Lectures related to Dirichlet Series: Properties and Examples

Covers the concept of integrals of paths with examples and applications.

Explores Cauchy sequences, convergence, bottoms, and series with illustrative examples.

Principal Component Analysis: Introduction

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Orthogonality and Least Squares Method

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

Principal Components: Properties & Applications

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Convex Functions

Covers the properties and operations of convex functions.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Online Lecturing: Integral Equations and Laplace Transform Methods

Explores integral equations, Laplace transform methods, and problem-solving techniques.

Mathematics: Functions and Series

Explores functions, series, and critical points in mathematics, including maximum, minimum, supremum, and infimum concepts.

Linear Algebra Basics

Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Fourier Series and Equations

Covers Fourier series, periodic functions, and Fourier transforms.

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Weak Solutions of Differential Equations

Explores weak solutions of differential equations and their properties.

Fourier Series: Convergence and Dirichlet Theorem

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Convergence Criteria

Covers convergence criteria for series, including comparison, Cauchy's root test, and d'Alembert's ratio test.

Equivalence Relations and Construction of R

Covers the construction of R and equivalence relations in sequences and linear recurrences.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Tensors: Motivations and Introduction

Covers the basics of tensors, including their definition, properties, and decomposition, starting with a motivating example involving Gaussian distributions.

Wurzelkriterium: Majorantenkriterium

Covers the Majorantenkriterium and Wurzelkriterium for convergence tests of series.