Boris Adamczewski: Mahler's method in several variables
Abstract: Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number
From playlist Combinatorics
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
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)
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
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
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation
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
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
Title: Algebraic Independence of Functions Satisfying Nonlinear Polynomial Mahler Equations
From playlist Differential Algebra and Related Topics VII (2016)
The Fundamental Theorem of Calculus | Algebraic Calculus One | Wild Egg
In this video we lay out the Fundamental Theorem of Calculus --from the point of view of the Algebraic Calculus. This key result, presented here for the very first time (!), shows how to generalize the Fundamental Formula of the Calculus which we presented a few videos ago, incorporating t
From playlist Algebraic Calculus One
The Secrets of Pi (and other transcendental numbers): 2022 Mahler Lecture Tour by Frank Calegari
Esteemed algebraic number theorist Professor Frank Calegari presented this public talk on the Secrets of Pi on 23 November 2022, hosted by SMRI. Event photo gallery: https://mathematical-research-institute.sydney.edu.au/news/frank-calegari-secrets-of-pi-photo-gallery/ 0:00 Introduction b
From playlist Public lectures
CTNT 2022 - p-adic Fourier theory and applications (by Jeremy Teitelbaum)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures
Title: Consistent Systems of Linear Differential and Difference Equations April 2016 Kolchin Seminar Workshop
From playlist April 2016 Kolchin Seminar Workshop
Gustav Mahler: Symphony No. 2 – 1st Movement . Analysis by Gerard Schwarz | Music | Khan Academy
Created by All-Star Orchestra. Watch the full performance here: https://www.youtube.com/watch?v=vGDEI7MuatA&feature=youtu.be Watch the next lesson: https://www.khanacademy.org/humanities/music/music-masterpieces-old-new/mahler-sym-2/v/gustav-mahler-second-symphony-an-appreciation-by-gilb
From playlist Masterpieces old and new | Music | Khan Academy
Lecture 22. Modernism and Mahler
Listening to Music (MUSI 112) In this final formal lecture of the course, Professor Wright discusses Modernism, focusing on Stravinsky's The Rite of Spring. He explores several musical reasons why The Rite of Spring caused a riot at its 1913 Paris premiere. Professor Wright then goes on t
From playlist Listening to Music with Craig Wright
Multiplicative Rational P-adic Approximation by Yann Bugeaud
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
Lecture 20. The Colossal Symphony: Beethoven, Berlioz, Mahler and Shostakovich
Listening to Music (MUSI 112) The history and development of the symphony is the topic of this lecture. Professor Wright leads the students from Mozart to Mahler, discussing the ways in which the genre of symphonic music changed throughout the nineteenth century, as well as the ways in wh
From playlist Listening to Music with Craig Wright
Marie-José Bertin - Des nombres de Salem à la mesure de Mahler de surfaces K3 (Part 2)
Le récent article de McMullen « Dynamics with small entropy on projective K3 surfaces » éclaire d’un jour nouveau les nombres de Salem. Ces entiers algébriques gardent cependant tout leur mystère. On peut tous les obtenir grâce à la construction de Salem (Boyd (1977)) et cependant on ignor
From playlist École d’été 2013 - Théorie des nombres et dynamique
Calculus - The Fundamental Theorem, Part 2
The Fundamental Theorem of Calculus. A discussion of the antiderivative function and how it relates to the area under a graph.
From playlist Calculus - The Fundamental Theorem of Calculus
Stanford Symphony Orchestra performs Mahler's Symphony No. 6
The 120 musicians of the Stanford Symphony Orchestra rehearse at Bing Concert Hall for a performance of Mahler's Symphony No. 6 in A minor, “Tragic." The 90-minute epic transports performers and audience members through Mahler's world of poetic landscape, sinister visions and profound love
From playlist Stanford Highlights