Mathematical constants | Geometry of numbers | Systolic geometry
In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be. The constant γn for integers n > 0 is defined as follows. For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) = 1, let λ1(L) denote the least length of a nonzero element of L. Then √γn is the maximum of λ1(L) over all such lattices L. The square root in the definition of the Hermite constant is a matter of historical convention. Alternatively, the Hermite constant γn can be defined as the square of the maximal systole of a flat n-dimensional torus of unit volume. (Wikipedia).
Series solution of the Hermite differential equation. Shows how to construct the Hermite polynomials. Join me on Coursera: Differential equations for engineers https://www.coursera.org/learn/differential-equations-engineers Matrix algebra for engineers https://www.coursera.org/learn/matr
From playlist Differential Equations with YouTube Examples
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (56 of 92) What is a Hermite Polynomial?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Hermite polynomial. Previous videos showed the solution best describe the quantum oscillator of the Schrodinger equation is the product of a constant that needed to be normalized, mu
From playlist THE "WHAT IS" PLAYLIST
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (57 of 92) Calculating Hermite Polynomial?
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the first few Hermitian polynomials stating with n=0 to n=3. Next video in this series can be seen at: https://youtu.be/9euxAKJDll0
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Lattice relations + Hermite normal form|Abstract Algebra Math Foundations 224 | NJ Wildberger
We introduce lattices and integral linear spans of vexels. These are remarkably flexible, common and useful algebraic objects, and they are the direct integral analogs of vector spaces. To understand the structure of a given lattice, the algorithm to compute a Hermite normal form basis is
From playlist Math Foundations
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
Hermitian Operators (Self-Adjoint Operators) | Quantum Mechanics
In this video, we will talk about Hermitian operators in quantum mechanics. If an operator A is a Hermitian operator, then it is the same as its adjoint operator A-dagger, which is defined via this equation here. Usually, the terms "Hermitian" and "self adjoint" are used interchangeably, h
From playlist Quantum Mechanics, Quantum Field Theory
Math 060 Fall 2017 112717C Hermitian Matrices Part 1
Definitions: complex conjugate, modulus, complex vector, conjugate transpose, complex inner product, conjugate matrix. Hermitian matrices. Hermitian matrices and the inner product. Hermitian matrices have 1. real eigenvalues, 2. orthogonal eigenspaces. Unitary matrices. Hermitian matr
From playlist Course 4: Linear Algebra (Fall 2017)
How to determine if an equation is a linear relation
👉 Learn how to determine if an equation is a linear equation. A linear equation is an equation whose highest exponent on its variable(s) is 1. The variables do not have negative or fractional, or exponents other than one. Variables must not be in the denominator of any rational term and c
From playlist Write Linear Equations
Mod-01 Lec-08 Cubic Spline Interpolation
Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in
From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics
10c Machine Learning: Polynomial Regression
Lecture on polynomial regression, including an intuitive alternative interpretation, basis expansion concepts and orthogonal basis through Hermite polynomials. Follow along with the demonstration workflow: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnaly
From playlist Machine Learning
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (55 of 92) Solution of the Oscillator
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the solution to the Schrodinger equation to the quantum mechanic oscillator. Assuming the potential energy (a function of the square of the amplitude, A^2) is greater or equal to 1, the soluti
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Quadratic forms and Hermite constant, reduction theory by Radhika Ganapathy
Discussion Meeting Sphere Packing ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Phong NGUYEN - Recent progress on lattices's computations 2
This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
A central limit theorem for Gaussian polynomials... pt1 -Anindya De
Anindya De Institute for Advanced Study; Member, School of Mathematics May 13, 2014 A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions In this talk, we will continue, the proof of the Central Limit theorem from my las
From playlist Mathematics
How to Determine if Functions are Linearly Independent or Dependent using the Definition
How to Determine if Functions are Linearly Independent or Dependent using the Definition If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Th
From playlist Zill DE 4.1 Preliminary Theory - Linear Equations
8. Quantum Mechanical Harmonic Oscillator
MIT 5.61 Physical Chemistry, Fall 2017 Instructor: Professor Robert Field View the complete course: https://ocw.mit.edu/5-61F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg This lecture covers the quantum mechanical treatment of the harmonic o
From playlist MIT 5.61 Physical Chemistry, Fall 2017
Spin Glass Phase at Zero Temperature in the Edwards--Anderson Model by Sourav Chatterjee
PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab
From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY
Overview of Linear equations - Free Math Videos - Online Tutor
👉 Learn how to determine if an equation is a linear equation. A linear equation is an equation whose highest exponent on its variable(s) is 1. The variables do not have negative or fractional, or exponents other than one. Variables must not be in the denominator of any rational term and c
From playlist Write Linear Equations
"Transcendental Number Theory: Recent Results and Open Problems" by Prof. Michel Waldschmidt
This lecture will be devoted to a survey of transcendental number theory, including some history, the state of the art and some of the main conjectures.
From playlist Number Theory Research Unit at CAMS - AUB