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
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
In this video, I give a very neat and elegant proof of Taylor’s theorem, just to show you how neat math can be! It is simply based on repeated applications of the fundamental theorem of calculus. Enjoy! Note: The thumbnail is taken from https://i.redd.it/kv7lk5kn31e01.jpg
From playlist Calculus
Number Theory - Fundamental Theorem of Arithmetic
Fundamental Theorem of Arithmetic and Proof. Building Block of further mathematics. Very important theorem in number theory and mathematics.
From playlist Proofs
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)
Unbounded Fast Escaping Wandering Domains - Adi Glücksam
Special Year Research Seminar Topic: Unbounded Fast Escaping Wandering Domains Speaker: Adi Glücksam Affiliation: Northwestern University Date: March 21, 2023 Complex dynamics explores the evolution of points under iteration of functions of complex variables. In this talk I will introduc
From playlist Mathematics
Error bounds for Taylor approximations -- Calculus II
This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.
From playlist Calculus II
Anna Miriam Benini: Polynomial versus transcendental dynamics
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 24, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Dynamical Systems and Ordinary Differential Equations
Images in Math - Pascal's Theorem
This video is about Pascal's Theorem.
From playlist Images in Math
Classify a polynomial then determining if it is a polynomial or not
👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio
From playlist Is it a polynomial or not?
Samit Dasgupta: An introduction to auxiliary polynomials in transcendence theory, Lecture I
Broadly speaking, transcendence theory is the study of the rationality or algebraicity properties of quantities of arithmetic or analytic interest. For example, Hilbert’s 7th problem asked ”Is a b always transcendental if a 6= 0, 1 is algebraic and b is irrational algebraic?” An affirmativ
From playlist Harmonic Analysis and Analytic Number Theory
Samit Dasgupta: An introduction to auxiliary polynomials in transcendence theory, Lecture II
Broadly speaking, transcendence theory is the study of the rationality or algebraicity properties of quantities of arithmetic or analytic interest. For example, Hilbert’s 7th problem asked ”Is a b always transcendental if a 6= 0, 1 is algebraic and b is irrational algebraic?” An affirmativ
From playlist Harmonic Analysis and Analytic Number Theory
Effective height bounds for odd-degree totally real points on some curves - Levent Alpoge
Joint IAS/Princeton University Number Theory Seminar Topic: Effective height bounds for odd-degree totally real points on some curves Speaker: Levent Alpoge Affiliation: Columbia University Date: November 12, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
What Makes P vs. NP So Hard? (P ≠ EXPTIME, Time Hierarchy, Baker-Gill-Solovay)
There are a lot of unsolved problems in complexity theory, but there are a few things we do know. We look at the Time Hierarchy Theorem, and also why the proof techniques don't transfer to P vs NP. Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen, Zachary Greenber
From playlist P vs NP
Number Theory | Lagrange's Theorem of Polynomials
We prove Lagrange's Theorem of Polynomials which is related to the number of solutions to polynomial congruences modulo a prime.
From playlist Number Theory
Jean-Luc Thiffeault: "On mix-norms and the rate of decay of correlations"
Transport and Mixing in Complex and Turbulent Flows 2021 "On mix-norms and the rate of decay of correlations" Jean-Luc Thiffeault - University of Wisconsin-Madison, Mathematics Abstract: Two quantitative notions of mixing are the decay of correlations and the decay of a mix-norm --- a ne
From playlist Transport and Mixing in Complex and Turbulent Flows 2021
Philipp Habegger: Equidistribution of roots of unity and the Mahler measure
CIRM VIRTUAL CONFERENCE Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the November 25, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide
From playlist Virtual Conference
Planarity in Higher Codimension Mean Curvature Flow - Keaton Naff
Analysis Seminar Topic: Planarity in Higher Codimension Mean Curvature Flow Speaker: Keaton Naff Affiliation: Columbia University Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Lie groups: Baker Campbell Hausdorff formula
This lecture is part of an online graduate course on Lie groups. We state the Baker Campbell Hausdorff formula for exp(A)exp(B). As applications we show that a Lie group is determined up to local isomorphism by its Lie algebra, and homomorphisms from a simply connected Lie group are deter
From playlist Lie groups
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