Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
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
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
The Field With One Element and The Riemann Hypothesis (Full Video)
A crash course of Deninger's program to prove the Riemann Hypothesis using a cohomological interpretation of the Riemann Zeta Function. You can Deninger talk about this in more detail here: http://swc.math.arizona.edu/dls/ Leave some comments!
From playlist Riemann Hypothesis
Here I prove the Heine-Borel Theorem, one of the most fundamental theorems in analysis. It says that in R^n, all boxes must be compact. The proof itself is very neat, and uses a bisection-type argument. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHG
From playlist Topology
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)
Convolution Theorem: Fourier Transforms
Free ebook https://bookboon.com/en/partial-differential-equations-ebook Statement and proof of the convolution theorem for Fourier transforms. Such ideas are very important in the solution of partial differential equations.
From playlist Partial differential equations
The Weyl algebra and the Heisenberg Lie algebra
In this video we give a simple teaser into the world of operator algebras. In particular, we talk about the Weyl algebra and compute some expressions that fulfill the property which defines the Heisenberg Lie algebra http://math.uchicago.edu/~may/REU2012/REUPapers/Lingle.pdf https://en.w
From playlist Algebra
Multidimensional Bolzano Weierstraß
In this video, I prove the celebrated Bolzano-Weierstraß theorem in n dimensions, which says that a bounded sequence in R^n must have a convergent subsequence. This is the most important fact in analysis, and a lot of nice results follow from it Bolzano-Weierstraß: https://youtu.be/PapmU
From playlist Topology
Calculus 1 (Stewart) Ep 22, Mean Value Theorem (Oct 28, 2021)
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart. PDF of the written notes, and a list of all episodes is at the class website. Class website: http://cstaecker.f
From playlist Math 1171 (Calculus 1) Fall 2021
Equidistribution of Unipotent Random Walks on Homogeneous spaces by Emmanuel Breuillard
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
What is Green's theorem? Chris Tisdell UNSW
This lecture discusses Green's theorem in the plane. Green's theorem not only gives a relationship between double integrals and line integrals, but it also gives a relationship between "curl" and "circulation". In addition, Gauss' divergence theorem in the plane is also discussed, whic
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell
Real Analysis Ep 32: The Mean Value Theorem
Episode 32 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is more about the mean value theorem and related ideas. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker
From playlist Math 3371 (Real analysis) Fall 2020
Pythagorean theorem - What is it?
► My Geometry course: https://www.kristakingmath.com/geometry-course Pythagorean theorem is super important in math. You will probably learn about it for the first time in Algebra, but you will literally use it in Algebra, Geometry, Trigonometry, Precalculus, Calculus, and beyond! That’s
From playlist Geometry
Wolfram Physics Project: Working Session Sept. 15, 2020 [Physicalization of Metamathematics]
This is a Wolfram Physics Project working session on metamathematics and its physicalization in the Wolfram Model. Begins at 10:15 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the
From playlist Wolfram Physics Project Livestream Archive
Johnathan Bush (7/8/2020): Borsuk–Ulam theorems for maps into higher-dimensional codomains
Title: Borsuk–Ulam theorems for maps into higher-dimensional codomains Abstract: I will describe Borsuk-Ulam theorems for maps of spheres into higher-dimensional codomains. Given a continuous map from a sphere to Euclidean space, we say the map is odd if it respects the standard antipodal
From playlist AATRN 2020
Worldwide Calculus: Extrema and the Mean Value Theorem
Lecture on 'Extrema and the Mean Value Theorem' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
Stokes' Theorem and Green's Theorem
Stokes' theorem is an extremely powerful result in mathematical physics. It allows us to quantify how much a vector field is circulating or rotating, based on the integral of the curl. @eigensteve on Twitter eigensteve.com databookuw.com %%% CHAPTERS %%% 0:00 Stoke's Theorem Overview
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
The Weierstrass Definition of the GAMMA FUNCTION! - Proving Equivalence!
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Gamma derive: https://youtu.be/0170T
From playlist Limits
Green's Theorem. Chris Tisdell UNSW
This is the 2nd lecture on Green's theorem and its use. In this lecture we explore some interesting applications of Green's theorem and present several examples. Also some proofs are discussed.
From playlist Vector Calculus @ UNSW Sydney. Dr Chris Tisdell