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
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
What is Abstract Algebra? (Modern Algebra)
Abstract Algebra is very different than the algebra most people study in high school. This math subject focuses on abstract structures with names like groups, rings, fields and modules. These structures have applications in many areas of mathematics, and are being used more and more in t
From playlist Abstract Algebra
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
A group is (in a sense) the simplest structure in which we can do the familiar tasks associated with "algebra." First, in this video, we review the definition of a group.
From playlist Modern Algebra - Chapter 15 (groups)
From playlist College Algebra
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
Matrix Algebra Basics || Matrix Algebra for Beginners
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add
From playlist Algebra
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
Why There's 'No' Quintic Formula (proof without Galois theory)
Feel free to skip to 10:28 to see how to develop Vladimir Arnold's amazingly beautiful argument for the non-existence of a general algebraic formula for solving quintic equations! This result, known as the Abel-Ruffini theorem, is usually proved by Galois theory, which is hard and not very
From playlist Summer of Math Exposition Youtube Videos
Richard Stanley - Increasing and decreasing subsequences (2006)
slides for this talk: https://www.mathunion.org/fileadmin/IMU/Videos/ICM2006/tars/stanley2006.pdf ICM Madrid Videos 24.08.2006 Increasing and decreasing subsequences Richard P. Stanley Massachusetts Institute of Technology, Cambridge, USA 24-Aug-06 · 09:00-10:00 h https://www.mathunion.
From playlist Mathematics
Numerical Integration of Chaotic Dynamics: Uncertainty Propagation & Vectorized Integration
This video introduces the idea of chaos, or sensitive dependence on initial conditions, and the importance of integrating a bundle of trajectories to propagate uncertainty. We also explore how to vectorize numerical integration in Python and Matlab to make the algorithm orders of magnitud
From playlist Engineering Math: Differential Equations and Dynamical Systems
Jānis Lazovskis (8/26/20): Moduli spaces of Morse functions for persistence
Title: Moduli spaces of Morse functions for persistence Abstract: I will present the results of a two year collaborative project formed to better understand how persistence interacts with Morse functions on surfaces. Restricting to the sphere, Morse--Smale functions can be decomposed into
From playlist AATRN 2020
Research Working Session: Tuesday, September 6, 2022 [Multicomputation]
This a research session on Multicomputation. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or through the official Twitch channel of Stephen Wolfram here: https://www.twitch.tv/stephen_wolfram/ Follow us on our official
From playlist Science and Research Livestreams
Robin Deeley: The K-theory of the stable algebra and stable Ruelle algebra of a Wieler solenoid
Talk by Robin Deeley in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on May 13, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
A Non-flag Arithmetic Regularity Lemma and Counting Lemma - Daniel Altman
Special Year Informal Seminar Topic: A Non-flag Arithmetic Regularity Lemma and Counting Lemma Speaker: Daniel Altman Affiliation: University of Oxford Date: March 10, 2023 We will discuss a version of the Green--Tao arithmetic regularity lemma and counting lemma which works in the gener
From playlist Mathematics
QED Prerequisites Geometric Algebra 26 The Lorentz Group
In this lesson we connect the idea of using rotors to transform multivectors with the notion of the Lorentz group. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use to produce the lectures is: https://apps.apple.com/us/app
From playlist QED- Prerequisite Topics
Mathematics Gone Radical - Denesting Roots
Train your logical thinking skills by trying out Brilliant! =D https://brilliant.org/FlammableMaths What Part of Math Don't You Understand? Merch! :D https://teespring.com/what-part-of-math-don-t-you-u Engineering Watch: https://stemerch.com/products/the-incredibly-unrigorous-engineering-w
From playlist Number Theory
symbols of inclusion (KristaKingMath)
► My Algebra 1 course: https://www.kristakingmath.com/algebra-1-course In this video we'll learn about symbols of inclusion, which are just different types of parentheses. PEMDAS and order of operations tells us that we have to start with the inner-most parentheses and work our way out.
From playlist Algebra 1
This is part of an online course on beginner/intermediate linear algebra, which presents theory and implementation in MATLAB and Python. The course is designed for people interested in applying linear algebra to applications in multivariate signal processing, statistics, and data science.
From playlist Linear algebra: theory and implementation