Topics in Combinatorics Lecture 15.8 --- Dimension arguments and sets with only two distances.
Let X be a subset of R^n such that there are only two possible distances between distinct elements of X. How large can X be? An example of such a set is the set of all 01 vectors with precisely two 1s, which has size n(n-1)/2. In this video I show how to prove an upper bound of (n+1)(n+4)/
From playlist Topics in Combinatorics (Cambridge Part III course)
Introduction to sets || Set theory Overview - Part 2
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
Introduction to additive combinatorics lecture 10.1 --- the structure and properties of Bohr sets.
An important informal idea in additive combinatorics is that of a "structured" set. One example of a class of sets that are rich in additive structure is the class of Bohr sets, which play the role in general finite Abelian groups that subspaces play in the special case of groups of the fo
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
The answer is: a lot of them! In this video, I show that F(R), the set of functions from R to R, has the same cardinality as P(R), the set of subsets of the real numbers, which, in a previous video, I’ve shown to be much bigger than R. This is set theory at its finest :)
From playlist Set theory
Sergei Konyagin: On sum sets of sets having small product set
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Combinatorics
Topics in Combinatorics lecture 3.6 --- bounds for factorials and binomial coefficients
Combinatorics is full of estimates, and for many of them one needs bounds on factorials and binomial coefficients. Fortunately, one can often get away with fairly crude bounds that have straightforward proofs. Here I discuss some of these bounds. 0:00 Introduction and brief struggle with
From playlist Topics in Combinatorics (Cambridge Part III course)
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
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
Number of Subsets Containing a Set of Elements | Set Theory, Combinatorics
How do we count the number of subsets that contain a particular collection of elements? We'll be answering this question with an example and a general solution in today's video set theory lesson! SOLUTION TO PRACTICE PROBLEM: There are 4 elements of S, so S has 2^4 subsets total. How man
From playlist Set Theory
Introduction to additive combinatorics lecture 1.0 --- What is additive combinatorics?
This is an introductory video to a 16-hour course on additive combinatorics given as part of Cambridge's Part III mathematics course in the academic year 2021-2. After a few remarks about practicalities, I informally discuss a few open problems, and attempt to explain what additive combina
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Timothy Gowers: Combinatorics, Szemerédis theorem and the sorting problem
Sir William Timothy Gowers is a British mathematician and a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. This video is a clip from the Abel Prize Announcement 2012. Gowers gives a brief introduction to t
From playlist Popular presentations
1. A bridge between graph theory and additive combinatorics
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 In an unsuccessful attempt to prove Fermat's last theorem
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Additive number theory: Extremal problems and the combinatorics of sum. (Lecture 4) by M. Nathanson
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
A glimpse of continuous combinatorics via natural quasirandomness - Leonardo Coregliano
Short Talks by Postdoctoral Members Topic: A glimpse of continuous combinatorics via natural quasirandomness Speaker: Leonardo Coregliano Affiliation: Member, School of Mathematics Date: September 23, 2021
From playlist Mathematics
The Selberg Sieve and Large Sieve (Lecture 4) by Satadal Ganguly
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
From graph limits to higher order Fourier analysis – Balázs Szegedy – ICM2018
Combinatorics Invited Lecture 13.8 From graph limits to higher order Fourier analysis Balázs Szegedy Abstract: The so-called graph limit theory is an emerging diverse subject at the meeting point of many different areas of mathematics. It enables us to view finite graphs as approximation
From playlist Combinatorics
Arithmetic progressions and spectral structure - Thomas Bloom
Computer Science/Discrete Mathematics Seminar II Topic: Arithmetic progressions and spectral structure Speaker: Thomas Bloom Affiliation: University of Cambridge Date: October 13, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Additive Number Theory: Extremel Problems and the Combinatorics....(Lecture 3) by M. Nathanson
Program Workshop on Additive Combinatorics ORGANIZERS: S. D. Adhikari and D. S. Ramana DATE: 24 February 2020 to 06 March 2020 VENUE: Madhava Lecture Hall, ICTS Bangalore Additive combinatorics is an active branch of mathematics that interfaces with combinatorics, number theory, ergod
From playlist Workshop on Additive Combinatorics 2020
Find a Set with Greatest Cardinality that is a Subset of Two Given Sets (Lists)
This video explains how to determine a set with greatest cardinality that is a subset of two given sets.
From playlist Sets (Discrete Math)
Using nonstandard natural numbers in Ramsey Theory - M. Di Nasso - Workshop 1 - CEB T1 2018
Mauro Di Nasso (Pisa) / 01.02.2018 In Ramsey Theory, ultrafilters often play an instrumental role. By means of nonstandard models, one can reduce those third-order objects (ultrafilters are sets of sets of natural numbers) to simple points. In this talk we present a nonstandard technique
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields