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Concept

Diophantine approximation

Related lectures (31)

Extreme Problems in Diophantine Approximation and Dynamics

Explores the Logarithmic Law, geodesic flows, hyperbolic surfaces, and rare events in probability.

Geometric Means: Ancient Theories and Modern Applications

Delves into ancient geometric means and their modern applications in geometry.

Diophantine Approximation on Manifolds: Lower Bounds

Covers Diophantine approximation on manifolds with a focus on lower bounds.

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Regulator Polynomial RST: Classic Servo Systems

Explores classic regulator systems, polynomial degrees of freedom, servo model modifications, and system adjustment through simplification and zero invoicing.

Matrix Functions: Theory and Computation

Covers the theory and computation of matrix functions, focusing on computing f(A) and particularly e^A, with special attention to the matrix exponential and common examples of matrix functions.

Submodular Maximization

Covers submodular function maximization using the greedy algorithm and its approximation guarantee.

Dynamics on homogeneous spaces and interactions with number theory

Explores dynamics on homogeneous spaces, Khintchine theorem, Sullivan's logarithm law, and interactions with number theory.

Untitled

Difference Equations and Controllers

Covers linear difference equations, controllers, discretization, and approximation techniques.

Optimisation with Constraints: Interior Point Algorithm

Explores optimization with constraints using KKT conditions and interior point algorithm on two examples of quadratic programming.

Interpolation: Lagrange polynomial and error analysis

Covers the interpolation of functions using Lagrange polynomials and error analysis, emphasizing the dependence on the function.

Properties of Natural Logarithm

Explores the properties of the natural logarithm function and its graphical representation.

Machine Learning for Solving PDEs: Random Feature Method

Explores the Random Feature Method for solving PDEs using machine learning algorithms to approximate high-dimensional functions efficiently.

Path Integral Quantum Mechanics

Explores real-time path integrals, time-correlation functions, and quantum dynamics approximations.

Radiative Transport Equation

Explores the Radiative Transport Equation in tissue optics, covering radiance, photon distribution, and numerical solutions like Monte Carlo simulations.

Symmetry in Modern Space Log in to Mediaspace to watch this video

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

Diophantine Approximation: Minbowski's Theorem Log in to Mediaspace to watch this video

Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.

Orthogonal Matrices and Least Squares Method Log in to Mediaspace to watch this video

Introduces orthogonal matrices, the least squares method, and their practical applications in linear algebra.

Convergence of Fourier Series Log in to Mediaspace to watch this video

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.