Lectures related to Pure mathematics

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Emphasizes mathematical rigor, clear communication, and exercise organization in teaching methods.

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Covers the concept of limits at infinity and provides insights into its application.

Explores the logarithmic derivative of the Zeta function using the Hadamard factorization.

Covers the Bayes discriminant rule for allocating individuals to populations based on measurements and prior probabilities.

Introduces Principal Component Analysis, focusing on maximizing variance in linear combinations to summarize data effectively.

Explores proximal operators, subgradient methods, and composite minimization in optimization.

Explores the properties and examples of Dirichlet series, highlighting their key characteristics and applications.

Demonstrates the practical application of theorems in calculus through two clever examples.

Covers the Implicit Functions Theorem, providing a general understanding of implicit functions.

Covers improper integrals, their definitions, properties, and examples in two and three dimensions.

Explores principal components, covariance, correlation, choice, and applications in data analysis.

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Explores the integration by parts technique through examples, showcasing its step-by-step application to functions like cos(x) and sin(x.

Covers the proof of the explicit formula for the non-vanishing of the zeta function at the 1-line.

Discusses the residue theorem and its applications in calculating complex integrals.

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.