Intuitionism | Constructivism (mathematics) | Formal theories of arithmetic
In mathematical logic, Heyting arithmetic is an axiomatization of arithmetic in accordance with the philosophy of intuitionism. It is named after Arend Heyting, who first proposed it. (Wikipedia).
Albert Visser: The absorption law for slow provability
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: The absorption law for slow provability states that, if it is provable that A is slowly provable, then A is provable. We give a simple proof of the absorption law for a v
From playlist Workshop: "Proofs and Computation"
Model Theory - part 04 - Posets, Lattices, Heyting Algebras, Booleans Algebras
This is a short video for people who haven't seen a Heyting algebras before. There is really nothing special in it that doesn't show up in wikipedia or ncatlab. I just wanted to review it before we use them. Errata: *at 3:35: there the law should read (a and (a or b) ), not (a and (a and
From playlist Model Theory
Ihsen Yengui: Algorithms for computing syzygies over VX 1,…,X n, V a valuation ring
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: I will present a general algorithm for computing a finite generating set for the syzygies of any finitely generated ideal of V[X_1,...,X_k] (V a valuation domain) which does
From playlist Workshop: "Constructive Mathematics"
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"
Using Clocks to Solve Fractions String 8
A fun string dealing with subtraction that leads to sixths and twelfths
From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents
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
This is a follow up to https://youtu.be/lDhKE2SKF08. In this video we zoom in on Negation and also discuss models such as the 3-valued one for intuitionistic propositional logic. The script I'm using you can find here: https://gist.github.com/Nikolaj-K/1478e66ccc9b7ac2ea565e743c904555
From playlist Logic
Using Clocks to Solve Fractions String 6
Here we use the clock model to deal with 3/18 and 3/9
From playlist Arithmetic and Pre-Algebra: Fractions, Decimals and Percents
Review of arithmetic with decimals II | Year 9 Maths 5 | NJ Wildberger
We continue our review or arithmetic with decimal numbers. How do we multiply two decimal numbers? How do we divide one decimal number by another? The trick is to realize that by suitably multiplying and dividing by powers of 10, these problems essentially reduce to arithmetic with ordinar
From playlist Year9Maths
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
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
I this video I show you how to create mathematical variables and how to do matrix arithmetic. This includes multiplication with scalars and proper matrix multiplication. This requires you to know the dimensions of the matrices, which can be determined using the .shape method.
From playlist Modern linear algebra using Python instead of a textbook
Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences
Geometric/arithmetic theta correspondences provide correspondences between automorphic forms and cohomology classes/algebraic cycles on Shimura varieties. I will give an introduction focusing on the example of unitary groups and highlight recent advances in the arithmetic theory (also know
From playlist 2022 Summer School on the Langlands program
Profinite Completions and Representation Rigidity - Ryan Spitler
Arithmetic Groups Topic: Profinite Completions and Representation Rigidity Speaker: Ryan Spitler Affiliation: Rice University Date: February 02, 2022 Taking up the terminology established in the first lecture, in 1970 Grothendieck showed that when two groups (G,H) form a Grothendieck pai
From playlist Mathematics
Logic 7 - First Order Logic | Stanford CS221: AI (Autumn 2021)
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai Associate Professor Percy Liang Associate Professor of Computer Science and Statistics (courtesy) https://profiles.stanford.edu/percy-liang Assistant Professor
From playlist Stanford CS221: Artificial Intelligence: Principles and Techniques | Autumn 2021
Arithmetic Sequences and Arithmetic Series - Basic Introduction
This video provides a basic introduction into arithmetic sequences and series. It explains how to find the nth term of a sequence as well as how to find the sum of an arithmetic sequence. It also discusses how to distinguish a finite sequence from an infinite series. It also includes a
From playlist New Precalculus Video Playlist
ʕ•ᴥ•ʔ Arithmetic Sequences and Series Problems and Examples
Quickly master how to solve arithmetic series. Watch more lessons like this and try our practice at https://www.studypug.com/algebra-help/sequences-and-series/arithmetic-series An arithmetic series is the sum of an arithmetic sequence. In this lesson, we will learn how to solve problems
From playlist AccuPlacer Exam Prep