# Abstract algebra

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the variety of groups. (Wikipedia).

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

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

Field Definition (expanded) - Abstract Algebra

The field is one of the key objects you will learn about in abstract algebra. Fields generalize the real numbers and complex numbers. They are sets with two operations that come with all the features you could wish for: commutativity, inverses, identities, associativity, and more. They

From playlist Abstract Algebra

Abstract Algebra: The definition of a Field

Learn the definition of a Field, one of the central objects in abstract algebra. We give several familiar examples and a more unusual example. ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Make a one-time PayPal donation: https://www

From playlist Abstract Algebra

16 You have made it to the first exciting video Operations

To be honest, the topics have been very dry up to now. Here is the first bit of excitement. Operations. Understanding operations is a fundamental priority in abstract algebra.

From playlist Abstract algebra

02 Introduction to sets

We start off by looking at the basics of sets.

From playlist Abstract 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

Learn Abstract Algebra from START to FINISH

In this video I talk about how to learn abstract algebra from start to finish. I go over some books which you can use to help you learn abstract algebra from the very basics all the way to graduate level abstract algebra. My Udemy Course on Abstract Algebra https://www.udemy.com/course/a

From playlist Book Reviews

Tour of My Abstract Algebra Book Collection

In this video I go over some of my abstract algebra books. I am pretty sure I have more but I am not 100% positive. I have more bookshelves and boxes I need to go through still, I have a lot of books!! There are a lot of books here. Keep in mind this collection has taken me years. If you

From playlist Book Reviews

Best Abstract Algebra Books for Beginners

In this video I go over the four best books for beginners trying to learn abstract algebra. I have over 25 abstract algebra books and I think these are the best four for people trying to learn. There are other good books and of course opinions vary, but these are four solid choices for any

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Abstract-ness | Introduction to algebra | Algebra I | Khan Academy

The general idea behind the word 'abstract' Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview_hist_alg/v/the-beauty-of-algebra?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI Missed the previous lesson? https://www.khanacademy.org/math/

From playlist Algebra Foundations

Quotient group example

Now that we know what a quotient group is, let's take a look at an example to cement our understanding of the concepts involved.

From playlist Abstract algebra

Obscure but Beautiful Abstract Algebra Book from the 1960s

This is a beautiful out of print book the 1960s. I spent a great deal of time using this book for self study. I used other books as well, but I did find a lot of good information in this book and I do think it is worth having. The book is called A First Course in Abstract Algebra and it wa

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Algebra by B.L. van der Waerden

In this video I will show you my two volume set of Algebra by B.L. van der Waerden. These are classic books on Abstract Algebra. Volume 1 https://amzn.to/3HZJL2r Volume 2 https://amzn.to/3vcIXQb Saracino Book https://amzn.to/3Gg0hKt Proof Writing Book: https://amzn.to/3YN5DnN Useful Math

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Math Books That Never Made It

These are math books that were never reprinted. We take a look at these books in this video. The books cover precalculus, calculus, and abstract algebra. Elementary Functions: An Approach to Precalculus Mathematics: https://amzn.to/3K9yc9N Essentials of Abstract Algebra: https://amzn.to/4

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On the long-term dynamics of nonlinear dispersive evolution equations - Wilhelm Schlag

Analysis Seminar Topic: On the long-term dynamics of nonlinear dispersive evolution equations Speaker: Wilhelm Schlag Affiliation: University of Chicago Visiting Professor, School of Mathematics Date: Febuary 14, 2018 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Legendary Abstract Algebra Book

In this video I talk about a great book for beginners who are learning abstract algebra. This one says Examination Copy on the cover which is really cool. This book has been reprinted by Dover so it's very affordable and widely available. The book is titled A Book of Abstract Algebra and i

From playlist Book Reviews

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