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57:29 SIAM_IP9_8:30am_08/04/2017 SIAM_IP9_8:30am_08/04/2017	SIAM_IP9_8:30am_08/04/2017 IP9 Caratheodory Style Theorems for Discrete Optimization and Game Theory function vector colloidal chemistry formal sciences point color communication linear programming greek alphabet mind number binary operations entity cognitive science mathematical logic learning economics theories of history real algebraic geometry mathematical optimization human behavior multi-dimensional non-negative cryptography abstract algebra cognitive psychology systems science question systems theory geometry start program elementary algebra systems data types social psychology topology evaluation optimization operations research group theory philosophical terminology transportation thing combination philosophy of mathematics mathematical notation mathematical objects polynomials mention algorithm elementary number theory functional analysis ring theory information retrieval matrices psychology complex systems theory algebra skills linear algebra applied mathematics information theory solution abstraction column colorful printing artificial intelligence natural resources set theory representation problem algebraic topology game theory theoretical computer science From Anton Leykin 8 plays 0 name Jesús A. De Loera, University of California, Davis, USA Date August 4th, 2017