Lectures related to Character and Modulus in Mathematics

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

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

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

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

Covers Fourier series convergence, Dirichlet theorem, and applications in signal processing.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

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

Explores multiple integrals, techniques, properties, and center of gravity calculation in various domains.

Explores copulas in multivariate statistics, covering properties, fallacies, and applications in modeling dependence structures.

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

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

Covers the statement of the Bernoulli's Hospital Rule and its application.

Covers the Bombieri-Vinogradov theorem and its implications for prime gaps and multiplicative sieve inequalities.

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

Explores maximum likelihood estimation and multivariate hypothesis testing, including challenges and strategies for testing multiple hypotheses.

Explores the Cauchy problem, emphasizing solution finding and verification processes.

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

Explores solving nonlinear systems of equations using Newton's method.

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

Explains the volume calculation by intersecting two cylinders using coordinates and integrals.