Use "extremal" in a sentence

1. The columns of the associated extremal problem may be interpreted as recipies for blending the different feed mixes.

2. Within the PROBCOMB (Sparse discrete structures) project, mathematicians found applications in areas ranging from extremal graph theory to additive and combinatorial number theory.

3. Topics include algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, graph theory, ordered sets, random methods, and topological combinatorics.

4. The syllabus includes: Convex sets, functions, and optimization problems; basics of Convex analysis; least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems; optimality conditions, duality theory, theorems of alternative, and