Maximum and Minimum Values: Theorems and Continuity

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Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

Covers Markov chains decomposition, LLN proof, Inventory Model application, and average costs.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Explores Coxeter groups, word length, simple reflections, and unique elements.

Explores locally Lipschitz functions, discussing differentiability, unique solutions, and function reduction.

Explores mixed-integer linear programming, binary variables, 0-1 knapsack, assignment problems, and LP relaxation strength.

Covers the computation and properties of the Hermite Normal Form (HNF) in matrix theory and lattice theory.

Explores Lagrange multipliers, minimax theorems, and convex subsets in optimal transport theory.

Explores regularity in higher dimensions for scalar problems and discusses weak sense solutions and interior regularity.

Explores Cauchy sequences, series definition, and convergence criteria.

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