Algebra

Algebra

Algebra (from Arabic ‏الجبر‎ (al-jabr) 'reunion of broken parts, bonesetting') is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word algebra is not only used for naming an area of mathematics and some subareas; it is also used for naming some sorts of algebraic structures, such as an algebra over a field, commonly called an algebra. Sometimes, the same phrase is used for a subarea and its main algebraic structures; for example, Boolean algebra and a Boolean algebra. A mathematician specialized in algebra is called an algebraist. (Wikipedia).

Algebra
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Algebra for beginners || Basics of Algebra

In this course you will learn about algebra which is ideal for absolute beginners. #Algebra is the branch of mathematics that helps in the representation of problems or situations in the form of mathematical expressions. It involves variables like x, y, z, and mathematical operations like

From playlist Algebra

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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

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Intro to Functions

As part of the college algebra series, this Center of Math video will teach you the basics of functions, including how they're written and what they do.

From playlist Basics: College Algebra

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College Algebra - full course

Algebra is one of the broad areas 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. In this course

From playlist Algebra

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301.2 Definition of a Group

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)

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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

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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

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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

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FIT2.3.3. Algebraic Extensions

Field Theory: We define an algebraic extension of a field F and show that successive algebraic extensions are also algebraic. This gives a useful criterion for checking algberaic elements. We finish with algebraic closures.

From playlist Abstract Algebra

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Kristin Courtney: "The abstract approach to classifying C*-algebras"

Actions of Tensor Categories on C*-algebras 2021 Mini Course: "The abstract approach to classifying C*-algebras" Kristin Courtney - Westfälische Wilhelms-Universität Münster Institute for Pure and Applied Mathematics, UCLA January 21, 2021 For more information: https://www.ipam.ucla.edu

From playlist Actions of Tensor Categories on C*-algebras 2021

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Rahim Moosa 11/14/14

Title: Differential Varieties with Only Algebraic Images

From playlist Fall 2014

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Homeschool Algebra 2 - What Every Homeschool Parent Needs to Know

TabletClass Math Homeschool: https://tabletclass.com/ How to homeschool Algebra 2 successfully. Need help with homeschooling Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus? Check out TabletClass Math for all your homeschooling needs: https://tabletclass.com/ .

From playlist Homeschool Math

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Homeschool Geometry Before Algebra 2

TabletClass Math: https://tabletclass.com/ This video explains why you should homeschool geometry before algebra 2.

From playlist Homeschool Math

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A geometric model for the bounded derived category of a gentle algebra, Sibylle Schroll, Lecture 1

Gentle algebras are quadratic monomial algebras whose representation theory is well understood. In recent years they have played a central role in several different subjects such as in cluster algebras where they occur as Jacobian algebras of quivers with potentials obtained from triangula

From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"

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Omar León Sánchez, University of Manchester

December 17, Omar León Sánchez, University of Manchester A Poisson basis theorem for symmetric algebras

From playlist Fall 2021 Online Kolchin Seminar in Differential Algebra

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Homeschool Algebra - What Every Homeschool Parent Needs to Know

TabletClass Math Homeschool: https://tabletclass.com/ How to homeschool Algebra successfully. Need help with homeschooling Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus? Check out TabletClass Math for all your homeschooling needs: https://tabletclass.com/ .

From playlist Homeschool Algebra

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What is a Module? (Abstract Algebra)

A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an

From playlist Abstract Algebra

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Higher Algebra 10: E_n-Algebras

In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin

From playlist Higher Algebra

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