Carathéodory's Theorem and Dimension Bound

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Derivative of an Integral with Parameter

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

Integration by Substitution

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

Lagrange Theorem: Applications and Proofs

Covers the application and proof of the Lagrange theorem in group theory.

Multivariate Statistics: Normal Distribution

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

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.

Counting on Fingers

Compares various finger counting systems and introduces binary representation.

Mathematics: Cylinders and Parametrizations

Discusses the mathematical concepts of cylinders and their parametrizations, including surface area, volume, and related exercises.

Supremum Theorem

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

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.

Linear Independence: The Wronskian Concept

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