Algebraic Structures: Groups, Rings, and Fields
This video covers the definitions for some basic algebraic structures, including groups and rings. I give examples of each and discuss how to verify the properties for each type of structure.
From playlist Abstract Algebra
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
Sets and other data structures | Data Structures in Mathematics Math Foundations 151
In mathematics we often want to organize objects. Sets are not the only way of doing this: there are other data types that are also useful and that can be considered together with set theory. In particular when we group objects together, there are two fundamental questions that naturally a
From playlist Math Foundations
Data structures: Introduction to Trees
See complete series on data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P In this lesson, we have described tree data structure as a logical model in computer science. We have briefly discussed tree as a non-linear hierarchical data structure, i
From playlist Data structures
An introduction to the general types of logic statements
From playlist Geometry
Graph Data Structure 1. Terminology and Representation (algorithms)
This is the first in a series of videos about the graph data structure. It mentions the applications of graphs, defines various terminology associated with graphs, and describes how a graph can be represented programmatically by means of adjacency lists or an adjacency matrix.
From playlist Data Structures
Fun with lists, multisets and sets IV | Data structures in Mathematics Math Foundations 161
In this video we complete our initial discussion of the four types of basic data structures by describing sets, which are unordered and without repetition. As usual we restrict ourselves to very concrete and specific examples: k-sets from n, where k is a natural number or zero, and n is a
From playlist Math Foundations
Arithmetical expressions as natural numbers | Data structures in Mathematics Math Foundations 194
Primitive natural numbers and Hindu Arabic numerals can be pinned down very concretely and precisely. But what about numbers expressed via more elaborate arithmetical expressions, perhaps involving towers of exponents, or hyperoperations? Is there a consistent and logical proper way of set
From playlist Math Foundations
SHM - 16/01/15 - Constructivismes en mathématiques - Thierry Coquand
Thierry Coquand (Université de Gothenburg), « Théorie des types et mathématiques constructives »
From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques
Stanford Seminar - On the Origin of Experience: The Shaping of Sense and the Complex World
"On the Origin of Experience: The Shaping of Sense and the Complex World" -Steven Ericsson-Zenith Colloquium on Computer Systems Seminar Series (EE380) presents the current research in design, implementation, analysis, and use of computer systems. Topics range from integrated circuits to
From playlist Engineering
Type Systems - Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study November 21, 2012
From playlist Mathematics
What are the basics of mathematical logic? | Intro to Math Structures VS1.1
So you want to prove things? Where do you start if you haven't ever written a proof before? In most cases, a course on discrete mathematics or mathematical structures is where someone writes their first proof and that starts with propositional calculus. In this video section, we go through
From playlist The CHALKboard 2022
Séminaire Bourbaki - 21/06/2014 - 4/4 - Thierry COQUAND
Théorie des types dépendants et axiome d'univalence Cet exposé sera une introduction à la théorie des types dépendants et à l'axiome d'univalence. Cette théorie est une alternative à la théorie des ensembles comme fondement des mathématiques. Guidé par une interprétation d'un type comme u
From playlist Bourbaki - 21 juin 2014
Inference: A Logical-Philosophical Perspective - Moderated Conversation w/ A.C. Paseau and Gila Sher
Inference: A Logical-Philosophical Perspective. Moderated Conversation with Gila Sher, Department of Philosophy, University of California, San Diego on the talk by Alexander Paseau, Faculty of Philosophy, University of Oxford. The Franke Program in Science and the Humanities Understandi
From playlist Franke Program in Science and the Humanities
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
Logic and Quantum Computing - Will Troiani
Will Troiani presents some of his research on the border of proof theory in logic, and quantum error correcting codes (QECCs). From the point of view of the Curry-Howard correspondence the essential content of a proof is a pattern of "equality" it sets up between occurrences of variables o
From playlist metauni festival 2023
Introducing Model Theory with Ehrenfeucht-Fraïssé Games on Linear Orderings #SOME2
Play along at home: https://trkern.itch.io/rosenstein Version with just finite linear orderings (and AI opponent): https://trkern.itch.io/efglo Watch a similar video on the model theory of graphs: https://www.youtube.com/watch?v=1lFjNDhAStk Play EF-Games on graphs: https://trkern.github.i
From playlist Summer of Math Exposition 2 videos
Isomorphic Structures of any Kind are `Equal' in HoTT: But What... Structure? - Peter Aczel
Peter Aczel The Unviersity of Manchester; Member,School of Mathematics February 7, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Fellow Short Talks: Professor David Pym, UCL
Bio David Pym is Professor of Information, Logic, and Security at UCL and is The Alan Turing Institute’s University Liaison Director for UCL. Heholds a PhD in logic and theoretical computer science from Edinburgh,and an MA and an ScD in mathematics from Cambridge. He is a Fellow of the IM
From playlist Short Talks
Data Structures: List as abstract data type
See complete series of videos in data structures here: http://www.youtube.com/playlist?list=PL2_aWCzGMAwI3W_JlcBbtYTwiQSsOTa6P&feature=view_all In this lesson, we will introduce a dynamic list structure as an abstract data type and then see one possible implementation of dynamic list using
From playlist Data structures