Contents xi VIl Appendix:Mathematical Background Introduction 1143 A Summations 1145 A.1 Summation formulas and properties 1145 A.2 Bounding summations //49 B Sets,Etc.1158 B.1 Sets 1158 B.2 Relations 1/63 B.3 Functions //66 B.4 Graphs 1168 B.5 Trees 1173 C Counting and Probability 1183 C.1 Counting 1183 C.2 Probability 1189 C.3 Discrete random variables 1196 C.4 The geometric and binomial distributions 120/ ★ C.5 The tails of the binomial distribution /208 D Matrices 1217 D.1 Matrices and matrix operations 1217 D.2 Basic matrix properties /222 Bibliography 1231 Index 1251Contents xi VIII Appendix: Mathematical Background Introduction 1143 A Summations 1145 A.1 Summation formulas and properties 1145 A.2 Bounding summations 1149 B Sets, Etc. 1158 B.1 Sets 1158 B.2 Relations 1163 B.3 Functions 1166 B.4 Graphs 1168 B.5 Trees 1173 C Counting and Probability 1183 C.1 Counting 1183 C.2 Probability 1189 C.3 Discrete random variables 1196 C.4 The geometric and binomial distributions 1201 ? C.5 The tails of the binomial distribution 1208 D Matrices 1217 D.1 Matrices and matrix operations 1217 D.2 Basic matrix properties 1222 Bibliography 1231 Index 1251