**Course: MATH 170B, Probability Theory II, Winter 2017**

**Prerequisite:** Math 170A.

**Course Content:** Convergence of random variables, laws of large numbers,
central limit theorem, Bernoulli process, Poisson process.

*Last update:* 21 March 2017

**Instructor:** Steven Heilman, heilman(@-symbol)ucla.edu

**Office Hours:** Fridays 830AM-930AM, Mondays 10AM-11AM, MS 5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
1PM-150PM, Geology 6704

**TA:** Yunfeng Zhang, zyf(@-symbol)math.ucla.edu

**TA Office Hours:** Mondays 3PM-4PM, Wednesdays 4PM-5PM, MS 3955

**Discussion Session Meeting Time/Location:** Thursdays, 1PM-150PM,
MS 5118

**Required Textbook:**
D. P. Bertsekas and John N. Tsitsiklis,
Introduction to Probability, 2nd edition.
(The book is freely available
online
, **though some sections are ordered differently than the textbook**.)

**Other Textbooks (not required):**
Elementary Probability for Applications, Durrett.
(or a more advanced text for someone who has at least taken 115a and 131a:)
Probability: Theory and Examples, Durrett.

**First Midterm:** Monday, January 30, 1PM-150PM, Public Affairs
1246

**Second Midterm:** Friday, February 24, 1PM-150PM, Boelter 2444

**Final Exam:** Tuesday, March 21, 3PM-6PM, Geology 3656

**Other Resources:**
An
introduction to mathematical
arguments, Michael Hutchings,
An Introduction to Proofs,
How to Write Mathematical Arguments

**Email Policy:**

- My email address for this course is heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.

- Late homework is not accepted.
- If you still want to turn in late homework, then the number of minutes late, divided by ten, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
- The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 8 homework assignments, assigned weekly on Thursday and
turned
in at the
**beginning**of the discussion section on the following Tuesday. - A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
- You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
- All homework assignments must be
**written by you**, i.e. you cannot copy someone else's solution verbatim. - Homework solutions will be posted on Friday after the homework is turned in.

- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
- We will use the MyUCLA gradebook.
- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.

** Tentative Schedule**: (This schedule may change slightly during the course.)

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Jan 9: Introduction | Jan 11: Review of Probability | Jan 12: Homework 0 (ungraded) | Jan 13: 4.1, Derived Distributions | |

2 | Jan 16: No class | Jan 18: 4.2, Covariance | Jan 19: Homework 1 due | Jan 20: 4.3, Conditional Expectation | |

3 | Jan 23: 4.3, Conditional Variance | Jan 25: 4.4, Moment Generating Function | Jan 26: Homework 2 due | Jan 27: 4.4, Fourier Transform | |

4 | Jan 30: Midterm #1 | Feb 1: 4.2, Convolution | Feb 2: Homework 3 due | Feb 3: 4.4, Random Sums of Random Variables | |

5 | Feb 6: 7.1, Markov and Chebyshev Inequalities | Feb 8: 7.2, Weak Law of Large Numbers | Feb 9: Homework 4 due | Feb 10: 7.3, Convergence in Probability | |

6 | Feb 13: 7.4, Central Limit Theorem | Feb 15: 7.4, Central Limit Theorem | Feb 16: Homework 5 due | Feb 17: 7.5, Strong Law of Large Numbers | |

7 | Feb 20: No class | Feb 22: 7.5, Strong Law of Large Numbers | Feb 23: No homework due | Feb 24: Midterm #2 | |

8 | Feb 27: 7.5, Strong Law of Large Numbers | Mar 1: 5.1, Bernoulli Process | Mar 2: Homework 6 due | Mar 3: 5.1, Bernoulli Process | |

9 | Mar 6: 5.1, Bernoulli Process | Mar 8: 5.2, Poisson Process | Mar 9: Homework 7 due | Mar 10: 5.2, Poisson Process | |

10 | Mar 13: 5.2, Poisson Process | Mar 15: Leeway | Mar 16: Homework 8 due | Mar 17: Review of course |

**Advice on succeeding in a math class:**

- Review the relevant course material
**before**you come to lecture. Consider reviewing course material a week or two before the semester starts. - When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the
lecture. Also, finish your homework at
least
**two days**before it is due, to alleviate deadline stress. - Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.