Continued fractions and their use for approximation to irrational numbers.
The determination of the nature and position of the quadric represented by the general equation of the second degree \[ (a, b, c, d, f, g, h, u, v, w \gamma x, y, z, 1)^2 = 0. \]
Give a proof of Cauchy's Theorem. Indicate some of its simplest applications (as for example in the theory of doubly periodic functions).
Fourier's Series.