Boolean algebra | Algebraic logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847), and set forth more fully in his An Investigation of the Laws of Thought (1854).According to Huntington, the term "Boolean algebra" was first suggested by Sheffer in 1913, although Charles Sanders Peirce gave the title "A Boolean Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880.Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics. (Wikipedia).
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
From playlist Week 1 2015 Shorts
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 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
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
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
The Algebra of Boole is not Boolean Algebra! (I) | Math Foundations 255 | N J Wildberger
We begin to introduce the Algebra of Boole, starting with the bifield of two elements, namely {0,1}, and using that to build the algebra of n-tuples, which is a linear space over the bifield with an additional multiplicative structure. This important abstract development played a key role
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
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
mod-25 lec-26 Introduction to Fluid Logic
Fundamentals of Industrial Oil Hydraulics and Pneumatics by Prof. R.N. Maiti,Department of Mechanical Engineering,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Fundamentals of Industrial Oil Hydraulics and Pneumatics (CosmoLearning Mechanical Engineering)
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"
Kurusch EBRAHIMI-FARD - Wick Products and Combinatorial Hopf Algebras
Wick products play a central role in both quantum field theory and stochastic calculus. They originated in Wick’s work from 1950. In this talk we will describe Wick products using combinatorial Hopf algebra. Based on joint work with F. Patras, N. Tapia, L. Zambotti. https://indico.math.c
From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday
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
EEVacademy #2 - Digital Logic Boolean & Demorgan's Theorems
Boolean Algebra & Demorgan's Theorems explained and how they are useful for circuit simplification. EEVblog Main Web Site: http://www.eevblog.com The 2nd EEVblog Channel: http://www.youtube.com/EEVblog2 Support the EEVblog through Patreon! http://www.patreon.com/eevblog EEVblog Amazon
From playlist EEVacademy
Boolean Algebra 3 – De Morgan’s Theorem
This video follows on from the one about simplifying complex Boolean expressions using the laws of Boolean algebra. In particular this video covers De Morgan’s theorem and how it can be applied, along with the other laws, to simplify complex Boolean expressions. It includes worked exampl
From playlist Boolean Algebra