Unit 1: Foundations of Probability Spaces
Unit 2: Constructing Probability Measures
Unit 3: Continuous Probability Spaces
Rigorous Probability Theory for Theoretical Physics
A rigorous introduction to probability theory, tailored for theoretical physicists, covering measure-theoretic foundations, limit theorems, and stochastic processes.
Unit 1: Introduction to Measures
Unit 2: Measure Properties
Unit 3: Lebesgue Measure
Unit 4: Measurable Functions
Unit 1: Random Variables: The Basics
Unit 2: Distribution Functions
Unit 3: Types of Random Variables
Unit 1: Introduction to Probability Density Functions
Unit 2: Working with Common PDFs
Unit 3: Advanced PDF Concepts
Unit 1: Defining Expectation
Unit 2: Calculating Expectations
Unit 3: Moments and Their Significance
Unit 1: Joint Distributions and Functions
Unit 2: Marginal and Conditional Distributions
Unit 3: Independence and Applications
Unit 1: Modes of Convergence
Unit 2: Relationships Between Modes
Unit 3: Examples and Applications
Unit 1: Preliminaries to the Laws
Unit 2: Weak Law of Large Numbers
Unit 3: Strong Law of Large Numbers
Unit 4: Applications and Extensions
Unit 1: Understanding the Central Limit Theorem
Unit 2: Proving and Applying the CLT
Unit 3: Advanced Applications and Considerations
Unit 1: Conditional Probability
Unit 2: Bayes' Theorem
Unit 3: Conditional Expectation
Unit 1: Introduction to Markov Chains
Unit 2: Transition Probabilities and Matrices
Unit 3: State Classification
Unit 1: Defining and Understanding Stationary Distributions
Unit 2: Computing Stationary Distributions
Unit 3: Convergence and Applications