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Dirichlet's approximation theorem
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Symmetry in Modern Space
Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.
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.
Diophantine Approximation: Minbowski's Theorem
Covers Minbowski's Theorem on Diophantine Approximation and Gram-Schmidt orthogonalization.
Convergence of Fourier Series
Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.
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Gram-Schmidt Algorithm
Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.
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.
Orthogonal Matrices and Least Squares Method
Introduces orthogonal matrices, the least squares method, and their practical applications in linear algebra.
Numerical Analysis: Jupyter Notebook Tutorial
Covers course organization, Jupyter Notebook for Python experimentation, algorithms, interpolation, solving equations, linear systems, and practical applications.
Neural Networks and Deep Learning
Covers formal neuron models, activation functions, and approximation results for neural networks.
Difference Equations and Controllers
Covers linear difference equations, controllers, discretization, and approximation techniques.
Fourier Series: Convergence and Dirichlet Theorem
Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.
Path Integral Quantum Mechanics
Explores real-time path integrals, time-correlation functions, and quantum dynamics approximations.
Properties of Natural Logarithm
Explores the properties of the natural logarithm function and its graphical representation.
Linear Algebra: Dot Product and Pre-Hilbertian Spaces
Explores pre-Hilbertian spaces, focusing on dot product properties and algebraic bases.
Interpolation: Lagrange polynomial and error analysis
Covers the interpolation of functions using Lagrange polynomials and error analysis, emphasizing the dependence on the function.
Optimisation with Constraints: Interior Point Algorithm
Explores optimization with constraints using KKT conditions and interior point algorithm on two examples of quadratic programming.
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