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This is all preamble stuff that you don't have to worry about.
Head down to where it says "Start here"
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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.

Collection of statistics formulae taken from the perennial text book Lind, Douglas A. et. al. (2015): Statistical Techniques in Business and Economics, 16 ed. (2015).

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.