Lectures related to Peierls argument

Covers Coppersmith's method for attacking RSA encryption by efficiently finding small roots of polynomials modulo N.

Covers the proof of the convergence rate theorem, emphasizing the correction of a missing factor sqrt{pi_j} in the proof.

Explores the proof of the Prime Number Theorem and its implications in number theory.

Explores differentiating under the integral sign and continuity of functions in integrals.

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.