Abstract algebra | Information theory
The term "information algebra" refers to mathematical techniques of information processing. Classical information theory goes back to Claude Shannon. It is a theory of information transmission, looking at communication and storage. However, it has not been considered so far that information comes from different sources and that it is therefore usually combined. It has furthermore been neglected in classical information theory that one wants to extract those parts out of a piece of information that are relevant to specific questions. A mathematical phrasing of these operations leads to an algebra of information, describing basic modes of information processing. Such an algebra involves several formalisms of computer science, which seem to be different on the surface: relational databases, multiple systems of formal logic or numerical problems of linear algebra. It allows the development of generic procedures of information processing and thus a unification of basic methods of computer science, in particular of distributed information processing. Information relates to precise questions, comes from different sources, must be aggregated, and can be focused on questions of interest. Starting from these considerations, information algebras are two-sorted algebras , where is a semigroup, representing combination or aggregation of information, is a lattice of domains (related to questions) whose partial order reflects the granularity of the domain or the question, and a representing focusing or extraction of information. (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
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
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
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
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
Linear algebra: Prove the Sherman-Morrison formula for computing a matrix inverse
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
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
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)
10A An Introduction to Eigenvalues and Eigenvectors
A short description of eigenvalues and eigenvectors.
From playlist Linear Algebra
Elliptic Curves - Lecture 3 - An introduction to Algebraic Geometry (part 1)
This video is part of a graduate course on elliptic curves that I taught at UConn in Spring 2021. The course is an introduction to the theory of elliptic curves. More information about the course can be found at the course website: https://alozano.clas.uconn.edu/math5020-elliptic-curves/
From playlist An Introduction to the Arithmetic of Elliptic Curves
Tom Leinster : The categorical origins of entropy
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 29, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
From playlist NPTEL : Probability and Stochastics for Finance
Workshop 1 "Operator Algebras and Quantum Information Theory" - CEB T3 2017 - L.Gao
Li Gao (UIUC) / 11.09.17 Title:Operator Algebras Aspects of Quantum Teleportation and Superdense Coding Abstract: Quantum teleportation and superdense coding are fundamental protocols in quantum information theory. They together describe the resource trade-off between quantum communicati
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Duality between estimation and control - Sanjoy Mitter
PROGRAM: Data Assimilation Research Program Venue: Centre for Applicable Mathematics-TIFR and Indian Institute of Science Dates: 04 - 23 July, 2011 DESCRIPTION: Data assimilation (DA) is a powerful and versatile method for combining observational data of a system with its dynamical mod
From playlist Data Assimilation Research Program
Homeschool Pre-Algebra - What Every Homeschool Parent Needs to Know
TabletClass Math Homeschool: https://tabletclass.com/ How to homeschool Pre-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 Pre-Algebra
Ewin Tang - On quantum linear algebra for machine learning - IPAM at UCLA
Recorded 25 January 2022. Ewin Tang of the University of Washington presents "On quantum linear algebra for machine learning" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: We will discuss quantum singular value transformation (QSVT), a simple unifying framework for quantum
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Xiang Tang: Cyclic Cocycles for Proper Lie Group Actions
Talk by Xiang Tang in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on February 23, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
IGA: Singularities of Hermitian Yang Mills Connections
After introducing some background about stable bundles and HYM connections, I will explain both the analytic and algebraic sides when studying singularities of HYM connections. It turns out that local algebraic invariants can be extracted to characterize the analytic side. In particular, t
From playlist Informal Geometric Analysis Seminar
Determining if a vector is a linear combination of other vectors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors
From playlist Linear Algebra
Sam is 10 yrs older than his sister. Next year he will be twice as old. How old is Sam now?
How to solve an algebra age word problem. 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 and quizzes. All c
From playlist GED Prep Videos