De Bruijn's theorem

Introduction to additive combinatorics lecture 1.8 --- Plünnecke's theorem

In this video I present a proof of Plünnecke's theorem due to George Petridis, which also uses some arguments of Imre Ruzsa. Plünnecke's theorem is a very useful tool in additive combinatorics, which implies that if A is a set of integers such that |A+A| is at most C|A|, then for any pair

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

Proof of Lemma and Lagrange's Theorem

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof of Lemma and Lagrange's Theorem. This video starts by proving that any two right cosets have the same cardinality. Then we prove Lagrange's Theorem which says that if H is a subgroup of a finite group G then the order of H div

From playlist Abstract Algebra

Introduction to additive combinatorics lecture 10.8 --- A weak form of Freiman's theorem

In this short video I explain how the proof of Freiman's theorem for subsets of Z differs from the proof given earlier for subsets of F_p^N. The answer is not very much: the main differences are due to the fact that cyclic groups of prime order do not have lots of subgroups, so one has to

From playlist Introduction to Additive Combinatorics (Cambridge Part III course)

Brill-Noether part 4: Noether's Theorem

From playlist Brill-Noether

6. Genome Assembly

MIT 7.91J Foundations of Computational and Systems Biology, Spring 2014 View the complete course: http://ocw.mit.edu/7-91JS14 Instructor: David Gifford Prof. Gifford talks about two different ways to assemble a genome de novo. The first approach is overlap layout consensus assemblers, as

From playlist MIT 7.91J Foundations of Computational and Systems Biology

de Bruijn Card Trick

Before christmas I showed you some sequences called de Bruijn sequences. They're designed to contain every combination of some numbers without any repeats http://youtu.be/iPLQgXUiU14 For example, this sequence 1111222212211212 contains every combination of 1 and 2 of length 4. So 1111 is

From playlist My Maths Videos

Charles Newman: Remarks on the Riemann hypothesis

Abstract: One fairly standard version of the Riemann Hypothesis (RH) is that a specific probability density on the real line has a moment generating function (Laplace transform) that as an analytic function on the complex plane has all its zeros pure imaginary. We’ll review a series of res

From playlist History of Mathematics

Lec 2 | MIT 6.172 Performance Engineering of Software Systems, Fall 2010

Lecture 2: Bit Hacks Instructor: Charles Leiserson View the complete course: http://ocw.mit.edu/6-172F10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.172 Performance Engineering of Software Systems

2020.07.09 Ronen Eldan - Localization and concentration of measures on the discrete hypercube (1/2)

For a probability measure $\mu$ on the discrete hypercube, we are interested in finding sufficient conditions under which $\mu$ either (a) Exhibits concentration (either in the sense of Lipschitz functions, or in a stronger sense such as a Poincare inequality), or (b) Can be decomposed as

From playlist One World Probability Seminar

Can you crack the combination lock? - Solution

The sequence 11221 contains all 2-digit combinations using the numbers 1 and 2. A sequence such as that is called a De Bruijn sequence. I show you three methods to find such sequence. The first two involve making diagrams called graphs, and either taking a path that visits every node of

From playlist My Maths Videos

Berge's lemma, an animated proof

Berge's lemma is a mathematical theorem in graph theory which states that a matching in a graph is of maximum cardinality if and only if it has no augmenting paths. But what do those terms even mean? And how do we prove Berge's lemma to be true? == CORRECTION: at 7:50, the red text should

From playlist Summer of Math Exposition Youtube Videos

Lagrange theorem

We finally get to Lagrange's theorem for finite groups. If this is the first video you see, rather start at https://www.youtube.com/watch?v=F7OgJi6o9po&t=6s In this video I show you how the set that makes up a group can be partitioned by a subgroup and its cosets. I also take a look at

From playlist Abstract algebra

Abstract Algebra | Lagrange's Theorem

We prove some general results, culminating in a proof of Lagrange's Theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

Markus Whiteland : k-abelian singletons and Gray codes for Necklaces

Abstract : k-abelian singletons in connection with Gray codes for Necklaces. This work is based on [1]. We are interested in the equivalence classes induced by k-abelian equivalence, especially in the number of the classes containing only one element, k-abelian singletons. By characterizin

From playlist Combinatorics

Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

Points, lines, planes, etc. - June Huh

Topic: Points, lines, planes, etc. Speaker: June Huh, Member, School of Mathematics Time/Room: 4:00pm - 4:15pm/S-101 More videos on http://video.ias.edu

From playlist Mathematics

!!Con West 2019 - Eric Weinstein: Value Your Types!

Presented at !!Con West 2019: http://bangbangcon.com/west You’re probably familiar with types in programming languages, such as “integer” or “list of integers.” But what if your type system were powerful enough to express types like “non-negative integer” or “list of strings where each st

From playlist !!Con West 2019

Riemann-Lebesgue Lemma

In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral

From playlist Real Analysis

Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

A Response to Steven Pinker on AI

Steven Pinker wrote an article on AI for Popular Science Magazine, which I have some issues with. The article: https://www.popsci.com/robot-uprising-enlightenment-now Related: "The Orthogonality Thesis, Intelligence, and Stupidity" (https://youtu.be/hEUO6pjwFOo) "AI? Just Sandbox it... -

From playlist Best Of