Lectures related to Diophantine approximation

Extreme Problems in Diophantine Approximation and Dynamics

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

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

Diophantine Approximation: Minbowski's Theorem

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

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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Orthogonal Matrices and Least Squares Method

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

Convergence of Fourier Series

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

Taylor Polynomials: Approximating Functions in Multiple Variables

Covers Taylor polynomials and their role in approximating functions in multiple variables.

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.

Interpolation Theory: Embedding and Completeness

Covers the embedding of spaces and the completeness of spaces, exploring the connection between interpolation theory and approximation theory.

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.

Numerical Analysis: Jupyter Notebook Tutorial

Covers course organization, Jupyter Notebook for Python experimentation, algorithms, interpolation, solving equations, linear systems, and practical applications.

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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.

Fermat's Equation: Integral Solutions and Gaussian Integers

Discusses Fermat's equation and Gaussian integers' properties.