| Lect # |
Date |
Topics |
Reading |
| 1 |
8/28 |
Introduction; basics of probability; polynomial verification |
MU 1.1, 1.2 |
| 2 |
9/2 |
Verifying matrix multiplications; Karger's algorithm |
MU 1.3, 1.4 |
| 3 |
9/4 |
Random variables and expectation; convex function; Jensen's inequality |
MU 2.1 |
| 4 |
9/9 |
Binomial and geometric distributions; coupon collector's
problem; quicksort |
MU 2.2, 2.4, 2.5 |
| 5 |
9/11 |
Conditional expectation; Markov's inequality; variance and moments |
MU 2.3, 3.1, 3.2 |
| 6 |
9/16 |
Chebyshev's inequality; sampling; randomized algorithm
for median finding |
MU 3.3, 3.4 |
| 7 |
9/18 |
Randomized median finding (continued), generating functions |
MU 3.4, 4.1 |
| 8 |
9/23 |
Chernoff bounds; set balancing; Poisson trials |
MU 4.2 - 4.4 |
| 9 |
9/25 |
Chernoff bounds (continued); randomized routing |
MU 4.2, 4.5 |
| 10 |
9/30 |
Randomized routing; wrapped butterfly network |
MU 4.5 |
| 11 |
10/2 |
Balls into bins; Poisson distribution and rare events |
MU 5.1 - 5.3 |
| 12 |
10/7 |
Midterm 1 (will cover Chapters 1-4) |
|
| 13 |
10/9 |
Poisson approximation for balls and bins; maximum load |
MU 5.4 |
| 14 |
10/14 |
Hashing; Bloom filters |
MU 5.5 |
| 15 |
10/16 |
Random graphs; connectivity |
MU 5.6 |
| 16 |
10/21 |
Probabilistic method; method of conditional expectations |
MU 6.1 - 6.3 |
| 17 |
10/23 |
More on the probabilistic method; thresholds in random
graphs; conditional expectation inequality |
MU 6.4 - 6.6 |
| 18 |
10/28 |
Markov chains; hitting times; randomized 2-SAT algorithm |
MU 7.1 |
| 19 |
10/30 |
The ruin problem; classification of states
| MU 7.2 |
| 20 |
11/4 |
Classification of chains; stationary distributions;
fundamental theorem |
MU 7.3 |
| 21 |
11/6 |
Reversibility; random walks on undirected graphs; cover time |
MU 7.3, 7.4 |
| 22 |
11/13 |
Midterm 2 (will cover up to Chapter 7) |
|
| 23 |
11/18 |
Introduction to Monte Carlo methods; FPRAS; FPAUS |
MU 10.1, 10.3 |
| 24 |
11/20 |
Markov chain Monte Carlo; Metropolis algorithm |
MU 10.3, 10.4 |
| 25 |
11/25 |
Mixing time; coupling; card shuffling |
MU 11.1, 11.2 |
| 26 |
12/2 |
Fingerprinting, pattern matching |
|
| 27 |
12/4 |
Fermat's primality test |
| 28 |
12/9 |
Miller and Rabin's primality test; Review |
|
|
12/18 |
Final Exam (3 Evans Hall, 12:30pm-3:30pm) |
|