Probabilistically Checkable Proofs and Boolean Analysis

Theoretical computer science relies heavily on proof verification and hardness of approximation, with the Probabilistically Checkable Proofs (PCP) theorem at its core. This course provides a structured introduction to the mathematics behind efficient proof verification, Fourier analysis of Boolean functions, and property testing. Through clear written modules, you will explore how proofs can be verified by reading only a tiny fraction of bits, bridging complexity theory and modern cryptography. What you'll learn: - Understand the core concepts of probabilistically checkable proofs and verification systems - Explore the exponential PCP theorem and its complexity implications - Master Fourier analysis fundamentals for Boolean functions - Analyze property testing algorithms, including the linearity testing framework - Examine error bounds, sound verification, and hardness of approximation principles - Apply analytical techniques to modern theoretical computer science problems The course begins with foundational definitions and complexity classes before building up to rigorous proofs and analytical techniques. It is designed for learners with an interest in theoretical computer science and discrete mathematics looking for a clear, accessible guide to probabilistic verification. Start reading today to deepen your understanding of modern complexity theory.