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.

Implicit Functions Theorem

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

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.

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.

Area: Axioms and Rectangles

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

Prime Numbers: Euclid's Theorem

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

Linear Independence: The Wronskian Concept

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

Prime Number Theorem

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

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