Probability Theory, Lecture 1, Spring 2016

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.

Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the UCLA Student Guide to Academic Integrity. If you are an OSD student, I would encourage you to discuss with me ways that I can improve your learning experience; I would also encourage you to contact the OSD office to confirm your exam arrangements at the beginning of the quarter.
Exam Resources: Here are the exams I used when I taught this course last quarter: Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions. Final Final Solutions. Here is a page containing old exams for another 170A class. Here is a 170A practice midterm (with solutions). Here is a 170A practice second midterm. Here is a 170A practice final. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close if not identical.

Homework Policy:

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.

Grading Policy:

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.

Homework

HW0 HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 (Solutions posted on CCLE)

Exam Solutions

Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions

Supplementary Notes

Math 170A Lecture Notes