Proofs and Refutations

Related lectures (32)

Page 3 of 4

Covers the Cauchy-Schwarz inequality and the Lagrange identity in R^n with related mathematical expressions and proofs.

Covers the definition of convex functions and their properties in optimization.

Explores Rolle's Theorem and its corollaries, including applications and proofs.

Explores convex sets, their properties, and applications in optimization.

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Explains the concept of Q as a subset of R and their properties.

Explores transience and recurrence in Markov chains, emphasizing birth and death chains and random walks.

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

Covers mathematical proofs by induction, inequalities, divisibility, and subsets.

Covers Burnside's Lemma, Schur Lemmas, and their proofs in group theory and quantum mechanics.