Lectures related to Mathematical Analysis: Factorial Generalization and Absorption

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Compression: Prediction

Covers the concepts of compression and prediction using prefix-free codes and distributions.

Probability and Statistics

Covers probability distributions, moments, and continuous random variables.

Compression

Covers the concept of compression and constructing prefix-free codes based on given information.

Distributions & Interpolation Spaces

Covers distributions, interpolation spaces, convergence, and the concept of dual spaces.

Elements of Statistics: Probability and Random Variables

Introduces key concepts in probability and random variables, covering statistics, distributions, and covariance.

Generalization Error

Discusses mutual information, data processing inequality, and properties related to leakage in discrete systems.

Fundamental Solutions of Laplace Equation

Explores fundamental solutions, Green's formula, distributions, and convergence in Laplace equation.

Distribution & Interpolation Spaces

Covers the concept of distributions with compact support and their interpolation spaces.

Introduction to Distributions

Covers Green's representation formula, fundamental solutions, and distribution properties.

Probabilistic Functions: Free Fields and Random Variables

Covers free fields and probabilistic functions, focusing on random variables and their properties.

Exponential Family: Distributions and Regularity

Covers the exponential family of distributions and the Ising model, explaining magnetism through dipoles and spins.

Cut-off Phenomenon: Proof Ideas

Explores proof ideas related to the cut-off phenomenon and its implications in random walks on hypercubes.

Understanding Statistics & Experimental Design

Covers statistics, experimental design, errors, distributions, implications of sample size, and null results.

Risk Analysis and Management: Basics I

Introduces the basics of risk analysis and management in civil engineering.

Probability Theory: Random Variables and Distributions

Introduces probability theory, random variables, and distributions, with a focus on their applications in atomic diffusion.

Signals & Systems I: Fourier Transformation and Distributions

Explores the Fourier transformation, Parseval relation, weak convergence, and generalized transformations in signals and systems.

Bivariate Maxima: Parametric Models and Distributions

Explores bivariate maxima, parametric models, distributions, and dependence functions in statistics.

Elements of Statistics: Probability, Distributions, and Estimation

Covers probability theory, distributions, and estimation in statistics, emphasizing accuracy, precision, and resolution of measurements.

Basics of Risk Analysis and Management

Introduces the basics of risk analysis and management in civil engineering, covering distributions, statistical reminders, and mathematical interpretation techniques.