Lectures related to Proof Techniques: Direct, Contraposition, Cases

Inductive Propositions: Reasoning and Evaluation Techniques

Discusses inductive propositions, their definitions, and applications in reasoning and evaluation techniques in Coq.

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

Fourier Transform: Properties and Applications

Covers the properties and applications of the Fourier transform and its relation to Heisenberg's uncertainty principle.

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Fourier Inversion Formula

Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.

Analysis IV: Measurable Sets and Properties

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

The Languages of Isabelle: Isar, ML, and Scala

Explores the languages of Isabelle, focusing on Isar, ML, and Scala, covering proof schemes, Natural Deduction rules, inductive definitions, and the LCF approach.