Functions • Introduction to Random Walks The tentative detailed syllabus of the course can be found at http://home.sandiego.edu/~pruski/m350f17schedule.html .

3. Tentative Detailed Schedule (part 1) 9/6 Introduction 9/8 Discrete Probability Distributions 9/11 Random Variables; Sample Spaces 9/13 Axioms of Probability; Uniform Distribution 9/15 Monte Carlo Procedures 9/18 Continuous Probability Densities 9/20 Density Functions of Continuous Random Variables 9/22 Cumulative Distribution Functions of Continuous RVs 9/25 Counting Problems 9/27 Permutations 9/29 Combinations 10/2 Bernoulli Trials; Binomial Distributions 10/4 Hypothesis Testing; Binomial Expansion 10/6 Discrete Conditional Probability 10/9 Independence; Joint Distributions; Bayes Formula 10/11 Continuous Conditional Probability 10/13 Joint Density and Cumulative Distribution Functions 10/16 Catch-Up Class 10/18 Midterm Exam 10/23 Discrete Distributions: Uniform, Geometric, etc. 10/25 Discrete Distributions: Poisson , Hypergeometric 10/27 Continuous Densities: Uniform, Exponential, Gamma 10/30 Functions of a Random Variable 11/1 Continuous Densities: Normal

4. Tentative Detailed Schedule (part 2) 11/3 Expected Value of a Random Variable 11/6 Expected Value of a Function of a Random Variable 11/8 Expected Value: Discrete and Continuous Random Variables 11/10 Variance 11/13 Variance: Discrete and Continuous Random Variables 11/15 Sums of Discrete Random Variables 11/17 Sums of Continuous Random Variables 11/20 Law of Large Numbers; Chebyshev Inequality 11/27 Law of Large Numbers: Continuous Variables 11/29 Central Limit Theorem for Binomial Distribution 12/1 Applications to Statistics 12/4 Central Limit Theorem for Discrete Independent Trials 12/6 Central Limit Theorem for Continuous Independent Trials 12/8 Generating Functions for Discrete Distributions 12/11 Generating Functions for Continuous Densities 12/13 Random Walks in Euclidean Space; Arc Sine Laws 12/15 Catch-Up Class 12/22 Final Exam (11 a.m.)

5. Course learning outcomes • Students will demonstrate a working knowledge of probability topics. This includes knowledge of theorems with complete assumptions. • Students will demonstrate the ability to use methods of probability theory and perform probability computations accurately and efficiently. • Students will demonstrate the ability to solve problems, including applications outside of mathematics. • Students will be able to construct simple proofs independently. • Students will demonstrate the ability to communicate mathematical ideas clearly.

6. Attendance; work; proofs • Regular attendance is really necessary. It is quite difficult to catch up with the material when you miss a class. It becomes virtually impossible, if you miss several classes. • A student is supposed to spend at least two hours at home for each class hour. Thus, you should expect spending at least 8 hours a week (more likely about 10 hours) doing your homework and preparing for quizzes/exams. • This is an upper-division mathematics course, so we will be doing quite some number of proofs. You will be expected to do some proofs in your homework assignments as well as during exams.

7. Textbook We will follow the textbook closely: C.M. Grinstead, J.L. Snell, Introduction to Probability, Second Revised Edition (Chapters 1 - 10, and the beginning of Chapter 12). The paperbound version of the text is available from the AMS bookshop, but the text "has now been made freely redistributable under the terms of the GNU Free Documentation License (FDL), as published by the Free Software Foundation. Briefly stated, the FDL permits you to do whatever you like with a work, as long as you don't prevent anyone else from doing what they like with it. This is the same license that is used for the Wikipedia." All details about how to download the text and the accompanying materials may be found at: http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html .

8. Office Hours and Contact Office hours (Dr. Lukasz Pruski, Serra 149, x. 4035): Monday 12:15 - 1:15 and 4:30 - 5:30 Wednesday 2:30 - 3:30 Thursday 3:30 - 4:30 Friday 2:30 - 3:30 and at other times, by appointment. Contact: The best way to contact me is by using e-mail (pruski@sandiego.edu). I read e-mail many times during the day and night, except for a few weekends when I am out of town. I have voice mail (x. 4035), but I sometimes forget to check it. You may call the Mathematics Department Executive Assistant, Tina, at x. 4706, as well.

9. Course Webpage and Assignments • A primitive webpage for the course is athttp://home.sandiego.edu/~pruski/m350f17.html . You should check the webpage daily for assignments, announcements, and links. • Homework Assignments will be assigned and collected roughly once a week. The assignments will be graded partly on effort. I will assign many odd-numbered exercises that have answers at the BOB (Back-Of-Book). The total homework assignment score will count for 25% of the course grade. No late assignments will be accepted unless you arrange it with me in advance.

10. Quizzes and Exams • There will be about 10 short pop-quizzes (not announced in advance). Quiz questions will refer to the recently covered material and to the new material you were supposed to read on your own. Three lowest quiz scores will be dropped, and the remaining scores will count for 25% of the course grade. Quizzes cannot be made up unless you have a valid reason for not taking the quiz and you notify me in advance of your absence. • The midterm exam (of closed-book variety) will take place on Wednesday, October 18, and its score will count for 20% of the course grade. A test can be made up only if you have an actual emergency and if you notify me in advance about your absence. • The final exam (Friday, December 22, 11:00 - 1:30) will be cumulative and its score will count for 30% of the course grade. The exam is also closed-book  • Calculator policy: No calculators, smart phones, iPods, tablets, etc. are allowed.

11. Grading Criteria Grading criteria are as follows: TotalPercentage Grade 90% and above A 80% - 90% B 60% - 80% C 50% - 60% D below 50% F Of course, pluses and minuses will be used, close to cutoff boundaries. In the unlikely case that the number of A's and B's falls below 40%, I will curve the grades up appropriately.

12. Academic Integrity The University of San Diego has clearly articulated its policies governing academic integrity and students are encouraged to carefully review the policy. Any deviation from these expectations will result in academic penalties as well as disciplinary actions. The area of greatest potential risk for inadvertent academic dishonesty is plagiarism. Students should also read closely the discussion of avoiding plagiarism that is included in USD’s academic integrity policy.

13. Academic Accommodations Any student with a documented disability needing academic adjustments or accommodations is requested to speak with me during the first two weeks of class. All discussions will remain confidential. A student attempting to access an academic accommodation for the first time should begin by contacting the Disability and Learning Difference Resource Center (DLDRC) in Serra Hall, Room 300 (619­-260­-4655). It is the student’s responsibility to schedule an “intake” meeting with the Director as soon as possible.