Haruki's Theorem says that given three intersecting circles that only intersect each other at two points that the lines connecting the inner intersecting points to the outer satisfy: where are the measure of segments connecting the inner and outer intersection points (Wikipedia).
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Complex analysis: Cauchy's theorem
This lecture is part of an online undergraduate course on complex analysis. We state Cauchy's theorem and show that it follows from Green's theorem and the Cauchy-Riemann equations. We use it to show that a holomorphic function on a simply connected region has an antiderivative. For the
From playlist Complex analysis
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
In this video, I explain function space and how to change the basis vectors we use to describe function. This lead us to a different understanding of Taylor series, Fourier series and most series. I also explain the Heisenberg uncertainty principle using function space. Additionnal video
From playlist Summer of Math Exposition Youtube Videos
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
Theory of numbers: Congruences: Euler's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Euler's theorem, a generalization of Fermat's theorem to non-prime moduli, by using Lagrange's theorem and group theory. As an application of Fermat's theorem we show there are infinitely many prim
From playlist Theory of numbers
Why should you read “Kafka on the Shore”? - Iseult Gillespie
Follow the entwined destinies of Kafka and Nakata in Haruki Murakami’s mind-bending novel “Kafka on the Shore.” -- Desperate to escape his tyrannical father and the family curse he feels doomed to repeat, Haruki Murakami’s teenage protagonist renames himself “Kafka” after his favorite au
From playlist New TED-Ed Originals
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
They Delivered on the Monsters - Still Untitled: The Adam Savage Project - 10/29/19
Surprise! Adam took an unannounced vacation and returns from being away for two weeks traveling to Spain and Italy. We hear about his adventures in those countries and his recommendations. Plus, discussions on the most recent Godzilla movie, HBO's Watchmen show, and a few books that Will a
From playlist The Adam Savage Project
Adam Savage's Top 5 Science Fiction Books
In this episode of Ask Adam Savage, Adam answers this question from fan Cody Limber: "I've read and loved nearly everything you've mentioned on the Still Untitled podcast, but I need recommendations for sci-fi books. What are your top 5 favorite sci-fi books?" Side note: Adam could not sto
From playlist Staff Favorites
Tested in 2019: Adam Savage's Favorite Things!
Adam caps off our staff's favorite things video series this year with his list of favorite stuff from 2019. It starts with his favorite new hat, and includes tools, books, a mind-blowing fan creation, and an awesome organization worth supporting. Thank you for watching our videos this past
From playlist Staff Favorites
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
We're all in this together. (0:00) Resolutions and channel plans in 2021 (7:50) Vorlesungen zur Philosophie der Mythologie: (Komplettausgabe, aus sämmtliche Werke, Zweite Abteilung, Erster und zweiter Band) by Friedrich Wilhem Joseph von Schelling (9:40) Lie Groups, Lie Algebras, and Repr
From playlist Reviews
Learning From the Best: Character Description
Today we look at how to describe character. Our examples come from Michael Punke's 'The Revenant', Haruki Murakami's '1Q84' and Virginia Woolf's 'To The Lighthouse'. Buy my revision guides in paperback on Amazon*: Mr Bruff’s Guide to GCSE English Language https://amzn.to/2GvPrTV Mr Bru
From playlist AQA English Language Paper 1
OSB 2015 - What stuttering taught me about marketing - not your typical soft skills talk
By, Sharon Steed Your weakness just might be your greatest strength.
From playlist Open Source Bridge 2015
Math 023 Fall 2022 120722 Introduction to Complex Numbers (Arithmetic)
Problem with real numbers: no solution to x^2 = -1. So we adjoin a symbol, i, to the real numbers, and require that all the basic laws (commutativity, associativity, distributivity, etc.) hold. Definition of complex number: a+bi, where a, b are real numbers. Definition of real part, com
From playlist Course 1: Precalculus (Fall 2022)
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
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
How to Make a Proper Cup of ENGLISH TEA: & the Dirty TRUTH about TEABAGS
For the perfect cup of English tea use loose tea (never teabags which will not give you the same taste and a very bad for the environment. As well as good quality tea you will need: good water, good milk (if you are using it) and a good quality ceramic tea set. In this video we'll take yo
From playlist All about Tea