**Course: MATH 170A, Probability Theory, Lecture 1, Spring 2016**

**Prerequisite:** Math 32B and Math 33A. Not open to students with credit for Electrical Engineering 131A or Statistics 100A.

**Course Content:** Probability distributions, random variables and vectors, expectation.

*Last update:* 24 May 2016

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

**Office Hours:** Wednesdays 11AM-12PM, 1PM-2PM, Fridays, 11AM-12PM, MS
5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
9AM-950AM, Geology 4645

**TA:** Joe Hughes, jfhughes(@-symbol)math.ucla.edu

**TA Office Hours:** Mondays 1PM-2PM, Thursdays 1PM-2PM, MS 3957

**Discussion Session Meeting Time/Location:** Tuesday, 9AM-950AM
Geology 4645

**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:** Friday, April 22, 9AM-950AM, HUMANTS 135

**Second Midterm:** Monday, May 16, 9AM-950AM, Geology 3656

**Final Exam:** Tuesday, June 7, 3PM-6PM, Boelter 5249

**Other Resources:**
Supplemental Problems from the textbook.
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 Tuesday 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 | Mar 28: 1.1, Sets | Mar 29: Homework 0 (ungraded) | Mar 30: 1.2, Probabilistic Models | Apr 1: 1.2, Probabilistic Models | |

2 | Apr 4: 1.3, Conditional Probability | Apr 5: Homework 1 due | Apr 6: 1.3, Conditional Probability | Apr 8: 1.4, Total Probability Theorem and Bayes' Rule | |

3 | Apr 11: 1.5, Independence | Apr 12: Homework 2 due | Apr 13: 1.5, Independence | Apr 15: 1.6, Counting | |

4 | Apr 18: 2.1, Discrete Random Variables | Apr 19: Homework 3 due | Apr 20: 2.2, Probability Mass Function | Apr 22: Midterm #1 | |

5 | Apr 25: 2.3, Functions of Random Variables | Apr 26: Homework 4 due | Apr 27: 2.4, Expectation and Variance | Apr 29, 2.5, Joint PMFs, Covariance and Variance | |

6 | May 2: 2.6, Conditioning | May 3, Homework 5 due | May 4: 2.6, Conditioning | May 6: 2.7, Independence | |

7 | May 9, 2.7, Independence | May 10: Homework 6 due | May 11: 3.1, Continuous random variables and PDFs | May 13: 3.1, Continuous random variables and PDFs | |

8 | May 16: Midterm #2 | May 17: No homework due | May 18: 3.2, Cumulative Distribution Functions | May 20: 3.3, Normal Random Variables | |

9 | May 23: Joint PDFs of Multiple Random Variables | May 24: Homework 7 due | May 25: 3.5, Conditioning | May 27: 3.5, Conditioning | |

10 | May 30: No class | May 31: Homework 8 due | Jun 1: The Continuous Bayes Rule | Jun 3, 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.