The lecture notes are based on Tom Coates' lecture on toric varieties. A few references:
M. Audin, Toric actions on symplectic manifolds
W. Fulton, Toric varieties
Cox-Schenck-Little, Toric varieties

Discret Hartley Transform is a unitary transform although its proof is hard to find in the Web. This short note explains that the Discrete Hartley Transform is an involution, which implies that this transform is unitary indeed.

This problem is an applied optimization problem. The problem is to minimize
the area of the triangle formed by a tangent line to the function y = 1⁄9 x2.
The triangle is defined by the origin, the x-intercept of the tangent line, and the
y-intercept of the tangent line. Only triangles formed in the first quadrant are
of concern.

Based on a guest lecture at Instituto Superior Técnico (University of Lisbon), I use calculus and abstract algebra to derive the Fourier Tranform using the Fourier Series.