Link to lectures Instructor: Prof. Jonathan Katz Book: “Introduction to Modern Cryptography” by Katz and Lindell ROUGH NOTES (!) Updated: 5/3/24 Week-1: Classical Cryptography focuses exclusively on ensuring secret communication between ${ 2 }$ parties sharing secret information in advance (That is, the focus is on private-key encryption s... Read more 16 Feb 2024 - 49 minute read
Link to Lectures Instructor: Prof. Michael Sipser Book: “Introduction to the Theory of Computation” by Michael Sipser ROUGH NOTES (!) Updated: 8/2/24 Lec-1: Computability Theory (1930s - 50s): What is computable or not ? Eg: Program verification, Pure mathematical truth Models of computation: Finite automata, Turing machines Complex... Read more 04 Feb 2024 - 27 minute read
Thm: Let ${ X }$ be a set with ${ \sigma -}$algebra ${ \mathfrak{M} }.$ Let ${ f : X \to [0, \infty] }$ be a measurable map. Then there exist simple measurable maps ${ 0 \leq s _1 \leq s _2 \leq \ldots (\leq f) }$ with pointwise limit ${ \lim _{n \to \infty} s _n (x) = f(x) }$ for all ${ x \in X }.$ Pf: We can try forming a sequence ${ \varphi... Read more 12 Dec 2023 - 1 minute read
Some old handwritten notes from Vinberg’s “Course in Algebra”: https://drive.google.com/file/d/11NX5FD3atPIR7HxcUqrColuBaKoC89xH/view?usp=sharing (App: Drawboard on Surface Pro) Read more 17 Oct 2023 - less than 1 minute read
Ref: Prof. Vershynin’s handwritten notes Lec-1: Consider the problem of numerically computing the integral of an ${ f : [0,1] ^d \to \mathbb{R} }.$ Breaking ${ [0,1] ^d }$ into (axis aligned) cubes of width ${ \epsilon },$ there are about ${ N \approx (\frac{1}{\epsilon}) ^{d} }$ many such smaller cubes. Now the integral ${ \int _{[0,1] ^d} f... Read more 07 Oct 2023 - 23 minute read