# Abstract algebraic logic

In mathematical logic, abstract algebraic logic is the study of the algebraization of deductive systemsarising as an abstraction of the well-known Lindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems. (Wikipedia).

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

AlgTopReview: An informal introduction to abstract algebra

This is a review lecture on some aspects of abstract algebra useful for algebraic topology. It provides some background on fields, rings and vector spaces for those of you who have not studied these objects before, and perhaps gives an overview for those of you who have. Our treatment is

From playlist Algebraic Topology

Determine if the Binary Operation Defined by the Table is Commutative and Associative

In this video we determine whether or not a binary operation is commutative and associative. The binary operation is actually defined by a table in this example. I hope this video helps someone.

From playlist Abstract Algebra

Logical challenges with abstract algebra II | Abstract Algebra Math Foundations 215 | NJ Wildberger

There is a very big jump in going from finite algebraic objects to "infinite algebraic objects". For example, there is a huge difference, if one is interested in very precise definitions, between the concept of a finite group and the concept of an "infinite group". We illustrate this imp

From playlist Math Foundations

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

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

Group equation examples Lesson 26

In this video we solve algebraic expressions using the properties of groups. It is always good to work through a few examples. You must get familiar with solving equations where the variables are group elements and not placeholders for numbers only.

From playlist Abstract algebra

Programming with Math (Exploring Type Theory)

As programs are getting more complex, it's time to go back to basics, to the old well tested approach to complexity called mathematics. Let compilers deal with the intricacies of Turing machines. Our strength is abstract thinking. Let's use it! EVENT: Øredev 2018 SPEAKER: Bartosz Milew

From playlist Software Development

Learn Mathematics from START to FINISH

This video shows how anyone can start learning mathematics , and progress through the subject in a logical order. There really is no finishing point but this will get you through all of the basic undergraduate mathematics from start to "finish". I also included some graduate topics. Here

From playlist Book Reviews

Isomorphisms in abstract algebra

In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4

From playlist Abstract algebra

Logical challenges with abstract algebra I | Abstract Algebra Math Foundations 214 | NJ Wildberger

While abstract algebra is not as problematic logically as modern analysis, it still suffers from very serious difficulties. In this video we begin laying out some of these logical reefs that we will have to steer clear from. And we look at the first one: which is distinguishing between des

From playlist Math Foundations

Why Algebraic Data Types Are Important

Strong static typing detects a lot of bugs at compile time, so why would anyone prefer to program in JavaScript or Python? The main reason is that type systems can be extremely complex, often with byzantine typing rules (C++ comes to mind). This makes generic programming a truly dark art.

From playlist Functional Programming

The mathematical work of Vladimir Voevodsky - Dan Grayson

Vladimir Voevodsky Memorial Conference Topic: The mathematical work of Vladimir Voevodsky Speaker: Dan Grayson Affiliation: University of Illinois, Urbana-Champaign Date: September 11, 2018 For more video please visit http://video.ias.edu

From playlist Mathematics

Wolfram Physics Project: Working Session Tuesday, Mar. 16, 2021 [Bibliographying Combinators]

This is a Wolfram Physics Project working session on bibliographying combinators. Begins at 4:33 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am

From playlist Wolfram Physics Project Livestream Archive

Cyril Demarche: Cohomological obstructions to local-global principles - lecture 1

Hasse proved that for quadrics the existence of rational points reduces to the existence of solutions over local fields. In many cases, cohomological constructions provide obstructions to such a local to global principle. The objective of these lectures is to give an introduction to these

From playlist Algebraic and Complex Geometry

A Book on Logic and Mathematical Proofs

This is an introductory book to help prepare people get into higher level mathematics. It is a good beginner book because it shows a lot of the steps in the examples and the partial solutions sometimes include the proofs. It also covers some abstract algebra and advanced calculus. This is

From playlist Cool Math Stuff

Epic Math Book on Complex Analysis

In this video I will show you one of my math books. Most of the discussion is centered on Chapter 0 which actually contains sets, logic, linear algebra, abstract algebra, topology, etc. The book is called Elements of Complex Analysis and it was written by Sonneschein and Green. Here it

From playlist Book Reviews

Learn Mathematics from START to FINISH (2nd Edition)

In this video I will show you how to learn mathematics from start to finish. I will give you three different ways to get started with mathematics. I hope this video helps someone. Here are the books Elementary Algebra https://amzn.to/3S7yG0Y Pre-Algebra https://amzn.to/3TpW8HK Discrete Ma

From playlist Book Reviews

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