The course will cover the basics as well as some of
the state-of-the-art results in pseudoranodmness, explicit
constructions in combinatorics, and their applications. The main
goal is to introduce the many fascinating questions and ideas in
pseudorandomness and to cover versatile tools that are useful in
other areas such as discrete mathematics (e.g., expanders),
algorithms (e.g., hashing, streaming algorithms), and cryptography
(extractors, hardness vs randomness).
Hours & Location: MW 4-5:50, Bunche 2156. Office
hours: Monday 2:30 - 3:30, 3732 BH.
The following is a tentative list of topics to be covered.
Pseudorandomness: why, what,
and how? (3 lectures)
What is pseudorandomness?
Derandomization of concrete algorithms (2 lecture)
Derandomizing by pairwise independence
Limited independence: the
swiss-army knife (2 lectures)
Universal hashing, k-wise independence
Applications and constructions
Error correcting codes (2 lectures)
Expander graphs (3 lectures)
The many views of expansion
expanders: Expander samplers
construction of expanders
Interlacing polynomials (3
Ramanujan Graphs from interlacing
Extractors and Ramsey Graphs (3 lectures)
Expansion beating eigenvalue bounds
Extractors and their applications
Ramsey graphs and 2-source extractors
: Basic knowledge of probability will
be the most helpful. The students are expected to be mathematically mature
and be able to follow and write down formal proofs. Familiarity with
discrete mathematics, combinatorics, and undergraduate-level algorithms will be helpful.
: We will have three
assignments (15% each), one mid-term (25%), and one final (30%). The
grading will also be flexible: students can, if they choose to,
exchange an homework for more scribing duties or an approved
research project (that can also be counted towards the report) for the final exam.
Policy and required text
: There will be no makeup
exams for the course; the mid-term will be held in class. A
reference for several lectures is the book Pseudorandomness
by Salil Vadhan. Links to appropriate papers or other online material (typically other lecture notes) will be provided for each
: The students are expected to fully
abide by UCLA's student conduct policies
including Section 102.01 on academic honesty. You will find a wealth
of helpful materials here
including the Student
Guide to Academic Integrity
. Academic dishonesty will be promptly
reported to the Dean of Students' Office for adjudication and
disciplinary action. Remember, cheating will have significant and
irrevocable consequences for your academic record and professional
future. Please don't cheat.
While collaboration with other students on
assignments is fine, each student must write their solutions independently and
should clearly mention the collaborators. You should never share
your written solutions with someone else or copy from someone else's
written solutions. Under no circumstances may you use solution sets to
problems from previous year courses or from similar courses elsewhere
or other resoruces on the web.