In computational learning theory, let C be a concept class over a domain X and c be a concept in C. A subset S of X is a witness set for c in C if c(S) verifies c (i.e., c is the only consistent concept with respect to c(S)). The minimum size of a witness set for c is called the witness size or specification number and is denoted by . The value is called the teaching dimension of C. * v * t * e (Wikipedia).
SET is an awesome game that really gets your brain working. Play it! Read more about SET here: http://theothermath.com/index.php/2020/03/27/set/
From playlist Games and puzzles
The perfect number of axioms | Axiomatic Set Theory, Section 1.1
In this video we introduce 6 of the axioms of ZFC set theory. My Twitter: https://twitter.com/KristapsBalodi3 Intro: (0:00) The Axiom of Existence: (2:39) The Axiom of Extensionality: (4:20) The Axiom Schema of Comprehension: (6:15) The Axiom of Pair (12:16) The Axiom of Union (15:15) T
From playlist Axiomatic Set Theory
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
Shading sets in Venn diagrams (3)
Powered by https://www.numerise.com/ Shading sets in Venn diagrams (3)
From playlist Set theory
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Set Theory (Part 2b): The Bogus Universal Set
Please feel free to leave comments/questions on the video below! In this video, I argue against the existence of the set of all sets and show that this claim is provable in ZFC. This theorem is very much tied to the Russell Paradox, besides being one of the problematic ideas in mathematic
From playlist Set Theory by Mathoma
What is the complement of a set? Sets in mathematics are very cool, and one of my favorite thins in set theory is the complement and the universal set. In this video we will define complement in set theory, and in order to do so you will also need to know the meaning of universal set. I go
From playlist Set Theory
Power Set of the Power Set of the Power Set of the Empty Set | Set Theory
The power set of the power set of the power set of the empty set, we'll go over how to find just that in today's set theory video lesson! We'll also go over the power set of the empty set, the power set of the power set of the empty set, and we'll se the power set of the power set of the p
From playlist Set Theory
How to Identify the Elements of a Set | Set Theory
Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times
From playlist Set Theory
Query Complexity of Black-Box Search - Ben Rossman
Ben Rossman Tokyo Institute of Technology November 5, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Strong Bounds for 3-Progressions: In-Depth - Zander Kelley
Computer Science/Discrete Mathematics Seminar II Topic: Strong Bounds for 3-Progressions: In-Depth Speaker: Zander Kelley Affiliation: University of Illinois Urbana-Champaign Date: March 21, 2023 Suppose you have a set S of integers from {1 , 2 , … , N} that contains at least N / C eleme
From playlist Mathematics
Zero Knowledge Proofs - Seminar 1 - Introduction
This seminar series is about the mathematical foundations of cryptography. In this series Eleanor McMurtry is explaining Zero Knowledge Proofs (ZKPs), a fascinating set of techniques that allow one participant to prove they know something *without revealing the thing*. You can join this s
From playlist Metauni
Circuit Lower Bounds for Nondeterministic Quasi-Polytime... - Cody Murray
Computer Science/Discrete Mathematics Seminar I Topic: Circuit Lower Bounds for Nondeterministic Quasi-Polytime: An Easy Witness Lemma for NP and NQP Speaker: Cody Murray Affiliation: Massachusetts Institute of Technology Date: March 26, 2018 For more videos, please visit http://video.ia
From playlist Mathematics
MIT 6.006 Introduction to Algorithms, Spring 2020 Instructor: Jason Ku View the complete course: https://ocw.mit.edu/6-006S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63EdVPNLG3ToM6LaEUuStEY This lecture introduces a single source shortest path algorithm that wor
From playlist MIT 6.006 Introduction to Algorithms, Spring 2020
6. Szemerédi's graph regularity lemma I: statement and proof
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX Szemerédi's graph regularity lemma is a powerful tool in
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Explicit rigid matrices in P^NP via rectangular PCPs - Prahladh Harsha
Computer Science/Discrete Mathematics - Special Seminar Topic: Explicit rigid matrices in P^NP via rectangular PCPs Speaker: Prahladh Harsha Affiliation: Tata Institute of Fundamental Research Date: February 06, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Bradley Nelson (2/19/22): Parameterized Vietoris-Rips Filtrations via Covers
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression which restrict simplices to lie in open sets in a cove
From playlist Vietoris-Rips Seminar
Aravind Srinivasan: Approximating integer programming problems by partial resampling
Partial resampling is a variant of the Moser-Tardos algorithm for the Lovasz Local Lemma; it was developed by Harris and the speaker (FOCS 2013). We present two families of applications of this framework for approximating column-sparse integer programs, parametrized by the maximum L1 norm
From playlist HIM Lectures: Trimester Program "Combinatorial Optimization"
Conversation on the paper "Persistent Extension and Analogous Bars: ..." by Yoon, Ghrist, Giusti
This is a research conversation about the paper "Persistent Extension and Analogous Bars: Data-Induced Relations Between Persistence Barcodes" by Hee Rhang Yoon, Robert Ghrist, Chad Giusti, available on arXiv at https://arxiv.org/abs/2201.05190. Thanks to Chad Giusti for telling us (Henry
From playlist Tutorials
MF150: What exactly is a set? | Data Structures in Mathematics Math Foundations | NJ Wildberger
What exactly is a set?? This is a crucial question in the modern foundations of mathematics. Here we begin an examination of this thorny issue, first by discussing the usual English usage of the term, as well as alternate terms, such as collection, aggregate, bunch, class, menagerie etc th
From playlist Math Foundations