Lectures related to Convex Functions

Mathematics of Data: Optimization Basics

Covers basics on optimization, including norms, Lipschitz continuity, and convexity concepts.

Terminologie: Functions Graph Discussion MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the terminology related to the graph of a function and intervals.

Real Functions: Definitions and Properties

Covers the definitions and basic properties of real functions, including domain, image set, notation, and graph.

Real Functions: Graphs and Properties

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Functions: Definitions and Notations

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

Transformations Affines MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Covers the concept of affine transformations in functions, including shifting and compressing functions.

Functions: Real Numbers and Graphs

Covers functions of real numbers, graphing, and affine functions.

Mathematics of Data: Optimization Basics

Covers optimization basics, including metrics, norms, convexity, gradients, and logistic regression, with a focus on strong convexity and convergence rates.

Tangent to Graph of a Function

Explores finding the equation of the tangent line to a function's graph at a point.

Function Properties: Injective, Surjective, Bijective

Explains injective, surjective, and bijective functions using examples and graphs.

Continuity and Fixed Points: Understanding Functions

Explores continuity, fixed points, and bijective functions in graphs.

Optimization Basics: Norms, Convexity, Differentiability

Explores optimization basics such as norms, convexity, and differentiability, along with practical applications and convergence rates.

Exponential Family

Covers the concept of the exponential family and discusses forward and backward maps, expensive computations, parameters, functions, and convexity.

Graphical Models: Representing Probabilistic Distributions

Covers graphical models for probabilistic distributions using graphs, nodes, and edges.

Convexity and Jacobians

Explores convexity, Jacobians, subdifferentials, and convergence rates in optimization and function analysis.

Geodesic Convexity: Basic Definitions

Introduces geodesic convexity on Riemannian manifolds and explores its properties.

Mathematical Analysis: Functions and Composition Log in to Mediaspace to watch this video

Covers the analysis of functions, composition, and mathematical induction.

Advanced Analysis II: Tangent Plan and Differentiability Log in to Mediaspace to watch this video

Explores tangent planes and differentiability in advanced analysis, emphasizing the properties of tangent planes and the conditions for differentiability.

Differentiable Functions and Lagrange Multipliers Log in to Mediaspace to watch this video

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Graphical Definition: Level Sets and Domains Log in to Mediaspace to watch this video

Covers the graphical definition of functions, focusing on level sets and domains.