Lectures in Geometric Combinatorics

Abstract algebra: Groups, rings and fields Convex polytopes: Definitions and examples Faces of polytopes Schlegel diagrams Gale diagrams Bizarre polytopes Triangulations of point configurations The secondary polytope The permutahedron Abstract algebra: Polynomial rings Grobner bases I Grobner bases II Initial complexes of toric ideals State polytopes of toric ideals Bibliography Index.