Unsolved problems in number theory | Continued fractions | Algebraic number theory

Hermite's problem

Hermite's problem is an open problem in mathematics posed by Charles Hermite in 1848. He asked for a way of expressing real numbers as sequences of natural numbers, such that the sequence is eventually periodic precisely when the original number is a cubic irrational. (Wikipedia).

Video thumbnail

Hermite differential equation

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

Video thumbnail

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

Video thumbnail

C36 Example problem solving a Cauchy Euler equation

An example problem of a homogeneous, Cauchy-Euler equation, with constant coefficients.

From playlist Differential Equations

Video thumbnail

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

Video thumbnail

C43 Example problem solving a Cauchy Euler equation

Another Cauchy-Euler equation example problem solved.

From playlist Differential Equations

Video thumbnail

C47 Example problem solving a Cauchy Euler equation

The last problem solved in this section, before we move on to another technique for linear differential equations.

From playlist Differential Equations

Video thumbnail

C37 Example problem solving a Cauchy Euler equation

Example problem solving a homogeneous Cauchy-Euler equation.

From playlist Differential Equations

Video thumbnail

C74 Example problem

A first example problem solving a linear, second-order, homogeneous, ODE with variable coefficients around a regular singular point.

From playlist Differential Equations

Video thumbnail

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

Video thumbnail

Under the Sea - With Helen Scales

A dive into the spiralling world of seashells and the bizarre animals that make them. Helen Scales explains how hermit crabs like to party and butterflies learnt to swim. Watch the Q&A: https://www.youtube.com/watch?v=GqBHjBDgLfY Subscribe for regular science videos: http://bit.ly/RiSubsc

From playlist Ri Talks

Video thumbnail

B25 Example problem solving for a Bernoulli equation

See how to solve a Bernoulli equation.

From playlist Differential Equations

Video thumbnail

Ch04n2: Integrals over Infinite Intervals, Gauss Laguerre, Gauss Hermite

Integrals over Infinite Intervals. Gauss Laguerre, Gauss Hermite Numerical Computation, chapter 4, additional video no 2. To be viewed after the video ch04n1. Wen Shen, Penn State University, 2018.

From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University

Video thumbnail

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

Video thumbnail

Advice for Amateur Mathematicians | The joy of maxel number theory and Hermite polyns |Wild Egg Math

We extend our two dimensional number theory point of view to the case of Hermite polynomials. These actually come in two different kinds: called the probabilists' and the physicists' versions. Can we find some interesting patterns when we express these in a two-dimensional setting as a tr

From playlist Maxel inverses and orthogonal polynomials (non-Members)

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

13. Monasticism

The Early Middle Ages, 284--1000 (HIST 210) Professor Freedman discusses some of the paradoxes of monasticism in the Early Middle Ages. To the modern mind, monks and learning make a natural pair. However, this combination is not an obvious outcome of early monasticism, which emphasized as

From playlist The Early Middle Ages, 284--1000 with Paul Freedman

Video thumbnail

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

Video thumbnail

C49 Example problem solving a system of linear DEs Part 1

Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.

From playlist Differential Equations

Related pages

Unit square | Carl Gustav Jacob Jacobi | Continued fraction | Minimal polynomial (field theory) | Floor and ceiling functions | Dyadic rational | Algebraic number | Polynomial | Generalized continued fraction | Rational number | Decimal representation | Sequence | Simplex | Natural number | Mathematics | Set (mathematics) | Integer | Real number | Charles Hermite | Irrational number | Cubic field