Lectures related to Levy Flights & Brownian Motion

Explores Fokker-Planck equations, escape rates, and first passage time analysis in statistical physics.

Explores building a roulette, probability distributions on curves, and properties of random surface models, including the groundbreaking Schramm-Loewner evolution processes.

Elements of Statistics: Probability and Random Variables

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

Levy Flights and Central Limit Theorem

Covers Levy flights, Central Limit Theorem, and Mesoscopic Master Equation with transition rates in an assurance system.

Introduction to Data Science

Introduces data science topics, evaluation methods, and course organization for the semester.

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.

Continuous Random Variables

Explores continuous random variables, density functions, joint variables, independence, and conditional densities.

Probability Distributions in Environmental Studies

Explores probability distributions for random variables in air pollution and climate change studies, covering descriptive and inferential statistics.

Advanced Probabilities: Random Variables & Expected Values

Explores advanced probabilities, random variables, and expected values, with practical examples and quizzes to reinforce learning.

Probability Distributions: Discrete and Continuous

Covers discrete and continuous probability distributions, including joint and conditional probabilities.

Air Pollution Analysis

Explores air pollution analysis using wind data, probability distributions, and trajectory models for air quality assessment.

Linear Regression: Theory and Applications

Covers the theory and practical applications of linear regression.

Probability and Statistics

Explores joint random variables, conditional density, and independence in probability and statistics.

Introduction to Continuous Random Variables: Probability Distributions

Introduces continuous random variables and their probability distributions, emphasizing their applications in statistics and data science.

Random Variables and Expected Value

Introduces random variables, probability distributions, and expected values through practical examples.

Martingales and Brownian Motion Construction

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.

Probability and Statistics

Covers Simpson's paradox, probability distributions, and real-life examples in probability and statistics.

Common Distributions: Moment Generating Functions

Explores common probability distributions, special distributions, and entropy concepts.

Statistical Thermodynamics: Density of States

Explores density of states in statistical thermodynamics and the use of Heaviside functions for energy level probabilities.

Quantization of Probability Distributions

Covers quantization of probability distributions, statistical k-means clustering, mean estimation, robust clustering methods, and open research questions.