Lectures related to Introduction to Proofs

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.

Ordinary Differential Equations: Definitions and Methods

Explores ordinary differential equations, proof methods, and historical examples from Euclid, emphasizing logical reasoning and step-by-step derivations.

Approximation in Sobolev Spaces

Covers the approximation of functions in Sobolev spaces using smooth functions.

Proof Techniques: Direct, Contraposition, Cases

Covers proof techniques like direct, contraposition, and cases with examples.

Implicit Functions Theorem

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

Newtonian Potential: Bounded Domains

Explores Newtonian potential in bounded domains, discussing its conditions and properties.

Prime Numbers: Euclid's Theorem

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

Area: Axioms and Rectangles

Covers the concept of area, axioms, and the area of rectangles.

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