Cover 1
Title 2
Copyright 3
Contents 4
IAS /Park City Mathematics Institute 6
Preface 8
Chapter 1. Abstract Algebra: Groups, Rings and Fields 10
Chapter 2. Convex Polytopes: Definitions and Examples 16
Chapter 3. Faces of Polytopes 24
Chapter 4. Schlegel Diagrams 34
Chapter 5. Gale Diagrams 46
Chapter 6. Bizarre Polytopes 56
Chapter 7. Triangulations of Point Configurations 66
Chapter 8. The Secondary Poly tope 82
Chapter 9. The Permutahedron 94
Chapter 10. Abstract Algebra: Polynomial Rings 102
Chapter 11. Grobner Bases I 110
Chapter 12. Grobner Bases II 120
Chapter 13. Initial Complexes of Toric Ideals 126
Chapter 14. State Polytopes of Toric Ideals 136
Bibliography 148
Index 150
A 150
B 150
C 150
D 150
E 150
F 150
G 151
H 151
I 151
L 151
M 151
N 151
O 151
P 151
R 152
S 152
T 152
U 152
V 152
Z 152
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