Lectures related to Proofs: Rules and Applications

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

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

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.

Predicate Logic: Translating Natural Language into Logic

Covers the translation of natural language sentences into predicate logic and the importance of quantifier order.

Sequent Calculus: Basics and Applications

Covers the basics and applications of Sequent Calculus in Logic and Proof Theory, including Cut Elimination and practical proof analysis.

Mathgraph Theorem Prover

Introduces the Mathgraph Theorem Prover, showcasing its unique approach to representing propositions and organizing graphs for first-order logic.

Propositional Logic: Translations and Equivalences

Covers translating natural language to propositional logic and proving tautologies.

Fundamental Groups

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