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 Poin t 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