Boolean algebra (structure)

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

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 Values

From playlist Week 1 2015 Shorts

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

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

Algebraic Structures: Groups, Rings, and Fields

This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.

From playlist Abstract Algebra

The Algebra of Boole is not Boolean Algebra! (II) | Math Foundations 256 | 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

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

The Monomial Structure of Boolean Functions - Shachar Lovett

Workshop on Additive Combinatorics and Algebraic Connections Topic: The Monomial Structure of Boolean Functions Speaker: Shachar Lovett Affiliation: University of California, San Diego Date: October 25, 2022  Let f:0,1n to 0,1 be a boolean function. It can be uniquely represented as a mu

From playlist 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

Stable and NIP regularity in groups - G. Conant - Workshop 1 - CEB T1 2018

Gabriel Conant (Notre Dame) / 01.02.2018 We use local stability theory to prove a group version of Szemer´edi regularity for stable subsets of finite groups. Toward generalizing this result to the NIP setting, we consider definable set systems of finite VC-dimension in pseudofinite groups

From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields

4.2.1 Sum of Products

MIT 6.004 Computation Structures, Spring 2017 Instructor: Chris Terman View the complete course: https://ocw.mit.edu/6-004S17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62WVs95MNq3dQBqY2vGOtQ2 4.2.1 Sum of Products License: Creative Commons BY-NC-SA More informati

From playlist MIT 6.004 Computation Structures, Spring 2017

What We've Learned from NKS Chapter 12: The Principle of Computational Equivalence [Part 2]

In this episode of "What We've Learned from NKS", Stephen Wolfram is counting down to the 20th anniversary of A New Kind of Science with [another] chapter retrospective. If you'd like to contribute to the discussion in future episodes, you can participate through this YouTube channel or th

From playlist Science and Research Livestreams

Tame topologies in non-archimedean geometry - Abhishek Oswal

Short Talks by Postdoctoral Members Topic: Tame topologies in non-archimedean geometry Speaker: Abhishek Oswal Affiliation: Member, School of Mathematics Date: September 25, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Wolfram Physics Project: Working Session Sept. 15, 2020 [Physicalization of Metamathematics]

This is a Wolfram Physics Project working session on metamathematics and its physicalization in the Wolfram Model. Begins at 10:15 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

From playlist Wolfram Physics Project Livestream Archive

Anna Marie Bohmann: Assembly in the Algebraic K-theory of Lawvere Theories

Talk by Anna Marie Bohmann in Global Noncommutative Geometry Seminar (Americas), https://globalncgseminar.org/talks/tba-30/, on April 29, 2022.

From playlist Global Noncommutative Geometry Seminar (Americas)

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

Squashing theories into Heyting algebras

This is the first of two videos on Heyting algebra, Tarski-Lindenbaum and negation: https://gist.github.com/Nikolaj-K/1478e66ccc9b7ac2ea565e743c904555 Followup video: https://youtu.be/ws6vCT7ExTY

From playlist Logic