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Probability, Primes & Computational Hardness →0/6
1

Introduction and Proofs

Tom Leighton · 44:09

2

Probability and Counting

Joe Blitzstein · 46:29

3

Story Proofs, Axioms of Probability

Joe Blitzstein · 45:40

4

Structure and Randomness in the Prime Numbers

Terence Tao · 47:51

5

Mathematics and Computation: The Landscape of P vs. NP

Avi Wigderson · 1:02:49

6

What Can the Theory of Cryptography Tell Us About AI Verification?

Shafi Goldwasser · 1:02:15

Story Proofs, Axioms of Probability

Joe BlitzsteinDistinguishedHarvard University

Professor of the Practice in Statistics

45:40·2013·undergraduate level
Path step 3: Replaces algebraic manipulation with intuitive story proofs and probabilistic axioms.

This lecture introduces combinatorial 'story proofs' as a method for establishing identities like Vandermonde's identity, emphasizing intuitive insight over algebraic manipulation. It then lays the foundational axioms of probability theory, including discussion of Bose-Einstein sampling.

MathematicsProbability & Information TheoryCombinatoricsProbability TheoryVandermonde's Identity

We fill in the "Bose-Einstein" entry of the sampling table, and discuss story proofs. For example, proving Vandermonde's identity with a story is easier and more insightful than going through a tedious algebraic derivation. We then introduce the axioms of probability.

Source: Harvard University via YouTubeWatch on YouTube
LecturerAll lecturers →
Joe BlitzsteinDistinguished

Author of Introduction to Probability · Harvard University

Joe Blitzstein is a Professor of the Practice in Statistics at Harvard University, renowned for his foundational textbook "Introduction to Probability" and popularizing probability theory.

1 course · 21 lecturesCanon
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Probability and Counting

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Structure and Randomness in the Prime Numbers

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