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
Geometry - Ch. 2: Reasoning and Proofs (12 of 46) What is Inductive Reasoning?
Visit http://ilectureonline.com for more math and science lectures! In this video I will review inductive reasoning (from previous videos) and its advantages and weaknesses. Inductive reasoning is used by 1) finding a pattern, and 2) perform observations (examples or trends) in order to d
From playlist GEOMETRY CH 2 PROOFS & REASONING
The Riemann Hypothesis and a New Math Tool (a new Indeterminate form)
In this video, you will see a mistake made by many(*) mathematicians. Also, you will see a simple proof for a new(**) indeterminate form that has an incredible connection to the Riemann hypothesis. Lastly, you will see a route to a new promising math tool to solve problems like the Rieman
From playlist Summer of Math Exposition 2 videos
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
Mathematical Induction Divisibility Proof (1 of 3: What is inductive logic?)
More resources available at www.misterwootube.com
From playlist Introduction to Proof by Mathematical Induction
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
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
Dale Miller: Focused proof systems
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual
From playlist Logic and Foundations
Damiano Mazza: Heterodox exponential modalities in linear logic
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual
From playlist Logic and Foundations
Discussion - Panel: What is the role of Topos in Information and Communication Technologies?
Mérouane Debbah (Huawei Technologies) Olivia Caramello (Università degli Studi dell'Insubria in Como) Daniel Bennequin (Univ. Paris-Diderot) Thierry Coquand (University of Göteborg) Jean-Claude Belfiore (Huawei France)
From playlist 4th Huawei-IHES Workshop on Mathematical Theories for Information and Communication Technologies
Difficulties with real numbers as infinite decimals ( I) | Real numbers + limits Math Foundations 91
There are three quite different approaches to the idea of a real number as an infinite decimal. In this lecture we look carefully at the first and most popular idea: that an infinite decimal can be defined in terms of an infinite sequence of digits appearing to the right of a decimal point
From playlist Math Foundations
Will Troiani - Introduction to proof nets (Part 1)
In the first of several talks on linear logic and proof nets, building towards the proof of the sequentialisation theorem, Will introduces the sequent calculus of multiplicative linear logic, proof structures and the translation between them. Lecture notes - https://cglseminar.github.io/n
From playlist Computation, Geometry, Logic seminar
Model Theory - part 06 - Quantifiers as Adjoints
In this video we start to talk about how one can view quantifiers as adjoints of certain functors.
From playlist Model Theory
Linear regression (5): Bias and variance
Inductive bias; variance; relationship to over- & under-fitting
From playlist cs273a
Klaus Mainzer: Constructivity and Computability. Perspectives for Mathematics [...]
Title: Klaus Mainzer: Constructivity and Computability. Perspectives for Mathematics, Computer Science, and Philosophy The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: Since antiquity, mathematical proofs were realized by
From playlist Workshop: "Constructive Mathematics"
Hugo Herbelin: A constructive proof of dependent choice, compatible with classical logic
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: Martin-Löf's type theory has strong existential elimination (dependent sum type) what allows to prove the full axiom of choice. However the theory is intuitionistic. We give
From playlist Workshop: "Constructive Mathematics"
Unpredictability, Undecidability, and Uncomputability
Quite a number of mathematical theorems prove that the power of mathematics has its limits. But how relevant are these theorems for science? In this video I want to briefly summarize an essay that I just submitted to the essay contest of the Foundational Questions Institute. This year the
From playlist Philosophy of Science
Mathematical Induction - Inequalities (4 of 4: Manipulating the inductive hypothesis)
More resources available at www.misterwootube.com
From playlist Introduction to Proof by Mathematical Induction
Proof synthesis and differential linear logic
Linear logic is a refinement of intuitionistic logic which, viewed as a functional programming language in the sense of the Curry-Howard correspondence, has an explicit mechanism for copying and discarding information. It turns out that, due to these mechanisms, linear logic is naturally r
From playlist Talks