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Editorial path·Theory & Algos·undergraduate·5 institutions

Probability, Primes & Computational Hardness

Discrete proof invariants, stochastic conditioning, pseudorandomness, and P vs. NP

Unites MIT discrete mathematics, Harvard STAT 110 probability, Terence Tao on structure vs. randomness in the primes, and IAS/Simons complexity theory.

Start Step 16 steps · 5h total
Introduction and Proofs (MIT 6.042J, Lecture 1)
Step 1 of 6

Curriculum sequence

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Step 1·MIT·Tom Leighton·6.042J· 44:09

Introduction and Proofs (MIT 6.042J, Lecture 1)

Establishes mathematical proof structure, predicates, and axiomatic deduction for CS.

Step 2·Harvard University·Joe Blitzstein·STAT 110· 46:29

Lecture 1: Probability and Counting | Statistics 110

Builds sample spaces and combinatorial symmetry from first principles.

Step 3·Harvard University·Joe Blitzstein·STAT 110· 45:40

Lecture 2: Story Proofs, Axioms of Probability | Statistics 110

Replaces algebraic manipulation with intuitive story proofs and probabilistic axioms.

Step 4·UCLA·Terence Tao· 47:51

Structure and Randomness in the Prime Numbers

Reveals how structured harmonics and pseudorandomness coexist inside the prime numbers.

Step 5·Institute for Advanced Study·Avi Wigderson· 1:02:49

Mathematics and Computation: The Landscape of P vs. NP

Maps efficient verification, NP-completeness, and hardness-versus-randomness dualities.

Step 6·Simons Institute (UC Berkeley)·Shafi Goldwasser· 1:02:15

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

Extends interactive cryptographic proof systems to trustworthy machine learning.