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
Geometric Algebra - Linear Transformations, Outermorphism, and the Determinant
In this video, we will review some basic concepts from linear algebra, such as the linear transformation, prove important theorems which ground matrix operations, extend the linear transformation on vectors to higher-graded elements to bivectors and trivectors, and define the determinant o
From playlist Geometric Algebra
Exponent Law: Geometric Interpretation
GeoGebra Resource Link: https://www.geogebra.org/m/wnnsr3en
From playlist Algebra 1: Dynamic Interactives!
Abstract Algebra - 11.1 Fundamental Theorem of Finite Abelian Groups
We complete our study of Abstract Algebra in the topic of groups by studying the Fundamental Theorem of Finite Abelian Groups. This tells us that every finite abelian group is a direct product of cyclic groups of prime-power order. Video Chapters: Intro 0:00 Before the Fundamental Theorem
From playlist Abstract Algebra - Entire Course
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
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
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
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Holomorphic rigid geometric structures on compact manifolds by Sorin Dumitrescu
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
Moduli of Representations and Pseudorepresentations - Carl Wang Erickson
Carl Wang Erickson Harvard University May 2, 2013 A continuous representation of a profinite group induces a continuous pseudorepresentation, where a pseudorepresentation is the data of the characteristic polynomial coefficients. We discuss the geometry of the resulting map from the moduli
From playlist Mathematics
Is the universe geometric or algebraic? by Minhyong Kim
EINSTEIN LECTURES DATE: 21 December 2018, 15:00 to 16:00 VENUE: Christ University, Main Auditorium, Hosur Road, Bengaluru - 29 In recent years, I have heard distinguished physicists ask this question with increasing frequency and urgency. In this lecture, I will try to convey to the audi
From playlist Einstein Lectures
What is algebra and geometry? | Is Euler's Number Geometric? | Part 2 -- Why are π and e linked?
Part 3: https://youtu.be/c7ilUAqAxyU The full series on Euler's number: Part 1: https://youtu.be/rbmUqseGOOM Part 2: https://youtu.be/YgScek3GkdI Part 3: https://youtu.be/c7ilUAqAxyU Part 4: https://youtu.be/oU5elvZL0uU Part 5: https://youtu.be/EoFhgYySUgk Given any conversation between
From playlist Is Euler's Number Geometric?
Nonetheless one should learn the language of topos: Grothendieck... - Colin McLarty [2018]
Grothendieck's 1973 topos lectures Colin McLarty 3 mai 2018 In the summer of 1973 Grothendieck lectured on several subjects in Buffalo NY, and these lectures were recorded, including 33 hours on topos theory. The topos lectures were by far the most informal of the series, with the most si
From playlist Number Theory
Ming Ng - Adelic Geometry via Topos Theory
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/NgSlidesToposesOnline.pdf Joint work with Steve Vickers In this talk, I will give a leisurely introduction to the t
From playlist Toposes online
Emily Cliff: Hilbert Schemes Lecture 3
SMRI Seminar Series: 'Hilbert Schemes' Lecture 3 The universal family on H Emily Cliff (University of Sydney) This series of lectures aims to present parts of Nakajima’s book `Lectures on Hilbert schemes of points on surfaces’ in a way that is accessible to PhD students interested in rep
From playlist SMRI Course: Hilbert Schemes
Algebraic Ending Laminations and Quasiconvexity by Mahan Mj
Surface Group Representations and Geometric Structures DATE: 27 November 2017 to 30 November 2017 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The focus of this discussion meeting will be geometric aspects of the representation spaces of surface groups into semi-simple Lie groups. Classi
From playlist Surface Group Representations and Geometric Structures
QED Prerequisites Geometric Algebra: Introduction and Motivation
This lesson is the beginning of a significant diversion from QED prerequisites. No student needs to understand Geometric Algebra in order to begin the study of QED. However, since we have pushed the formal structure of Maxwell's Equations as far as I know how to go, I think it makes sense
From playlist QED- Prerequisite Topics
Geometric Algebra - Duality and the Cross Product
In this video, we will introduce the concept of duality, involving a multiplication by the pseudoscalar. We will observe the geometric meaning of duality and also see that the cross product and wedge product are dual to one another, which means that the cross product is already contained w
From playlist Geometric Algebra