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
25:30Big O and friends
This lecture introduces the formal definitions and applications of Big O, Big Omega, Little O, and Little Omega notation, alongside related asymptotic forms such as poly() and O-tilde. It references foundational texts including 'Asymptopia' and 'Concrete Mathematics' for rigorous mathematical treatment.
Big O and friends -- big/little O, big/little Omega, poly, O-tilde, standard form functions. Lecture 2a 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.