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
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
Not-So-Close Packed Crystal Structures
A description of two crystal structures that are created from not-so-close packed structures.
From playlist Atomic Structures and Bonding
A formal definition of a Graph and its properties
From playlist Graph Theory
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
Introductory coverage of fundamental data structures. Part of a larger series teaching programming. Visit http://codeschool.org
From playlist Data Structures
This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com
From playlist Number Sense - Decimals, Percents, and Ratios
Higher data structures | Data structures in Mathematics Math Foundations 163
Lists, ordered sets (osets), multisets (msets) and sets are the four key types of data structures. In this video we begin looking at how we can combine these types in a nested fashion, by considering for example lists of lists, or sets of msets etc. This will give us a lot more flexibili
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
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
Benedikt Ahrens - Univalent Foundations and the UniMath library - IPAM at UCLA
Recorded 13 February 2023. Benedikt Ahrens of Delft University of Technology presents "Univalent Foundations and the UniMath library" at IPAM's Machine Assisted Proofs Workshop. Abstract: Univalent Foundations (UF) were designed by Voevodsky as a foundation of mathematics that is "invarian
From playlist 2023 Machine Assisted Proofs Workshop
Benedikt Ahrens - Le principe d'univalence: le transfer du raisonnement à traver les equivalence
Le raisonnement à équivalence près est omniprésent en mathématique, et les mathématiciens le font implicitement. Pour les mathématiques sur ordinateurs, ce n'est pas si simple : il faut donner tous les détails éxplicitement. C'est pour cela que Voevodsky a créé les fondements univalents, a
From playlist Workshop Schlumberger 2022 : types dépendants et formalisation des mathématiques
Towards elementary infinity-toposes - Michael Shulman
Vladimir Voevodsky Memorial Conference Topic: Towards elementary infinity-toposes Speaker: Michael Shulman Affiliation: University of San Diego Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Type Systems and Proof Assistant - Vladimir Voevodsky
Vladimir Voevodsky Professor, School of Mathematics, IAS October 10, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Egbert Rijke: Daily applications of the univalence axiom - lecture 1
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 21, 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 M
From playlist Combinatorics
Laurent Lafforgue - 1/4 Classifying toposes of geometric theories
Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/LafforgueSlidesToposesOnline.pdf The purpose of these lectures will be to present the theory of classifying topose
From playlist Toposes online
Type Systems I - Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study November 28, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Univalent foundations and the equivalence principle - Benedikt Ahrens
Short Talks by Postdoctoral Members Benedikt Ahrens - September 21, 2015 http://www.math.ias.edu/calendar/event/88134/1442858400/1442859300 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
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
Univalence from a computer science point-of-view - Dan Licata
Vladimir Voevodsky Memorial Conference Topic: Univalence from a computer science point-of-view Speaker: Dan Licata Affiliation: Wesleyan University Date: September 14, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics