Abstract Algebra: The definition of a Ring
Learn the definition of a ring, one of the central objects in abstract algebra. We give several examples to illustrate this concept including matrices and polynomials. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦♦ We recommend th
From playlist Abstract Algebra
Ring Examples (Abstract Algebra)
Rings are one of the key structures in Abstract Algebra. In this video we give lots of examples of rings: infinite rings, finite rings, commutative rings, noncommutative rings and more! Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W ♦♦♦♦♦♦♦♦♦
From playlist Abstract Algebra
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
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
Krzysztof Krupinski: Amenable theories
The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: I will introduce the notion of an amenable theory as a natural counterpart of the notion of a definably amenable group. Roughly speaking, amenability means that th
From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"
Invertible matrices and systems of linear equations II | Linear Algebra MATH1141 | N J Wildberger
We continue showing that an n by n matrix is invertible precisely when the equation Ax=b has a unique solution for any b. Along the way we will need to look at the matrix formulation of elementary row operations, and how these elementary matrices are invertible. This is a rather subtle but
From playlist Higher Linear Algebra
Gilles Pisier: The lifting property for C*-algebras
Talk by Gilles Pisier in Global Noncommutative Geometry Seminar (Americas) on January 14, 2022 in https://globalncgseminar.org/talks/the-lifting-property-for-c-algebras/
From playlist Global Noncommutative Geometry Seminar (Americas)
Harold Dales: Multi-norms and Banach lattices
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
Gregory Margulis - The Abel Prize interview 2020
00:00 congratulations to Gregory Margulis 01:33 when did you interests in mathematics start? 02:33 growing up in Moscow in the 50’s and 60’s and being included in mathematical circles 05:47 mathematical Olympiads 06:32 early career and the paper with Kazhdan 08:03 Margulis at the Institute
From playlist Gregory Margulis
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
Amos Nevo: Representation theory, effective ergodic theorems, and applications - Lecture 1
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Dynamical Systems and Ordinary Differential Equations
Quaternion algebras via their Mat2x2(F) representations
In this video we talk about general quaternion algebras over a field, their most important properties and how to think about them. The exponential map into unitary groups are covered. I emphasize the Hamiltionion quaternions and motivate their relation to the complex numbers. I conclude wi
From playlist Algebra
Measurable equidecompositions – András Máthé – ICM2018
Analysis and Operator Algebras Invited Lecture 8.8 Measurable equidecompositions András Máthé Abstract: The famous Banach–Tarski paradox and Hilbert’s third problem are part of story of paradoxical equidecompositions and invariant finitely additive measures. We review some of the classic
From playlist Analysis & Operator Algebras
Nuclear C*-algebras: From quasidiagonality to classification and back again – W. Winter – ICM2018
Analysis and Operator Algebras Invited Lecture 8.20 Structure of nuclear C*-algebras: From quasidiagonality to classification and back again Wilhelm Winter Abstract: I give an overview of recent developments in the structure and classification theory of separable, simple, nuclear C*-alge
From playlist Analysis & Operator Algebras
Random groups IV - Goulnara Arzhantseva
Women and Mathematics Title: Random groups IV Speaker: Goulnara Arzhantseva Affiliation: University of Vienna Date: May 19, 2017 For more videos, please visit http://video.ias.edu
From playlist Women and Mathematics 2017
Abstract Algebra | What is a ring?
We give the definition of a ring and present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Laurent Bartholdi: Amenable groups - Lecture 2
Abstract: I shall discuss old and new results on amenability of groups, and more generally G-sets. This notion traces back to von Neumann in his study of the Hausdorff-Banach-Tarski paradox, and grew into one of the fundamental properties a group may / may not have -- each time with import
From playlist Mathematical Aspects of Computer Science
Asymptotic Bounded Cohomology and Uniform Stability of high-rank lattices - Bharatram Rangarajan
Arithmetic Groups Topic: Asymptotic Bounded Cohomology and Uniform Stability of high-rank lattices Speaker: Bharatram Rangarajan Affiliation: Hebrew University Date: March 16, 2022 In ongoing joint work with Glebsky, Lubotzky, and Monod, we construct an analog of bounded cohomology in an
From playlist Mathematics
We prove that Z is isomorphic to 3Z. Here Z is the set of all integers and 3Z is the set of all multiples of 3. Both form groups under addition. I hope this helps someone who is learning abstract algebra. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvc
From playlist Abstract Algebra Videos
Some 20+ year old problems about Banach spaces and operators on them – W. Johnson – ICM2018
Analysis and Operator Algebras Invited Lecture 8.17 Some 20+ year old problems about Banach spaces and operators on them William Johnson Abstract: In the last few years numerous 20+ year old problems in the geometry of Banach spaces were solved. Some are described herein. © Internatio
From playlist Analysis & Operator Algebras