Lectures related to Analysis IV: Convolution and Hilbert Structure

Covers the extension of functional calculus to simple functions and the concept of *-homomorphism.

Covers linear algebra concepts with a focus on functions and their properties.

Covers measurability, independence of sets, sigma-algebras, cylinder sets, co-algebras, uniqueness, and extension of measures.

Introduction to Analysis

Covers the basics of analysis, including proofs, sets, rational and real numbers, and the concept of infimum.

Sets and Functions

Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.