"Infinite sequences": what are they? | Real numbers and limits Math Foundations 99 | N J Wildberger
This lecture tries to clarify the big gap between the (finite) sequences we introduced in the last lecture, and "infinite" or "ongoing sequences" (we introduce the term "on-sequence") as are found in Sloane's Online Encyclopedia of Integer Sequences. We concentrate discussion on three such
From playlist Math Foundations
Prove that the Catalan numbers are integers: a number theoretic approach
We prove, for the 2nd time, that the Catalan numbers are integers: a number theoretic approach We proved this fact using a combinatorial approach In a previous video here: https://youtu.be/73HppmrSEIw (Prove that n+1 divides 2n choose n. And Catalan numbers) The new proof in this video i
From playlist Elementary Number Theory
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
The Collatz Conjecture and Fractals
Visualizing the dynamics of the Collatz Conjecture though fractal self-similarity. Support this channel: https://www.patreon.com/inigoquilez Tutorials on maths and computer graphics: https://iquilezles.org Code for this video: https://www.shadertoy.com/view/llcGDS Donate: http://paypal.m
From playlist Maths Explainers
A Beautiful Proof of Ptolemy's Theorem.
Ptolemy's Theorem seems more esoteric than the Pythagorean Theorem, but it's just as cool. In fact, the Pythagorean Theorem follows directly from it. Ptolemy used this theorem in his astronomical work. Google for the historical details. Thanks to this video for the idea of this visual
From playlist Mathy Videos
Ptolemy's theorem and generalizations | Rational Geometry Math Foundations 131 | NJ Wildberger
The other famous classical theorem about cyclic quadrilaterals is due to the great Greek astronomer and mathematician, Claudius Ptolemy. Adopting a rational point of view, we need to rethink this theorem to state it in a purely algebraic way, without resort to `distances' and the correspon
From playlist Math Foundations
[Discrete Mathematics] Catalan Numbers
In this video we introduce the Catalan Numbers, which is a way of looking at lattice paths from (0,0) to (n,n) where it never crosses the diagonal line. This is also the number of ways to multiply n+1 products. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1
From playlist Discrete Math 2
Watch more videos on http://www.brightstorm.com/math/geometry SUBSCRIBE FOR All OUR VIDEOS! https://www.youtube.com/subscription_center?add_user=brightstorm2 VISIT BRIGHTSTORM.com FOR TONS OF VIDEO TUTORIALS AND OTHER FEATURES! http://www.brightstorm.com/ LET'S CONNECT! Facebook ► https
From playlist Geometry
More ways of deriving Catalan numbers | DDC #3
Catalan numbers are so extensively studied that there are a number of different ways to derive those, including reflection, mentioned in the previous video, as well as bijection, and generating function, which are mentioned in this video. Useful link: (The document) https://drive.google.
From playlist Deep Dive into Combinatorics (DDC)
Complexity problems in enumerative combinatorics – Igor Pak – ICM2018
Combinatorics Invited Lecture 13.9 Complexity problems in enumerative combinatorics Igor Pak Abstract: We give a broad survey of recent results in enumerative combinatorics and their complexity aspects. © International Congress of Mathematicians – ICM www.icm2018.org Os direitos s
From playlist Combinatorics
The ABC Conjecture, Brian Conrad (Stanford) [2013]
slides for this talk: https://drive.google.com/file/d/1J04zXCQYgn9MdgDUo63rH719cruiQJVo/view?usp=sharing The ABC Conjecture Brian Conrad [Stanford University] Stony Brook Mathematics Colloquium Video September 12, 2013 http://www.math.stonybrook.edu/Videos/Colloquium/video_slides.php?
From playlist Number Theory
Martina Lanini: Parking spaces and Catalan combinatorics for complex reflection groups
Abstract: Recently, Armstrong, Reiner and Rhoades associated with any (well generated) complex reflection group two parking spaces, and conjectured their isomorphism. This has to be seen as a generalisation of the bijection between non-crossing and non-nesting partitions, both counted by t
From playlist Algebra
Catalan's Conjecture - Numberphile
With Dr Holly Krieger from Murray Edwards College, University of Cambridge. Have a look at Brilliant (and get 20% off) here: https://brilliant.org/Numberphile More links & stuff in full description below ↓↓↓ More Numberphile videos with Dr Krieger: http://bit.ly/HollyKrieger Her Twitter:
From playlist Women in Mathematics - Numberphile
Andrew Sutherland: Introduction to Sato-Tate distributions
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 Jean-Morlet Chair - Shparlinski/Kohel
Vic Reiner, Lecture III - 13 February 2015 (49)
Vic Reiner (University of Minnesota) - Lecture III http://www.crm.sns.it/course/4036/ Many results in the combinatorics and invariant theory of reflection groups have q-analogues for the finite general linear groups GLn(Fq). These lectures will discuss several examples, and open question
From playlist Vertex algebras, W-algebras, and applications - 2014-2015
Stanford Lecture: Donald Knuth—"(3/2)-ary Trees" (2014)
Donald Knuth's 20th Annual Christmas Tree Lecture: (3/2)-ary Trees (2014) December 2, 2014 In previous lectures Professor Knuth has discussed binary trees, ternary trees, quaternary trees, etc., which are enumerated by the coefficients of important functions called generalized binomial se
From playlist Donald Knuth Lectures
Dana MacKenzie - 2184 (Oh, the Absurdity) - G4G13 Apr 2018
People born in 2184 will be doubly lucky: at age 3, their age will be the 7th root of the year; at age 13 their age will be the cube root of the year. Do any other years have this magic property?
From playlist G4G13 Videos
An introduction to the abc conjecture - Héctor Pastén Vásquez
Members’ Seminar Topic: An introduction to the abc conjecture Speaker: Héctor Pastén Vásquez Date: Monday, March 21 In this talk I will discuss some classical and new applications of the abc conjecture, its relation to conjectures about elliptic curves, and some (admittedly weak) uncon
From playlist Mathematics
The Millin Series (A nice Fibonacci sum)
We derive the closed form for the Millin series, which involves reciprocals of the 2^nth Fibonacci numbers. We use Catalan's identity, the convergence of a subsequence, and the golden ratio. Catalan's Identity: https://youtu.be/kskAtiWC_w8 Another reciprocal Fibonacci sum: https://youtu.b
From playlist Identities involving Fibonacci numbers
Homogeneous spaces, algebraic K-theory and cohomological(...) - Izquierdo - Workshop 2 - CEB T2 2019
Diego Izquierdo (MPIM Bonn) / 24.06.2019 Homogeneous spaces, algebraic K-theory and cohomological dimension of fields. In 1986, Kato and Kuzumaki stated a set of conjectures which aimed at giving a Diophantine characterization of the cohomological dimension of fields in terms of Milnor
From playlist 2019 - T2 - Reinventing rational points