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
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
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
Model Theory - part 04 - Posets, Lattices, Heyting Algebras, Booleans Algebras
This is a short video for people who haven't seen a Heyting algebras before. There is really nothing special in it that doesn't show up in wikipedia or ncatlab. I just wanted to review it before we use them. Errata: *at 3:35: there the law should read (a and (a or b) ), not (a and (a and
From playlist Model Theory
Canonical structures inside the Platonic solids I | Universal Hyperbolic Geometry 49 | NJ Wildberger
Each of the Platonic solids contains somewhat surprising addition structures that shed light on the symmetries of the object. Here we look at the tetrahedron, and investigate a remarkable three-fold symmetry which is contained inside the obvious four-fold symmetry of the object. We connect
From playlist Universal Hyperbolic Geometry
Delta-Star is a polyhedral object which I invented in 1996. The type of Delta-Star corresponds to Deltahedrons. It expands and shrinks. Especially highly symmetric tetrahedron,octahedron,icosahedron types and hexahedron,decahedron types can transform smoothly.
From playlist Handmade geometric toys
Paul Grigas - Offline and Online Learning for Contextual Stochastic Optimization - IPAM at UCLA
Recorded 03 March 2023. Paul Grigas of the University of California, Berkeley, presents "Offline and Online Learning for Contextual Stochastic Optimization" at IPAM's Artificial Intelligence and Discrete Optimization Workshop. Abstract: Often the parameters of an optimization task are pred
From playlist 2023 Artificial Intelligence and Discrete Optimization
Klaus Künnemann: A tropical approach to non archimedean Arakelov theory I
The lecture was held within the framework of the Junior Hausdorff Trimester Program Algebraic Geometry. (04.2.2014)
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Canonical structures inside Platonic solids II | Universal Hyperbolic Geometry 50 | NJ Wildberger
The cube and the octahedron are dual solids. Each has contained within it both 2-fold, 3-fold and 4-fold symmetry. In this video we look at how these symmetries are generated in the cube via canonical structures. Along the way we discuss bipartite graphs. This gives us more insight into t
From playlist Universal Hyperbolic Geometry
The basic framework for geometry (I) | Arithmetic and Geometry Math Foundations 23 | N J Wildberger
This video begins to lay out proper foundations for planar Euclidean geometry, based on arithmetic. We follow Descartes and Fermat in working in a coordinate plane, but a novel feature is that we use only rational numbers. Points and lines are the basic objects which need to be defined. T
From playlist Math Foundations
Wolfram Language 12.1 Algorythm R&D Summary
Roger Germundsson
From playlist Wolfram Technology Conference 2019
Update on Tropical Schemes by Diane Maclagan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is the study of
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)
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
Tropical motivic integration - S. Payne - Workshop 2 - CEB T1 2018
Sam Payne (Yale University) / 09.03.2018 Tropical motivic integration. I will present a new tool for the calculation of motivic invariants appearing in Donaldson-Thomas theory, such as the motivic Milnor fiber and motivic nearby fiber, starting from a theory of volumes of semi-algebraic
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Rolf Schneider: Hyperplane tessellations in Euclidean and spherical spaces
Abstract: Random mosaics generated by stationary Poisson hyperplane processes in Euclidean space are a much studied object of Stochastic Geometry, and their typical cells or zero cells belong to the most prominent models of random polytopes. After a brief review, we turn to analogues in sp
From playlist Probability and Statistics
Joseph Huchette: "Neural network verification as piecewise linear optimization"
Deep Learning and Combinatorial Optimization 2021 "Neural network verification as piecewise linear optimization" Joseph Huchette - Rice University Abstract: Neural networks are incredibly powerful tools for prediction in important domains such as image classification and machine translat
From playlist Deep Learning and Combinatorial Optimization 2021
Bernd Schulze: Characterizing Minimally Flat Symmetric Hypergraphs
Scene analysis is concerned with the reconstruction of d-dimensional objects, such as polyhedral surfaces, from (d-1)-dimensional pictures (i.e., projections of the objects onto a hyperplane). This theory is closely connected to rigidity theory and other areas of discrete applied geometry,
From playlist HIM Lectures 2015
Title: Towards Soft Voronoi Diagrams Symbolic-Numeric Computing Seminar
From playlist Symbolic-Numeric Computing Seminar
Lattice Structures in Ionic Solids
We've learned a lot about covalent compounds, but we haven't talked quite as much about ionic compounds in their solid state. These will adopt a highly ordered and repeating lattice structure, but the geometry of the lattice depends entirely on the types of ions and their ratio in the chem
From playlist General Chemistry