Lectures related to The Pigeonhole Principle: Basics and Applications

Introduces categories as collections of objects with morphisms and identity morphisms.

Covers functions, including even and odd functions, periodicity, and function operations.

Explores real functions, covering parity, periodicity, and polynomial functions.

Covers set theory operations and functions, including injections and surjections.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Explores differentiating under the integral sign and continuity of functions in integrals.

Covers the concept of partial derivatives and their applications in mathematical analysis.

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Introduces the fundamentals of functions in microcontroller programming, emphasizing naming rules and step-by-step development.

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Covers control structures, loops, and functions in C language, emphasizing the importance of local variables and avoiding global variables.

Covers functions, differentiability, Taylor expansions, and integrals, providing fundamental concepts and practical applications.

Covers entropy, its definition, and its implications in thermodynamics.

Covers the definitions and notations related to functions.

Explores differentiating under the integral sign and conditions for differentiation, with examples and extensions to functions on open intervals.

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

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Covers the study of functions, focusing on convexity criteria within closed subintervals.