Lectures related to Nonlinear Dynamics: Chaos and Complex Systems

Covers the Lebesgue integration of simple functions and the approximation of nonnegative functions from below using piecewise constant functions.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Covers selected topics in mathematics, including Taylor approximations and algebraic structures of Z and K[X].

Covers the properties of the Lebesgue measure and its existence.

Explores the fundamental concepts of real numbers, including sets, operations, and properties like supremum and infimum.