Concept

Monoid (category theory)

Related lectures (26)

Introduces the basics of Diffie-Hellman cryptography, covering algorithms, monoids, and key agreement protocols.

Covers matrix equations as linear combinations, vector spaces, and geometric interpretations.

Hamilton-Jacobi Equation: Analytical Mechanics

Explores the Hamilton-Jacobi equation in analytical mechanics, focusing on eigenvalues, constants of motion, and system predictability.

Abstract algebra and type classes

Covers abstract algebra concepts using type classes in Scala, including defining monoids, generalizing reduce functions, and typeclass laws.

Formal Languages: Concepts

Covers the fundamental concepts of formal languages, including alphabets, words, languages, and word equality.

Group Theory: Direct Sum of Abelian Groups

Explores the arithmetic of direct sum of abelian groups and the process of turning a monoid into a commutative group.

Categories and Functors: An Introduction

Provides an overview of categories, functors, and natural transformations in mathematics.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Quasi-Categories: Active Learning Session

Covers fibrant objects, lift of horns, and the adjunction between quasi-categories and Kan complexes, as well as the generalization of categories and Kan complexes.

Hamilton-Jacobi Equations: Phase Portrait

Explores Hamilton-Jacobi equations, phase portrait, and period calculation using action-angle variables for system trajectories.

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Linear Algebra: Cofactors and Eigenvectors

Explains cofactors, eigenvectors, eigenvalues, and studying linear applications.

Postnikov tower + cool stuff

Covers the Postnikov tower, homotopy fibers, suspension, and the James construction.

Local Rings and Residues

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Linear Algebra: Vector Spaces

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Natural Transformations: Examples and Applications

Explores natural transformations between functors in different categories and their applications.

Diagonalization: Eigenvectors and Eigenvalues

Covers the diagonalization of matrices using eigenvectors and eigenvalues.

Characterizing Fibrations in Chain Complexes

Explores the characterization of fibrations and acyclic fibrations in chain complexes.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Gram-Schmidt Algorithm

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.