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
25:30Harmonic Numbers Asymptotics
This lecture from CMU's graduate CS Theory Toolkit rigorously derives the asymptotic behavior of the nth harmonic number H_n, employing both elementary series manipulation and the integral approximation method. It references seminal texts in discrete mathematics and asymptotic analysis.
Working out the asymptotics of the nth harmonic number H_n, first with naive methods, and then with the integral method. Lecture 2b 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.