Simplex Algorithm

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Explores the transition from sparse to dense graphs and their real-world applications.

Covers applied probability, stochastic processes, Markov chains, rejection sampling, and Bayesian inference methods.

Covers approximation algorithms for optimization problems, LP relaxation, and randomized rounding techniques.

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

Covers the properties and operations of convex functions.

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

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

Covers random variables, variances, and covariance, as well as the probability in random graphs.

Covers graphical models for probability distributions and factor graphs representation.

Covers linear programming, weighted bipartite matching, and vertex cover problems in optimization.