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
25:30Markov and Chebyshev Inequalities
This lecture details Markov's and Chebyshev's Inequalities, or the First and Second Moment Methods, for bounding tail probabilities given only means or variances.
Markov's Inequality and Chebyshev's Inequality --- aka, the First Moment Method and the Second Method Method. How to bound the probability of a random variable being far from its mean when you only know its mean, or only know its mean and variance. Lecture 5a 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.
Resources for this lecture:
Chapter 2, "Basic tail and concentration bounds" of Wainwright's book "High dimensional statistics"