Lectures related to Proof by contradiction

Covers examples of direct and indirect proofs in mathematics.

Explores optimal transport in heat equations and metric spaces.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

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

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

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

Covers proof techniques including direct proof, contraposition, contradiction, cases, and counterexample.

Covers the concepts of contraposition and contradiction in proofs.

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Covers the concept of compression and distance boards.

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

Explores geodesic convexity in metric spaces and its applications, discussing properties and the stability of inequalities.

Introduces Cartesian product and induction for proofs using integers and sets.

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

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

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

Introduces informal proofs, explores practical applications, and explains theorem proofs using direct and indirect methods.

Explores the coupling of Markov chains and the proof of the ergodic theorem, emphasizing distribution convergence and chain properties.