Mathematical logic | Unification (computer science) | Universal algebra | Free algebraic structures
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X. Other synonyms for the notion include absolutely free algebra and anarchic algebra. From a category theory perspective, a term algebra is the initial object for the category of all X-generated algebras of the same signature, and this object, unique up to isomorphism, is called an initial algebra; it generates by homomorphic projection all algebras in the category. A similar notion is that of a Herbrand universe in logic, usually used under this name in logic programming, which is (absolutely freely) defined starting from the set of constants and function symbols in a set of clauses. That is, the Herbrand universe consists of all ground terms: terms that have no variables in them. An atomic formula or atom is commonly defined as a predicate applied to a tuple of terms; a ground atom is then a predicate in which only ground terms appear. The Herbrand base is the set of all ground atoms that can be formed from predicate symbols in the original set of clauses and terms in its Herbrand universe. These two concepts are named after Jacques Herbrand. Term algebras also play a role in the semantics of abstract data types, where an abstract data type declaration provides the signature of a multi-sorted algebraic structure and the term algebra is a concrete model of the abstract declaration. (Wikipedia).
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
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
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)
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
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
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
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 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
Like Terms – 100% of Algebra Students NEED to Understand This
Like terms and how to combine like terms - algebra basics. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes an
From playlist GED Prep Videos
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3)
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3) In this video lesson we construct the Lie group elements of SO(3) starting from the defining property of SO(3) and the Lie algebra of so(3). To do this we review the Caley-Hamilton theorem that a square matrix satisfies its own cha
From playlist Lie Groups and Lie Algebras
Algebraic Expressions – Algebra Basics
Algebraic expressions are extremely important in algebra. This video will explain the basic idea of an algebraic expression to include like terms, variables and coefficients. Need more help in math? Check out my math courses below: TabletClass Math Academy https://tabletclass-academy.tea
From playlist GED Prep Videos
CERIAS Security: An Algebra for Specifying High-level Security Policies 2/5
Clip 2/5 Speaker: Qihua Wang · Purdue University A high-level security policy states an overall requirement for a sensitive task. One example of a high-level security policy is a separation of duty policy, which requires a sensitive task to be performed by a team of at least k users.
From playlist The CERIAS Security Seminars 2006
Like Terms - Understand In 10 Minutes
Understanding like terms is a must in algebra. In this video I review the main ideas you need to know about like terms. Specifically, I will teach you what a term is in algebra to include coefficients. I will also discuss how to identify like terms and lastly how to add or subtract like t
From playlist Pre-Algebra
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
"Terms" Are Like The "Words" Of Algebra
Algebra Tutor Walk Through Video: Terms (Section 1) This topic is for anyone just starting to learn about using letters to represent numbers. Download Algebra Tutor free and follow along: App Store: https://apps.apple.com/gb/app/algebra-tutor/id1570412941 Google Play: https://play.google.
From playlist Summer of Math Exposition Youtube Videos
Joakim Arnlind - Discrete Minimal Surface Algebras
https://indico.math.cnrs.fr/event/4272/attachments/2260/2714/IHESConference_Joakim-ARNLIND.pdf
From playlist Space Time Matrices
Bad Math Glossary, or Soviet Propaganda?
A review of "The Algebra Tutor, Algebra 1 and Algebra 2, Volume 1". A textbook/workbook by Willie L. Thomas. It has a great propaganda-esque cover design, and a very finicky glossary to put it nicely. #mathbook #math 00:00 Rest of the Review 19:33 The Bad Glossary 23:00 End Buy a copy o
From playlist The Math Library
Combining Like Terms (Basic Algebra Concept)
Combining like terms is a basic algebra concept. This video will explain the details of knowing the parts of an algebra term and identifying like terms. For more math help please visit http://tabletclass.com
From playlist GED Prep Videos
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