Lectures related to Counting Poker Dices: Combinatorial and Analytical Proofs

Prime Number Theorem

Explores the proof of the Prime Number Theorem and its implications in number theory.

Prime Numbers: Euclid's Theorem

Explores prime numbers and Euclid's Theorem through a proof by contradiction.

Proof of Explicit Formula

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Modular Arithmetic: Foundations and Applications

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Derivative of an Integral with Parameter

Covers deriving integrals with parameters and their derivatives, including special cases and proofs.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Multivariate Statistics: Normal Distribution

Covers the multivariate normal distribution, properties, and sampling methods.

Supremum Theorem

Explores the Supremum Theorem, its properties, proofs, and exercises.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Principal Components: Properties & Applications

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

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Carathéodory's Theorem and Dimension Bound

Explores Carathéodory's Theorem and its dimension implications for set representation.

Calculus of Variations: Gradient Young Theorem

Covers the Gradient Young Theorem in the calculus of variations, discussing proofs and applications.

Copulas: Properties and Applications

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

Compact Sets and Convergence

Explains compact sets, convergence, and absolute convergence in real analysis.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Injective Functions: Properties and Examples

Covers the properties of injective functions and demonstrates their proofs through examples and visual aids.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Integration Techniques: Fundamental Theorems and Methods

Discusses integration techniques, focusing on integration by parts and substitution methods, with practical examples and theoretical insights.

Introduction to Real Numbers and Their Properties

Introduces real numbers, their properties, and their significance in analysis.