Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the equational theory of the two values 0 and 1 (whose interpretation need not be numerical). Common to Boolean algebras, groups, and vector spaces is the notion of an algebraic structure, a set closed under some operations satisfying certain equations. Just as there are basic examples of groups, such as the group of integers and the symmetric group Sn of permutations of n objects, there are also basic examples of Boolean algebras such as the following. * The algebra of binary digits or bits 0 and 1 under the logical operations including disjunction, conjunction, and negation. Applications include the propositional calculus and the theory of digital circuits. * The algebra of sets under the set operations including union, intersection, and complement. Applications are far-reaching because set theory is the standard foundations of mathematics. Boolean algebra thus permits applying the methods of abstract algebra to mathematical logic and digital logic. Unlike groups of finite order, which exhibit complexity and diversity and whose first-order theory is decidable only in special cases, all finite Boolean algebras share the same theorems and have a decidable first-order theory. Instead, the intricacies of Boolean algebra are divided between the structure of infinite algebras and the algorithmic complexity of their syntactic structure. (Wikipedia).
Boolean Algebra 2 – Simplifying Complex Expressions
This video follows on from the one about the laws of Boolean algebra. It explains some useful interpretations of the laws of Boolean algebra, in particular, variations of the annulment and distributive laws. It goes on to demonstrate how Boolean algebra can be applied to simplify comple
From playlist Boolean Algebra
Boolean Algebra: Sample Problems
In this video, I work through some sample problems relating to Boolean algebra. Specific, I work through examples of translating equivalences from logical or set notation to Boolean notation, and also a derivation using Boolean equivalences.
From playlist Discrete Mathematics
Boolean Algebra 1 – The Laws of Boolean Algebra
This computer science video is about the laws of Boolean algebra. It briefly considers why these laws are needed, that is to simplify complex Boolean expressions, and then demonstrates how the laws can be derived by examining simple logic circuits and their truth tables. It also shows ho
From playlist Boolean Algebra
Francesco Ciraulo: Notions of Booleanization in pointfree Topology
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: Boolean algebras play a key role in the foundations of classical mathematics. And a similar role is played by Heyting algebras for constructive mathematics. But this is
From playlist Workshop: "Constructive Mathematics"
A Quick Overview of BOOLEAN ALGEBRA (symbols, truth tables, and laws)
Error in Video (9:32, 11:30): When talking about the last laws in the columns for equivalences, I say "DeMorgan's Law" when I mean to say "Distributive Law". In this video on #Logic, we learn the basics of #BooleanAlgebra and compare the notation for propositional logic with it. We cover
From playlist Logic in Philosophy and Mathematics
From playlist Week 1 2015 Shorts
The Algebra of Boole is not Boolean algebra! (III) | Math Foundations 257 | N J Wildberger
We continue discussing George Boole's original algebra which can be framed as arithmetic over the bifield B_2={0,1} and vector spaces/algebra over it. We have seen how to reformulate Aristotle's syllogistic construction in terms of Boole's algebra, and use simple algebra to prove his syllo
From playlist Boole's Logic and Circuit Analysis
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
Boolean function analysis: beyond the Boolean cube (continued) - Yuval Filmus
http://www.math.ias.edu/seminars/abstract?event=129061 More videos on http://video.ias.edu
From playlist Mathematics
10/18/18 Konstantin Mischaikow
A Combinatorial/Algebraic Topological Approach to Nonlinear Dynamics
From playlist Fall 2018 Symbolic-Numeric Computing
Canonical forms for logic circuits | Math Foundations 263 | N J Wildberger
A key problem in circuit analysis is to associate to a logical circuit, typically made of logic gates such as AND, OR, NOT, XOR, NAND and NOR, an algebraic expression that captures the effect of that circuit on all possible inputs. Such an effect is called a Boolean function, and it acts o
From playlist Boole's Logic and Circuit Analysis
Matthew Foreman: Welch games to Laver ideals
Recorded during the meeting "XVI International Luminy Workshop in Set Theory" the September 16, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Au
From playlist Logic and Foundations
MathZero, The Classification Problem, and Set-Theoretic Type Theory - David McAllester
Seminar on Theoretical Machine Learning Topic: MathZero, The Classification Problem, and Set-Theoretic Type Theory Speaker: David McAllester Affiliation: Toyota Technological Institute at Chicago Date: May 14, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Reconstruction of arithmetic circuits by Chandan Saha
Discussion Meeting Workshop on Algebraic Complexity Theory ORGANIZERS: Prahladh Harsha, Ramprasad Saptharishi and Srikanth Srinivasan DATE: 25 March 2019 to 29 March 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Algebraic complexity aims at understanding the computational aspects o
From playlist Workshop on Algebraic Complexity Theory 2019
Live CEOing Ep 163: Geometric Computing in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Geometric Computing in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Chi-Keung Ng: Ortho-sets and Gelfand spectra
Talk by Chi-Keung Ng in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on June 9, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
This is Lecture 23 of the COMP300E (Programming Challenges) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Hong Kong University of Science and Technology in 2009. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/programmingchallenges
From playlist COMP300E - Programming Challenges - 2009 HKUST
David McAllester - Dependent Type Theory from the Perspective of Mathematics, Physics, and (...)
Dependent type theory imposes a type system on Zemelo-Fraenkel set theory (ZFC). From a mathematics and physics perspective dependent type theory naturally generalizes the Bourbaki notion of structure and provides a universal notion of isomorphism and symmetry. This comes with a universal
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Replacing truth tables and Boolean equivalences | MathFoundations274 | N J Wildberger
While Propositional Logic is a branch of philosophy, concerned with systematizing reasoning using connectives such as AND, OR, NOT, IMPLIES and EQUIVALENT, the Algebra of Boole provides a mathematical framework for modelling some of this. With this approach we ignore the issue of the mean
From playlist Boole's Logic and Circuit Analysis