2D Case: Polynomial Encroaching

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Explores polygons, polyhedra, regularity, and starred configurations in Euclidean geometry, highlighting historical context and limitations.

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Focuses on proving the Cellular Approximation Theorem, introducing polyhedra and piecewise linear maps.

Explores symmetry in modern geometry, emphasizing reflections, rotations, and practical applications in computer-aided design.

Covers the theory of linear and integer programming, focusing on the integer hull and rational polyhedra.

Explores basic solutions in linear constraints and the equivalence with vertices.

Covers the basics of linear optimization, including equations, polyhedrons, feasible directions, and optimal solutions.

Explores integer programs, nonconvex optimization, constraints, and geometric aspects of linear programming for optimal solutions.

Covers an overview of convex optimization, affine sets, polyhedra, ellipsoids, and convex functions.