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
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
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)
Theory of numbers: Fermat's theorem
This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se
From playlist Theory of numbers
Mikhail Lyubich: Story of the Feigenbaum point
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Dynamical Systems and Ordinary Differential Equations
Number Theorem | Gauss' Theorem
We prove Gauss's Theorem. That is, we prove that the sum of values of the Euler phi function over divisors of n is equal to n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
The Drinfeld-Sokolov reduction of admissible representations of affine Lie algebras - Gurbir Dhillon
Workshop on Representation Theory and Geometry Topic: The Drinfeld--Sokolov reduction of admissible representations of affine Lie algebras Speaker: Gurbir Dhillon Affiliation: Yale University Date: April 03, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Stanford Seminar - Applying Theory to Practice (and Practice to Theory)
"Applying Theory to Practice (and Practice to Theory)" -Ron Fagin This seminar features leading Industrial and academic experts on big data analytics, information management, data mining, machine learning, and large-scale data processing. Learn more: http://stanford.io/1CnPxC8 0:00 Intr
From playlist Statistics and Data Science
Fermat's Last Theorem for rational and irrational exponents
Fermat's Last Theorem states the equation x^n + y^n = z^n has no integer solutions for positive integer exponents greater than 2. However, Fermat's Last Theorem says nothing about exponents that are not positive integers. Note: x, y and z are meant to be positive integers, which I should
From playlist My Maths Videos
Theory of numbers: Multiplicative functions
This lecture is part of an online undergraduate course on the theory of numbers. Multiplicative functions are functions such that f(mn)=f(m)f(n) whenever m and n are coprime. We discuss some examples, such as the number of divisors, the sum of the divisors, and Euler's totient function.
From playlist Theory of numbers
Cascadia Ruby Conf 2012 A Taste of Prolog by Aja Hammerly
Help us caption & translate this video! http://amara.org/v/FGiV/
From playlist Cascadia Ruby 2012
Bayes, Medical Diagnostics, and Nomograms
(April 11, 2012) Joe Marasco shares his beliefs on how modern diagnostics and medical testing can be changed to give patients a clearer understanding of the results. He suggests implementing a new protocol using Bayes theorem and certain medical technologies to help explain testing results
From playlist Engineering
Proof & Explanation: Gauss's Lemma in Number Theory
Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z
From playlist Quadratic Residues
Nicole Schweikardt: Databases and descriptive complexity – lecture 1
Recording during the meeting "Spring school on Theoretical Computer Science (EPIT) - Databases, Logic and Automata " the April 11, 2019 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by wor
From playlist Numerical Analysis and Scientific Computing
Knot Categorification From Mirror Symmetry (Lecture- 2) by Mina Aganagic
PROGRAM QUANTUM FIELDS, GEOMETRY AND REPRESENTATION THEORY 2021 (ONLINE) ORGANIZERS: Aswin Balasubramanian (Rutgers University, USA), Indranil Biswas (TIFR, india), Jacques Distler (The University of Texas at Austin, USA), Chris Elliott (University of Massachusetts, USA) and Pranav Pan
From playlist Quantum Fields, Geometry and Representation Theory 2021 (ONLINE)
Number Theory | A very special case of Fermat's Last Theorem
We prove a very simple case of Fermat's Last Theorem. Interestingly, this case is fairly easy to prove which highlights the allure of the theorem as a whole -- especially given the fact that much of modern number theory was developed as part of the program that ended in the full proof. ht
From playlist Number Theory
Character Tables for S5 and A5
Representation Theory of Finite Groups: We compute the character tables of S5, the symmetric group on 5 letters, and A5, the subgroup of even permutations. We note that A5 is isomorphic to the group of rigid motions of an icosahedron.
From playlist Representation Theory
Ilya Dumanski - Schubert varieties in the Beilinson-Drinfeld Grassmannian
Ilya Dumanski (MIT) The Borel-Weil theorem states that the space of sections of a certain line bundle on the flag variety is isomorphic to the irreducible representation of the corresponding reductive group. The classical result of Demazure describes the restriction of sections to the Sch
From playlist Azat Miftakhov Days Against the War
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