Explores Doob inequalities, martingales, and Holder's inequality in probability theory.
Covers optimization problems and techniques to find maximum and minimum values of functions.
Covers optimization problems, focusing on finding extrema of functions subject to constraints.
Explores the Ito Lemma and its variants, discussing localization and proof techniques.
Covers directional derivatives, implicit functions, and the concept of the maximum.
Covers directional derivatives, implicit functions, and finding equations of tangents.
Covers the concept of partial derivatives and their applications in optimization and tangent plane approximation.
Introduces the basics of ordinary differential equations, exploring global solutions, uniqueness, higher dimensions, Lipschitz functions, and finding solutions.
