Lectures related to Set theory

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

Sets and Operations: Introduction to Mathematics

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

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

Homotopical Algebra: Examples and Adjunctions

Explores homotopical algebra examples and adjunctions, focusing on left and right adjoints in group functors and coproducts.

Recap of Group Theory

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

Active Learning: Group Structures and Symmetric Actions

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

Two Definitions of Group Action

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

Implementation of Lists: Arrays and Iterators

Covers the implementation of lists using arrays, iterators, and various methods.

Limits and colimits: Two examples

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

Standard Properties: Distance and Norm

Covers the standard properties of distance and norm in vector spaces.

Cartesian Product in Linear Algebra

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

Adjunctions and Limits: Exploring Functors and Co-limits

Covers adjunctions and limits, focusing on functors, co-limits, and their applications in category theory.

Counting Basics: Set Theory and Permutations

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

Regularity Lemmas and Density Theorems

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

Determinantal Point Processes and Extrapolation

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Differential Forms on Manifolds

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

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

The Role of Symmetries

Delves into symmetries in physics, covering group theory, perturbation, and quantification.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Limits and Colimits in Functor Categories

Explores limits and colimits in functor categories, focusing on equalizers, pullbacks, and their significance in category theory.