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
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
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
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
Eriko Hironaka - Lehmer's Problem and Dilatations of Mapping Classes
Eriko Hironaka talks at the Worldwide Center of Mathematics "Lehmer's Problem and Dilatations of Mapping Classes"
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Lehmer Factor Stencils: A paper factoring machine before computers
In 1929, Derrick N. Lehmer published a set of paper stencils used to factor large numbers by hand before the advent of computers. We explain the math behind the stencils, which includes modular arithmetic, quadratic residues, and continued fractions, including my favourite mathematical vi
From playlist Joy of Mathematics
Patrick Ingram, The critical height of an endomorphism of projective space
VaNTAGe seminar on June 9, 2020. License: CC-BY-NC-SA. Closed captions provided by Matt Olechnowicz
From playlist Arithmetic dynamics
Hard Lefschetz Theorem and Hodge-Riemann Relations for Combinatorial Geometries - June Huh
June Huh Princeton University; Veblen Fellow, School of Mathematics November 9, 2015 https://www.math.ias.edu/seminars/abstract?event=47563 A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conj
From playlist Members Seminar
How they found the World's Biggest Prime Number - Numberphile
Featuring Matt Parker... More links & stuff in full description below ↓↓↓ See part one at: https://youtu.be/tlpYjrbujG0 Part three on Numberphile2: https://youtu.be/jNXAMBvYe-Y Matt's interview with Curtis Cooper: https://youtu.be/q5ozBnrd5Zc The previous record: https://youtu.be/QSEKzFG
From playlist Matt Parker (standupmaths) on Numberphile
Lyapunov Stability via Sperner's Lemma
We go on whistle stop tour of one of the most fundamental tools from control theory: the Lyapunov function. But with a twist from combinatorics and topology. For more on Sperner's Lemma, including a simple derivation, please see the following wonderful video, which was my main source of i
From playlist Summer of Math Exposition Youtube Videos
Why Do We Need a 23 Million Digit Prime Number?
Finding the biggest prime number might not only have applications in computing, it could also win you some serious money. Here’s how. The ‘Ham Sandwich Theorem’ Will Change How You See the Universe… Seriously - https://youtu.be/uhNqEs7vDGg Read More: How a FedEx employee discovered th
From playlist Elements | Seeker
Burnside's Lemma (Part 2) - combining math, science and music
Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be
From playlist Traditional topics, explained in a new way
Harold Stark - The origins of conjectures on derivatives of L-functions at s=0 [1990’s]
slides for this talk: http://www.msri.org/realvideo/ln/msri/2001/rankin-L/stark/1/banner/01.html The origins of conjectures on derivatives of L-functions at s=0 Harold Stark http://www.msri.org/realvideo/ln/msri/2001/rankin-L/stark/1/index.html
From playlist Number Theory
CTNT 2018 - "The Biggest Known Prime Number" by Keith Conrad
This is lecture on "The Biggest Known Prime Number", by Keith Conrad, during CTNT 2018, the Connecticut Summer School in Number Theory. For more information about CTNT and other resources and notes, see https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2018 - Guest Lectures
Factor Stencils Review / HowTo
Factor stencils based on a design from the 1920s by D. N. Lehmer. His will factor any number up to 3,000,000,000,000. Mine are smaller, so only factor up to 200,000. This is episode 37 of my video series about calculating devices. Visit my site for PDFs and SVGs to download and make your
From playlist Calculating Devices Review / HowTos
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
Weil conjectures 5: Lefschetz trace formula
This talk explains the relation between the Lefschetz fixed point formula and the Weil conjectures. More precisely, the zeta function of a variety of a finite field can be written in terms of an action of the Frobenius group on the cohomology groups of the variety. The main problem is then
From playlist Algebraic geometry: extra topics
Why is Pi, too: The wrong, amazing proof #SoME2
After making another video which became too long, I made this short one as my submission for #some2 Here is the link to the 1900 paper of Lehmer https://www.jstor.org/stable/i340649 Proof of the lemma I mentioned: 1) https://books.google.nl/books/about/An_Introduction_to_the_Theory_of_
From playlist Summer of Math Exposition 2 videos
New World's Biggest Prime Number (PRINTED FULLY ON PAPER) - Numberphile
Matt Parker on the latest Mersenne Prime to take the title of "world's biggest prime". He had it printed! More links & stuff in full description below ↓↓↓ More from this interview very soon, including details of how the prime was found. PART TWO: https://youtu.be/lEvXcTYqtKU PART THREE o
From playlist Matt Parker (standupmaths) on Numberphile
Theory of numbers: Gauss's lemma
This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di
From playlist Theory of numbers