Arithmetic | Model theory | Mathematical logic | Formal theories of arithmetic
In mathematical logic, a non-standard model of arithmetic is a model of (first-order) Peano arithmetic that contains non-standard numbers. The term standard model of arithmetic refers to the standard natural numbers 0, 1, 2, …. The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934). (Wikipedia).
Regularity and non-standard models of arithmetic #PaCE1
Follow-up video: https://youtu.be/7HKnOOvssvs Discussed text, including all links: https://gist.github.com/Nikolaj-K/101c2712dc832dec4991bf568869abc8 Curt's call: https://youtu.be/V93GQaDtv8w Timestamps: 00:00:00 Introduction 00:02:55 Wittgenstein and predicates (optional) 00:11:12 Skolems
From playlist Logic
What are Non-Classical logics?
Some of the general classes of non-classical logics I touch in this videos are linear logic, relevant logic, modal logic, many-valued logics, minimal logic, paraconsistent logics and so on and so forth. Let me know if I should dive deeping into a certain scene? https://en.wikipedia.org/wi
From playlist Programming
The mostly absent theory of real numbers|Real numbers + limits Math Foundations 115 | N J Wildberger
In this video we ask the question: how do standard treatments of calculus and analysis deal with the vexatious issue of defining real numbers and their supposed arithmetic?? We pull out a selection of popular Calculus and Analysis texts, and go through them with a view of finding out: wha
From playlist Math Foundations
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
Coordinate Systems From Non-Standard Bases | Definitions + Visualization
We've all used the standard coordinate system where (x,y) means x to the right and y up. However, for any subspace and a basis of that subspace, we can define a coordinate system. The same vector can thus be written in multiple coordinate systems. We describe what exactly we mean by this,
From playlist Linear Algebra (Full Course)
Pre-Calculus - The vocabulary of linear functions and equations
This video will introduce you to a few of the terms that are commonly used with linear functions and equations. Pay close attention to how you can tell the difference between linear and non-linear functions. For more videos please visit http://www.mysecretmathtutor.com
From playlist Pre-Calculus
Standard Error of the Estimate used in Regression Analysis (Mean Square Error)
An example of how to calculate the standard error of the estimate (Mean Square Error) used in simple linear regression analysis. This typically taught in statistics. Like us on: http://www.facebook.com/PartyMoreStud... Link to Playlist on Regression Analysis http://www.youtube.com/cour
From playlist Linear Regression.
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
Yifeng Liu - Derivative of L-functions for unitary groups (3/3)
In this lecture series, we will focus on the recent advance on the Beilinson-Bloch conjecture for unitary Shimura varieties, more precisely, a Gross-Zagier type formula for automorphic forms on unitary groups of higher ranks. We will start from the general theory of height pairings between
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Linear Algebra for the Standard C++ Library
Linear algebra is a mathematical discipline of ever-increasing importance in today's world, with direct application to a wide variety of problem domains, such as signal processing, computer graphics, medical imaging, machine learning, data science, financial modeling, and scientific simula
From playlist C++
Foundations S2 - Seminar 7 - Nonstandard models of arithmetic
A seminar series on the foundations of mathematics, by Will Troiani and Billy Snikkers. In this lecture Billy uses ultrafilters to construct nonstandard models of arithmetic, the hypernaturals. Near the end is some discussion of how to read this as talking about the limits of first order l
From playlist Foundations seminar
Using nonstandard natural numbers in Ramsey Theory - M. Di Nasso - Workshop 1 - CEB T1 2018
Mauro Di Nasso (Pisa) / 01.02.2018 In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Fin Math L8-1: The EU Call in the Bachelier Model
Welcome to Financial Mathematics. In the 8th lesson we consider different topics. In this first video we look at the value of a EU call, when we change the underlying stochastic process. In particular, we will consider the case of the Bachelier model, in which the Geometric Brownian motio
From playlist Financial Mathematics
This is part of a series of lectures on the Zermelo-Fraenkel axioms for set theory. We discuss the axiom of infinity, and give some examples of models where it does not hold. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52EKVgPi-p50fRP2_SbG
From playlist Zermelo Fraenkel axioms
Efficient Zero Knowledge Proofs - A Modular Approach (Lecture 2) by Yuval Ishai
DISCUSSION MEETING : FOUNDATIONAL ASPECTS OF BLOCKCHAIN TECHNOLOGY ORGANIZERS : Pandu Rangan Chandrasekaran DATE : 15 to 17 January 2020 VENUE : Madhava Lecture Hall, ICTS, Bangalore Blockchain technology is among one of the most influential disruptive technologies of the current decade.
From playlist Foundational Aspects of Blockchain Technology 2020
Arithmetic theta series - Stephan Kudla
Workshop on Representation Theory and Analysis on Locally Symmetric Spaces Topic: Arithmetic theta series Speaker: Stephan Kudla Affiliation: University of Toronto Date: March 8, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Wolfram Physics Project: Working Session Tuesday, Nov. 2, 2021 [Topos Theory]
This is a Wolfram Physics Project working session about Topos Theory in the Wolfram Model. 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 announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
Parametric and nonparametric tests
Parametric tests are most commonly used in healthcare research. They include tests such as Student's t-test and ANOVA. There is, however a rich set of non-parametric tests that are much more appropriate to use in certain circumstances.
From playlist Learning medical statistics with python and Jupyter notebooks