Lectures related to Degree of a field extension

Delves into the construction and optimality of the E8 lattice as the densest sphere packing in dimension eight.

Explains linear independence, basis, and matrix rank with examples and exercises.

Green's Theorem: Boundary and Normal Vectors

Explores boundaries, normal vectors, and Green's theorem application in transforming integrals.

3-dimensional Anosov flows: U(1)-extension and Exponential Mixing

Explores the U(1)-extension of Anosov diffeomorphisms and the proof of exponential mixing through uniform contractivity and cancellation by complex phases.

Differentiability and Limits

Explores differentiability, limits, and open sets in multivariable functions, with a focus on local minimums and continuity.