Recurrence and transience: proofs

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Probability Theory: Integration and Convergence

Covers topics in probability theory, focusing on uniform integrability and convergence theorems.

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Introduces Markov chains and Metropolis Hastings algorithm in stochastic simulation.

Analysis IV: Convolution and Hilbert Structure

Explores convolution, uniform continuity, Hilbert structure, and Lebesgue measure in analysis.

Distributions and Derivatives

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

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Covers classical testing of qubits, including measuring in different bases and obtaining uniform results.

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Theoreus Chain Role: Lipschitz Sit

Covers the Theoreus Chain Role for Lipschitz functions and its practical applications.

Measure Spaces: Integration and Inequalities

Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Advanced Physics I: Orders of Magnitude

Explores the triumph of determinism in modern mechanics and the methodology of scientific development, with practical exercises on estimating surgical mask usage and analyzing atomic bomb energy.