Superior Mathematics from an Elementary Point of View

Introduction
Creative Telescoping and DFT
Convolutions and ballot problems
Chebyshev and Legendre polynomials
The glory of Fourier, Laplace, Feynman and Frullani
The Basel problem
Special functions and special products
The Cauchy-Schwarz inequality and beyond
Remarkable results in Linear Algebra
The Fundamental Theorem of Algebra
Quantitative forms of the Weierstrass approximation Theorem
Elliptic integrals and the AGM
Bessel functions and the Gauss circle problem
The Gauss circle problem
Dilworth, Erdos-Szekeres, Brouwer and Borsuk-Ulam's Theorems
Continued fractions and elements of Diophantine Approximation
Symmetric functions and elements of Analytic Combinatorics
Spherical Trigonometry