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
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
Required Textbook: D. P. Bertsekas and John N. Tsitsiklis,
Introduction to Probability, 2nd edition. (The book is freely available
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
Supplemental Problems from the textbook.
introduction to mathematical
arguments, Michael Hutchings,
An Introduction to Proofs,
How to Write Mathematical Arguments
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
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.
- My email address for this course is heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from
, and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.
Here are the exams I used when I taught this course last quarter:
Exam 1 Solutions
Exam 2 Solutions.
Here is a
page containing old exams for another 170A class.
Here is a 170A practice midterm (with solutions).
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.
- 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
in at the beginning of the discussion section on the following
- 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
- 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|
||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
||Apr 11: 1.5, Independence
||Apr 12: Homework 2 due
||Apr 13: 1.5, Independence
||Apr 15: 1.6, Counting
||Apr 18: 2.1, Discrete Random Variables
||Apr 19: Homework 3 due
||Apr 20: 2.2, Probability Mass Function
||Apr 22: Midterm #1
||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
||May 2: 2.6, Conditioning
||May 3, Homework 5 due
||May 4: 2.6, Conditioning
||May 6: 2.7, Independence|
||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
||May 16: Midterm #2
||May 17: No homework due
||May 18: 3.2, Cumulative Distribution Functions
||May 20: 3.3, Normal Random Variables|
||May 23: Joint PDFs of Multiple Random Variables
||May 24: Homework 7 due
||May 25: 3.5, Conditioning
||May 27: 3.5, Conditioning|
||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.
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
Strategies, and come to office hours.