Lectures related to ExVR Workshop: Introduction and Showcase

Limits and Colimits in Functor Categories

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

Active Learning Session: Group Theory

Explores active learning in Group Theory, focusing on products, coproducts, adjunctions, and natural transformations.

Sets and Operations: Introduction to Mathematics

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

Adjunctions and Limits: Exploring Functors and Co-limits

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

Equilibrium in 3D: System Isolation and Constraints

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

Relations in Computer Science

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

Group Theory Fundamentals

Introduces the basics of group theory, defining groups, categories, and groupoids.

Internal Transport: Mass Balance and Maxwell-Stefan Equation

Explores internal transport phenomena, focusing on mass balance and the Maxwell-Stefan Equation in single pores.

Clustering: k-means

Explains k-means clustering, assigning data points to clusters based on proximity and minimizing squared distances within clusters.

Adjunctions: Constructing Desired Adjoints

Explores constructing desired adjoints in specific categories like Set.

Nonlinear Dynamics: Chaos and Complex Systems

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Categories and Functors

Covers categories, functors, and presheaf categories, exploring the relationships between objects and morphisms.

Determinantal Point Processes and Extrapolation

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

Analysis IV: Convolution and Hilbert Structure

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Lebesgue Integration: Cantor Set

Explores the construction of the Lebesgue function on the Cantor set and its unique properties.

Simplicial and Cosimplicial Objects: Examples and Applications

Covers simplicial and cosimplicial objects in category theory with practical examples.

Cartesian Product and Induction

Introduces Cartesian product and induction for proofs using integers and sets.

Limits and colimits in Top

Covers the concepts of limits and colimits in the category of Topological Spaces, emphasizing the relationship between colimit and limit constructions and adjunctions.

Display Screen: Microcontrollers Basics

Covers the basics of displaying information on a screen using microcontrollers and utilizing the serial monitor for various purposes.

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.