A simplified guide on how to prep up on Mathematics for Artificial Intelligence, Machine Learning and Data Science: Optimization (Important Pointers only) Module IV : Optimization I. Convex Sets and Convex Functions 1. Convex Sets A convex set is a subset of a vector space that, for any two points within the set, the line segment connecting them is also within the set. A set C C in a vector space is convex if, for any x , y ∈ C x, y \in C and any λ \lambda such that 0 ≤ λ ≤ 1 , the point λ x + ( 1 − λ ) y \lambda x + (1 - \lambda) y is also in C C . Properties of Convex Sets: Intersection: The intersection of convex sets is also convex. Convex Hull: The smallest convex set containing a given set of points is called the convex hull of those points. Half-spaces and Hyperplanes: Half-spaces and hyperplanes are examples of convex sets. Eg: Line segments, Circles, Polyhedrons 2. Convex Functions A convex function is a function f : R n → R where...