You can download the book chapters corresponding to the lectures below,
which are handed out in class.
Here is a copy of volume
(Updated!
4/30) Here is a copy of part of volume II (Chapter 5, 6
and 7).
We will continue to update the draft as we make corrections.
Lecture # |
Date |
Title |
Download |
Lecture 1 |
Jan 29 |
Introduction (Course overview) |
|
Chapter
2. The Power of Randomness |
|||
Lecture 2 |
Feb 3 |
Randomized Algorithms and Complexity
Classes |
Sec. 2.1-2.2 |
Lecture 3 |
Feb 5 |
Continue on Complexity Classes,
Error Reduction, Sampling and Approximation Problems |
Sec. 2.3.1-2.3.2 |
Lecture 4 |
Feb 10 |
Approx #DNF, MAX-CUT, S-T
Connectivity |
Sec. 2.3.3-2.4.1 |
Lecture 5 |
Feb 12 |
Random Walk, Markov Chain Monte
Carlo, Start of Basic Derandomization
Techniques |
Sec. 2.4-3.2 |
Chapter
3. Basic Derandomization Techniques |
|||
Lecture 6 |
Feb 17 |
Basic Derandomization Techniques |
Sec. 3.2-3.5 |
Lecture 7 |
Feb 19 |
Pairwise and k-wise |
Sec. 3.5 |
Chapter
4. Expander Graphs |
|||
Lecture 8 |
Feb 26 |
Definition, Measures of Expansion,
Existence of Expanders |
Sec. 4.1 |
Lecture 9 |
Mar 10 |
Random Walks on Expanders |
Sec. 4.2 |
Lecture 10 |
Mar 12 |
Explicit Constructions via Graph
Operations |
Sec. 4.3 |
Lecture 11 |
Mar 17 |
USTCONN in L and start Randomness
Extractors |
Sec. 4.4 ¡V 5.1 |
Chapter
5. Randomness Extractors |
|||
Lecture 12 |
Mar 19 |
Seeded Extractors, Connections with
Hash Functions and Expanders |
Sec. 5.1-2 |
Lecture 13 |
Mar 31 |
Block Source, Reducing General
Source to Block Source, Lossless Condenser and
Expander |
Sec. 5.2, 5.4.1 |
Lecture 14 |
Apr 2 |
Extractor Construction and start
Error-Correction Code |
Sec. 5.3, 6.1 |
Chapter
6. List-Decodable Codes |
|||
Lecture 15 |
Apr 7 |
Existential Bounds and Explicit
Codes |
Sec. 6.1 |
Lecture 16 |
Apr 9 |
List-Decoding Algorithms ¡V
Reed-Solomon Codes and Parvaresh-Vardy Codes |
Sec. 6.2.1-4 |
Lecture 17 |
Apr 14 |
List-decoding Views of Expanders and
Extractors |
Sec. 6.2.5 |
Chapter
7. Pseudorandom Generators |
|||
Lecture 18 |
Apr 16 |
Definition and Survey of
Cryptographic PRGs |
Sec. 7.1-2 |