Mathematical proofs | Model theory | Articles containing proofs
In mathematical logic, especially set theory and model theory, the back-and-forth method is a method for showing isomorphism between countably infinite structures satisfying specified conditions. In particular it can be used to prove that * any two countably infinite densely ordered sets (i.e., linearly ordered in such a way that between any two members there is another) without endpoints are isomorphic. An isomorphism between linear orders is simply a strictly increasing bijection. This result implies, for example, that there exists a strictly increasing bijection between the set of all rational numbers and the set of all real algebraic numbers. * any two countably infinite atomless Boolean algebras are isomorphic to each other. * any two equivalent countable atomic models of a theory are isomorphic. * the Erdős–Rényi model of random graphs, when applied to countably infinite graphs, always produces a unique graph, the Rado graph. * any two many-complete recursively enumerable sets are recursively isomorphic. (Wikipedia).
How to Solve a Recurrence Relation using Backtracking: a_n = 2a_(n-1)
In this video I go through the steps of solving a recurrence relation using something called backtracking. This is a simple example so if you are new to this it may be useful. This is something you typically see in a discrete math class. I hope this video helps someone:)
From playlist Recurrence Relations
Solving equations by "working backwards"
There are lots of ways to think about how to solve an equation. This video demonstrates the "Working backwards" technique. For more videos, please visit http://www.MathVillage.info
From playlist All about Expressions and Equations
Convergence of Newton's Method | Lecture 17 | Numerical Methods for Engineers
Calculation of the order of convergence of Newton's method. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?s
From playlist Numerical Methods for Engineers
Using mathematical induction to prove a formula
👉 Learn how to apply induction to prove the sum formula for every term. Proof by induction is a mathematical proof technique. It is usually used to prove that a formula written in terms of n holds true for all natural numbers: 1, 2, 3, . . . To prove by induction, we first show that the f
From playlist Sequences
8: Shifted Inverse Power Method - Learning Linear Algebra
Full Learning Linear Algebra playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs Find eigenvalues and eigenvectors with this modified form of the power method! With the shifted inverse power method, we can find the eigenvalue closest to any number, instead of
From playlist Awesome Concept Explanations
Interpolation | Lecture 43 | Numerical Methods for Engineers
An explanation of interpolation and how to perform piecewise linear interpolation. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.yout
From playlist Numerical Methods for Engineers
Order of Convergence |Lecture 16 | Numerical Methods for Engineers
Definition of the order of convergence of a root-finding method. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchas
From playlist Numerical Methods for Engineers
8: Eigenvalue Method for Systems - Dissecting Differential Equations
How to find eigenvalues: https://youtu.be/hpE9Iom55N0 When we start looking at how multiple quantities change, we get systems of differential equations. What do we use for systems of equations? Linear algebra, of course! Full dissecting differential equations playlist: https://www.youtub
From playlist Dissecting Differential Equations
Amartya Banerjee - Electronic Structure Calculations of Chiral Matter - IPAM at UCLA
Recorded 03 May 2022. Amartya Banerjee of the University of California, Los Angeles, presents "Electronic Structure Calculations of Chiral Matter - From First Principles Methods to Machine Learning Techniques" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop.
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Lecture 15 (CEM) -- Finite-Difference Time-Domain
This lecture introduces the finite-difference time-domain method. It includes the basic method, derivation of the update equations, and some implementation issues such as Fourier transforms and calculation of transmittance and reflectance. This lecture is NOT intended to leave the studen
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
Computer Vision in the Study of Art
(January 13, 2012) David Stork describes how we can use computers and computer generated imagery to gain a better understanding of paintings and other forms of art. Stanford University: http://www.stanford.edu/ Stanford School of Engineering: http://engineering.stanford.edu/ Stanford CS
From playlist Lecture Collection | Human-Computer Interaction Seminar (2011-2012)
Numerical Hydrodynamics: Part 3 by Ian Hawke
PROGRAM: GRAVITATIONAL WAVE ASTROPHYSICS (ONLINE) ORGANIZERS : Parameswaran Ajith, K. G. Arun, Sukanta Bose, Bala R. Iyer, Resmi Lekshmi and B Sathyaprakash DATE: 18 May 2020 to 22 May 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been cancelled. Howe
From playlist Gravitational Wave Astrophysics (Online) 2020
MACHINE SHOP TIPS #99 Aligning Lathe Centers TEST BAR METHOD tubalcain
Tubalcain aligns the centers on an ATLAS lathe using the "test bar method".
From playlist #1 MACHINE SHOP TIPS tubalcain playlist #1 thru #100
Valuation Approaches & Paradigms Part 3: TEEB@YALE
Valuation approaches & paradigms; Biophysical approaches; the Total Economic Value (TEV) framework & its various valuation methods; acknowledging uncertainties in valuation ; Insurance value and Resilience ; Quasi-Option Values ; Valuation across Stakeholders ; Valuation in developing coun
From playlist TEEB @ Yale
Coding Math: Episode 44 - Kinematics Part II
This week we wrap up forward kinematics, creating a fairly realistic walk cycle. Support Coding Math: http://patreon.com/codingmath Source Code: http://github.com/bit101/codingmath
From playlist Episodes
17. Bonjour, NSStream, GameKit
(March 2, 2010) Alan Cannistraro covers networking: automatic configuration in Bonjour, asynchronous communication in NSStream, and GameKit. Part of Stanford's Winter Quarter 2010 iPhone Application Development (CS193P) course. Stanford University: http://www.stanford.edu/ Stanfo
From playlist Lecture Collection | iPhone Application Development (Winter 2010)
Physics Students Need to Know These 5 Methods for Differential Equations
Differential equations are hard! But these 5 methods will enable you to solve all kinds of equations that you'll encounter throughout your physics studies. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up Sign up for my newsletter for additional physics les
From playlist Physics Help Room
Differential Equations: Separation of Variables
This video provides several examples of how to solve a DE using the technique of separation of variables. website: http://mathispower4u.com blog: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
Professor Mark Girolami: "Probabilistic Numerical Computation: A New Concept?"
The Turing Lectures: The Intersection of Mathematics, Statistics and Computation - Professor Mark Girolami: "Probabilistic Numerical Computation: A New Concept?" Click the below timestamps to navigate the video. 00:00:09 Introduction by Professor Jared Tanner 00:01:38 Profess
From playlist Turing Lectures