Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
The Lie-algebra of Quaternion algebras and their Lie-subalgebras
In this video we discuss the Lie-algebras of general quaternion algebras over general fields, especially as the Lie-algebra is naturally given for 2x2 representations. The video follows a longer video I previously did on quaternions, but this time I focus on the Lie-algebra operation. I st
From playlist Algebra
Paulo Oliva: On a Dialectica like version of Kleene numerical realizability
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Kleene's original notion of realizability (1945) makes use of all (partial) computable functions as potential realisers. Later Kreisel (1959) presented a "modified" notio
From playlist Workshop: "Proofs and Computation"
Commutative algebra 57: Krull versus Hilbert
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We continue the previous video by showing that the Krull dimension of a Noetherian local ring is at most the dimension defined
From playlist Commutative algebra
From playlist CS124 - Full Course
Andrew Mathas: Cyclotomic KLR algebras (Part 2 of 4)
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The cyclotomic KLR algebras are certain quotients of the quiver Hecke algebras, or Khovanov–Lauda–Rouquier algebras. These algebras are important because
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Group Definition (expanded) - Abstract Algebra
The group is the most fundamental object you will study in abstract algebra. Groups generalize a wide variety of mathematical sets: the integers, symmetries of shapes, modular arithmetic, NxM matrices, and much more. After learning about groups in detail, you will then be ready to contin
From playlist Abstract Algebra
Pattern Matching with Regular Expressions
From playlist CS50 Seminars 2012
Andrew Mathas: Cyclotomic KLR algebras (Part 1 of 4)
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The cyclotomic KLR algebras are certain quotients of the quiver Hecke algebras, or Khovanov–Lauda–Rouquier algebras. These algebras are important because
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Ring Definition (expanded) - Abstract Algebra
A ring is a commutative group under addition that has a second operation: multiplication. These generalize a wide variety of mathematical objects like the integers, polynomials, matrices, modular arithmetic, and more. In this video we will take an in depth look at the definition of a rin
From playlist Abstract Algebra
Andrew Mathas: Cyclotomic KLR algebras (Part 3 of 4)
The lecture was held within the framework of the Hausdorff Trimester Program: Symplectic Geometry and Representation Theory. Abstract: The cyclotomic KLR algebras are certain quotients of the quiver Hecke algebras, or Khovanov–Lauda–Rouquier algebras. These algebras are important because
From playlist HIM Lectures: Trimester Program "Symplectic Geometry and Representation Theory"
Michael Rathjen: The Ubiquity of Schütte's Search Trees
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Progressions of theories along paths through Kleene's $\mathcal O$, adding the consistency of the previous theory at every successor step, can deduce every true $\Pi^0_1$
From playlist Workshop: "Proof, Computation, Complexity"
Hugo Herbelin: Computing with Markov's principle
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Computing with Markov's principle via a realizability interpretation is standard, using unbounded search as in Kleene's realizability or by selecting the first valid wit
From playlist Workshop: "Proofs and Computation"
Algebra for Beginners | Basics of Algebra
#Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. Table of Conten
From playlist Linear Algebra
Gérard H E Duchamp - Kleene Stars in Shuffle Algebras
We present some bialgebras and their monoid of characters. We entend, to the case of some rings, the well-known theorem (in the case when the scalars form a field) about linear independence of characters. Examples of algebraic independence of subfamilies and identites derived from their gr
From playlist Combinatorics and Arithmetic for Physics: 02-03 December 2020
Makoto Fujiwara: Bar theorem and bar recursion for continuous functions with continuous modulus
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: (joint work with Tatsuji Kawai) Bar induction is originally discussed by L. E. J. Brouwer under the name of “bar theorem” in his intuitionistic mathematics but first formali
From playlist Workshop: "Constructive Mathematics"
[Discrete Mathematics] Combinatorial Families
We talk about combinatorial families and the kleene star. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz Discrete Mathematics 2: https://
From playlist Discrete Math 2
MathWorks Excellence in Innovation Project 208: RC Car Modelling and Trajectory Tracking Control
Github project repository : https://github.com/Arttrm/MW_EiI_208_Trajectory_Planning_and_Tracking MathWorks Excellence in Innovation Projects : https://github.com/mathworks/MathWorks-Excellence-in-Innovation
From playlist MathWorks Excellence in Innovation
Arthur Bartels: K-theory of group rings (Lecture 1)
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Arthur Bartels: K-theory of group rings The Farrell-Jones Conjecture predicts that the K-theory of group rings RG can be computed in terms of K-theory of group rings RV where V vari
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Iosif Petrakis: Bishop spaces and the problem of constructivizing general topology
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: According to Bishop (see [1], p.28), the constructivization of general topology is impeded by two obstacles. First, the classical notion of a topological space is not constru
From playlist Workshop: "Constructive Mathematics"