Lectures related to Proofs: Direct and Indirect Methods

Proof Techniques: Direct, Contraposition, Cases

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

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Linear Algebra: Properties and Operations

Explores subset properties, contraposition, and equivalence in linear algebra.

Prime Number Theorem

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

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Proofs and Logic: Introduction

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

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.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.