1. Boolean functions and the Fourier expansion🔗

Boolean functions on the discrete cube, multilinear representations, the parity basis, Fourier identities, probability densities, convolution, and the BLR test.

1. 1.1. On analysis of Boolean functions
2. 1.2. The “Fourier expansion”: functions as multilinear polynomials
3. 1.3. The orthonormal basis of parity functions
4. 1.4. Basic Fourier formulas
5. 1.5. Probability densities and convolution
6. 1.6. Highlight: Almost linear functions and the BLR Test