Explores analytical trajectories, emphasizing critical points, inequalities, and analyticity.
Explores Carathéodory's Theorem and its dimension implications for set representation.
Explores the logarithmic derivative of the Zeta function using the Hadamard factorization.
Explores the Cauchy problem, emphasizing solution finding and verification processes.
Introduces proximal operators, gradient methods, and constrained optimization, exploring their convergence and practical applications.
Covers the concept of limits of sequences, including definitions, examples, boundedness, and more.
Covers implicit functions, Taylor polynomials, and tangent equations.
Explores gradient descent methods for smooth convex and non-convex problems, covering iterative strategies, convergence rates, and challenges in optimization.
Explores spectral gap and mixing time in Markov chains, including their definitions and behavior.
Explores Taylor polynomials of order 2 and their applications in differential calculus and polar coordinates.
