Set Theory (Part 7): Natural Numbers and Induction
Please feel free to leave comments/questions on the video and practice problems below! In this video, I discuss the von Neumann construction of the natural numbers and relate the idea of natural numbers to inductive sets. The axiom of infinity is also introduced here as one of the ZFC axi
From playlist Set Theory by Mathoma
Applications of additive combinatorics to Diophantine equations - Alexei Skorobogatov
Alexei Skorobogatov Imperial College London April 10, 2014 The work of Green, Tao and Ziegler can be used to prove existence and approximation properties for rational solutions of the Diophantine equations that describe representations of a product of norm forms by a product of linear poly
From playlist Mathematics
Berry's Paradox - An Algorithm For Truth
Go to https://expressvpn.com/upandatom and find out how you can get 3 months free. Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collections/up-and-at
From playlist Math
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
MIT 6.868J The Society of Mind, Fall 2011 View the complete course: http://ocw.mit.edu/6-868JF11 Instructor: Marvin Minsky In this lecture, students discuss Chapter 4 of The Emotion Machine, covering topics such as the relationship between pain, hurt, and perception, and how the mind expl
From playlist MIT 6.868J The Society of Mind, Fall 2011
Avi Wigderson: Randomness and pseudorandomness
Abstract: The talk is aimed at a general audience, and no particular background will be assumed. Is the universe inherently deterministic or probabilistic? Perhaps more importantly - can we tell the difference between the two? Humanity has pondered the meaning and utility of randomness fo
From playlist Abel Lectures
Unpredictability - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Shannon 100 - 27/10/2016 - Jean Louis DESSALLES
Information, simplicité et pertinence Jean-Louis Dessalles (Télécom ParisTech) Claude Shannon fonda la notion d’information sur l’idée de surprise, mesurée comme l’inverse de la probabilité (en bits). Sa définition a permis la révolution des télécommunications numériques. En revanche, l’
From playlist Shannon 100
Marvin Minsky Toshiba Professor of Media Arts and Sciences and Computer Science and Engineering, emeritus Head, Society of Mind Group Marvin Minsky was the Toshiba professor of media arts and sciences and computer science and engineering emeritus at MIT. Professor Minsky was a pioneer in
From playlist AI talks
Ulrich Berger: On the Computational content of Brouwer's Theorem
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: The usual formulation of Brouwer's Theorem ('every bar is inductive')involves quantification over infinite sequences of natural numbers. We propose an alternative formulation
From playlist Workshop: "Constructive Mathematics"
Transcendental numbers powered by Cantor's infinities
In today's video the Mathologer sets out to give an introduction to the notoriously hard topic of transcendental numbers that is both in depth and accessible to anybody with a bit of common sense. Find out how Georg Cantor's infinities can be used in a very simple and off the beaten track
From playlist Recent videos
HSC Science Extension Module 1 Induction and Deduction
HSC Science Extension Module 1 Foundations of Scientific Thinking Induction and Deduction
From playlist Y12 Sci Ex Mod 1 Foundations of Scientific Thinking
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Oxford 4b The Argument Concerning Induction
A course by Peter Millican from Oxford University. Course Description: Dr Peter Millican gives a series of lectures looking at Scottish 18th Century Philosopher David Hume and the first book of his Treatise of Human Nature. Taken from: https://podcasts.ox.ac.uk/series/introduction-david
From playlist Oxford: Introduction to David Hume's Treatise of Human Nature Book One | CosmoLearning Philosophy
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Precalculus 11.5a - Mathematical Induction
Mathematical Induction. First in a short series of videos. From the Precalculus class taught by Derek Owens. These are older videos, from the original course, posted by request.
From playlist Precalculus Chapter 11 (Selected videos)
Petra Hozzova - Automation of Induction in Saturation - IPAM at UCLA
Recorded 17 February 2023. Petra Hozzova of Technische Universität Wien, Institute of Logic and Computation, presents "Automation of Induction in Saturation" at IPAM's Machine Assisted Proofs Workshop. Abstract: Induction in saturation-based first-order theorem proving is a new exciting di
From playlist 2023 Machine Assisted Proofs Workshop
Introducing Infinity | Set Theory, Section 3.1
In this video we define inductive sets, the natural numbers, the axiom of infinity, and the standard order relation on the natural numbers. My Twitter: https://twitter.com/KristapsBalodi3 Intro (0:00) Defining Natural Numbers as Sets (1:19) Definition of Inductive Sets (5:07) The Axiom o
From playlist Axiomatic Set Theory