Lectures related to Analytical Trajectories: Key Ingredients

Analytical Solutions: EDO

Explores the analytical solutions of ordinary differential equations, emphasizing the identification and solving process for various EDO types.

Inequality Resolution: x + 4 / 2x + 1

Focuses on solving an inequality using a sign table method.

Morse Theory: Critical Points and Non-Degeneracy

Covers Morse theory, focusing on critical points and non-degeneracy.

Maximum Likelihood Estimation: Multivariate Statistics

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

Absolute Values: Equations and Inequalities

Explores absolute values in equations and inequalities, focusing on solving |f(x)| = g(x).

Principal Components: Properties & Applications

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

Laurent Series and Convergence: Complex Analysis Fundamentals

Introduces Laurent series in complex analysis, focusing on convergence and analytic functions.

Lipschitz Gradient Theorem

Covers the Lipschitz gradient theorem and its applications in function optimization.

Local Extrema of Functions

Discusses local extrema of functions in two variables around the point (0,0).

Analyse 1: Introduction

Introduces the EPFL MOOC Analyse 1, emphasizing understanding over memorization.

Sets and Operations: Introduction to Mathematics

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

Optimization with Constraints: Theory and Applications

Covers the theory and applications of optimization with constraints, including key concepts and numerical methods.

Optimization Methods: Convergence and Trade-offs

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

Discriminant Analysis: Bayes Rule

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

Complex Integration and Cauchy's Theorem

Discusses complex integration and Cauchy's theorem, focusing on integrals along curves in the complex plane.

Infinite Limits: Real Functions

Delves into real functions, specifically exploring limits at infinity and discussing sequence divergence.

Residue Theorem: Applications in Complex Analysis

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

Optimal Transport: From Theory to Applications

Explores the history, theory, and applications of optimal transport in various fields, showcasing its importance in solving complex mathematical problems.

Powers and Roots: Understanding Irrational Equations

Delves into powers and roots, emphasizing irrational equations and the disjunction of cases.

Logarithmic Derivative of Zeta

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