How to do CS Theory || @ CMU || Lecture 1b of CS Theory Toolkit
35:51Street Fighting Mathematics || @ CMU || Lecture 1c of TCS Toolkit
26:10Big O and friends || @ CMU || Lecture 2a of CS Theory Toolkit
28:10Harmonic Numbers Asymptotics || @ CMU || Lecture 2b of CS Theory Toolkit
22:18Asymptotics Tricks || @ CMU || Lecture 2c of CS Theory Toolkit
25:00The Central Binomial Coefficient || @ CMU || Recitation 1 of CS Theory Toolkit
1:00:26Birthday Paradox Asymptotics || @ CMU || Lecture 3a of CS Theory Toolkit
18:09Lecture 3b: Factorial Asymptotics, Stirling's Formula (15-750)
28:26Lecture 3c: Binomial Coefficients Asymptotics (15-750)
35:57Lecture 4a: Central Limit Theorem (15-750)
24:22Lecture 4b: Gaussian Random Variables (15-750)
38:31Lecture 4c: Berry --Esseen Theorem (15-750)
16:07Lecture 5a: Markov and Chebyshev Inequalities (15-750)
38:22Lecture 5b: Proof of the Chernoff Bound (15-750)
24:34Lecture 5c: Chernoff, Hoeffding, etc. bounds (15-750)
17:47Lecture 6a: Computational Models: Turing Machines (15-750)
25:31Lecture 6b: Computational Models: Circuits (15-750)
29:07Lecture 6c: The Word RAM Model (15-750)
25:30Lecture 4a: Central Limit Theorem (15-750)
This lecture provides a rigorous statement of the Central Limit Theorem, covering sums of independent random variables and standardization techniques.
Sums of independent random variables, refresher on properties of variance, standardizing random variables, and a statement of the Central Limit Theorem. Lecture 4a 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:
Feller's book, "Introduction to probability theory and its applications"
Lecture 3c: Binomial Coefficients Asymptotics (15-750)
Next · Lecture 11Lecture 4b: Gaussian Random Variables (15-750)