Contents IAS /Park Cit y Mathematic s Institut e Preface Chapter 1 . Abstrac t Algebra : Groups , Ring s an d Field s Chapter 2 . Conve x Polytopes : Definition s an d Example s Chapter 3 . Face s o f Polytope s Chapter 4 . Schlege l Diagram s Chapter 5 . Gal e Diagram s Chapter 6 . Bizarr e Polytope s Chapter 7 . Triangulation s o f Point Configuration s Chapter 8 . Th e Secondar y Pol y tope Chapter 9 . Th e Permutahedro n Chapter 10 . Abstrac t Algebra : Polynomia l Ring s Chapter 11 . Grobne r Base s I Chapter 12 . Grobne r Base s I I

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