How to do CS Theory
35:51Street Fighting Mathematics
26:10Big O and friends
28:10Harmonic Numbers Asymptotics
22:18Asymptotics Tricks
25:00The Central Binomial Coefficient
1:00:26Birthday Paradox Asymptotics
18:09Factorial Asymptotics, Stirling's Formula
28:26Binomial Coefficients Asymptotics
35:57Central Limit Theorem
24:22Gaussian Random Variables
38:31Berry–Esseen Theorem
16:07Markov and Chebyshev Inequalities
38:22Proof of the Chernoff Bound
24:34Chernoff, Hoeffding, etc. bounds
17:47Computational Models: Turing Machines
25:31Computational Models: Circuits
29:07The Word RAM Model
25:30Proof of the Chernoff Bound
This lecture delivers a proof of Chernoff's Bound for large deviations, focusing on the simple case of sums of independent fair coin flips.
From the Fourth Moment Method to the Sixth Moment Method to... Chernoff's Bound on large deviations. A proof in the simplest case of sums of independent fair coin flips. Lecture 5b of "CS Theory Toolkit": a semester-long graduate course on math and CS fundamentals for research in theoretical computer science, taught at Carnegie Mellon University.
Markov and Chebyshev Inequalities
Next · Lecture 15Chernoff, Hoeffding, etc. bounds