The deep structure of the rational numbers | Real numbers and limits Math Foundations 95
The rational numbers deserve a lot of attention, as they are the heart of mathematics. I am hopeful that modern mathematics will (slowly) swing around to the crucial realization that a lot of things which are currently framed in terms of "real numbers" are more properly understood in terms
From playlist Math Foundations
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
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
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
What's the difference between concrete and cement? Concrete is the most important construction material on earth and foundation of our modern society. At first glance it seems rudimentary, but there is a tremendous amount of complexity involved in every part of designing and placing conc
From playlist Civil Engineering
Ordered Fields In this video, I define the notion of an order (or inequality) and then define the concept of an ordered field, and use this to give a definition of R using axioms. Actual Construction of R (with cuts): https://youtu.be/ZWRnZhYv0G0 COOL Construction of R (with sequences)
From playlist Real Numbers
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
The realm of natural numbers | Data structures in Mathematics Math Foundations 155
Here we look at a somewhat unfamiliar aspect of arithmetic with natural numbers, motivated by operations with multisets, and ultimately forming a main ingredient for that theory. We look at natural numbers, together with 0, under three operations: addition, union and intersection. We will
From playlist Math Foundations
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
Lie Fu: Real structures on hyper-Kähler manifolds
CONFERENCE Recording during the thematic meeting : "Real Aspects of Geometry" the October 31, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Algebraic and Complex Geometry
Twisted real structures for spectral triples
Talk by Adam Magee in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 31, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Mumford-Tate Groups and Domains - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics March 28, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
Holomorphic Curves in Compact Quotients of SL(2,C) by Sorin Dumitrescu
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
An introduction to spectral data for Higgs bundles.. by Laura Schaposnik
Higgs bundles URL: http://www.icts.res.in/program/hb2016 DATES: Monday 21 Mar, 2016 - Friday 01 Apr, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: Higgs bundles arise as solutions to noncompact analog of the Yang-Mills equation. Hitchin showed that irreducible solutio
From playlist Higgs Bundles
Behavior of Welschinger Invariants Under Morse Simplification - Erwan Brugalle
Erwan Brugalle Universite de Paris 6 November 9, 2012 Welschinger invariants, real analogs of genus 0 Gromov-Witten invariants, provide non-trivial lower bounds in real algebraic geometry. In this talk I will explain how to get some wall-crossing formulas relating Welschinger invariants o
From playlist Mathematics
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
Higgs bundles and higher Teichmüller components (Lecture 1) by Oscar Garcia
DISCUSSION MEETING : MODULI OF BUNDLES AND RELATED STRUCTURES ORGANIZERS : Rukmini Dey and Pranav Pandit DATE : 10 February 2020 to 14 February 2020 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore Background: At its core, much of mathematics is concerned with the problem of classif
From playlist Moduli Of Bundles And Related Structures 2020
Stein Structures: Existence and Flexibility - Kai Cieliebak
Kai Cieliebak Ludwig-Maximilians-Universitat, Munich, Germany March 2, 2012
From playlist Mathematics
Stein Structures: Existence and Flexibility - Kai Cieliebak
Kai Cieliebak Ludwig-Maximilians-Universitat, Munich, Germany March 1, 2012
From playlist Mathematics
http://www.tabletclass.com explains the real number system
From playlist Pre-Algebra