Lectures related to Hausdorff Dimension and Brownian Motion

Explores the Cartesian product in linear algebra and the method of induction for proving propositions.

Explores Regularity Lemmas and Density Theorems for graph partitioning and structure identification.

Covers the concept of the Cartesian product, emphasizing the order of elements in pairs.

Covers the study of lifting properties in categories, focusing on the left and right lifting properties.

Explores two definitions of group action on a set, focusing on properties and applications.

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

Focuses on the pushout and pullback constructions in sets, illustrating colimits and limits with explicit examples.

Explains set difference and complement calculation with clear examples.

Explores the concept of a commutative semi-ring based on set theory properties.

Explores commutative groups, Euler's Totient Function, and Cartesian products in group theory.

Provides a recap of group theory, defining a group as a set with a multiplication operation.

Covers the main rules of counting for combinatorial objects and introduces various counting techniques.

Covers the Pigeonhole Principle, its applications, and examples of its guarantees.

Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.

Covers the construction of integers through equivalence relations and their properties in mathematics.

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Focuses on injective functions in linear algebra, demonstrating how to verify properties and prove injectivity.

Covers the basics of real numbers and set theory, including subsets, intersections, unions, and set operations.

Explores active learning implications in understanding group structures and symmetric actions.

Explores stochastic processes in continuous time, emphasizing Brownian motion and related concepts.