Things Fourier

For some reason several classes at MIT this year involve Fourier analysis. I was always confused about this as a high schooler, because no one ever gave me the ``orthonormal basis'' explanation, so here goes. As a bonus, I also prove a form of Arrow's Impossibility Theorem using binary Fourier analysis, and then talk about… Continue reading Things Fourier

18.099 Transcript: Bourgain’s Theorem

As part of the 18.099 Discrete Analysis reading group at MIT, I presented section 4.7 of Tao-Vu's Additive Combinatorics textbook. Here were the notes I used for the second half of my presentation. 1. Synopsis We aim to prove the following result. Theorem 1 (Bourgain) Assume \$latex {N \ge 2}&fg=000000\$ is prime and \$latex {A,… Continue reading 18.099 Transcript: Bourgain’s Theorem

18.099 Transcript: Chang’s Theorem

As part of the 18.099 discrete analysis reading group at MIT, I presented section 4.7 of Tao-Vu's Additive Combinatorics textbook. Here were the notes I used for the first part of my presentation. 1. Synopsis In the previous few lectures we've worked hard at developing the notion of characters, Bohr sets, spectrums. Today we put… Continue reading 18.099 Transcript: Chang’s Theorem