Lectures related to Advanced Counting: Quiz

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Counting with Recurrence Relations: Fibonacci Sequence and Bit Strings

Covers the definition of recurrence relations and their application in counting problems.

Optimization Methods: Convergence and Trade-offs

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

Recursive Sequences: Convergence and Limits

Covers the study of recursive sequences, focusing on convergence and limits.

Sets and Operations: Introduction to Mathematics

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

Discriminant Analysis: Bayes Rule

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

Principal Components: Properties & Applications

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

Primal-dual Optimization: Extra-Gradient Method

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

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Copulas: Properties and Applications

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

Multiple Integrals: Techniques and Properties

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

Implicit Functions Theorem

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

Integration by Substitution

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

Logarithmic Derivative of Zeta

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

Dirichlet Series: Properties and Examples

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

Maximum Likelihood Estimation: Multivariate Statistics

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

Applications of Theorems

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

Bernoulli's Hospital Rule

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

Principal Component Analysis: Introduction

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

Nonlinear Systems: Equations and Solutions

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