Discrete Mathematics: Elementary and Beyond

290 Index

point at infinity, 218
point of a graph, 126
polyhedron, 194
Pr ̈ ufer code, 150, 152
extended, 150
prime factorization, 245, 250
prime field, 109, 219, 237
prime number, 83, 88, 219, 245
Prime Number Theorem, 94
Principle of Induction, 27, 29,
199, 203
prism
pentagonal, 194
triangular, 194
probability space, 78
pseudoprime, 118
public key cryptography, 247
pyramid
pentagonal, 194
Pythagoras, 92
Pythagorean triple, 100
Pythagoreans, 92

Ray-Chaudhuri, D.K., 228
recurrence, 66
relatively prime, 99, 249
remainder, 87, 248
Rivest, R., 247

sample space, 77
Schoolgirls’ Walking Schedule, 228
Secure Socket Layer, 250
security, 249
set, 4
cardinality, 5
complement, 21
difference, 6
disjoint, 6
element, 4
empty, 5
intersection, 6
ordered, 17
subset, 5, 20
ordered, 19, 20
symmetric difference, 6

union, 6

Venn diagram, 6

SET, game, 237

Shamir, A., 247

Sieve Formula, 34

signature, 249

star, 130

Steiner system, 224–229, 237

coloring, 227

Steiner, J., 224

subgraph, 131

substitution code, 242

Swiercz, S., 220

symmetric difference of sets, 6

Szekeres, Gy ̈orgy, 184

Tarry, G., 220

tetrahedron, 194

Thiel, L., 220

Traveling Salesman Problem, 161

tree, 10, 11, 141–157, 191

branch, 146

edge, 10

greedy, 159

labeled, 158

leaf, 143

node, 10

root, 142

rooted, 142

spanning, 142

Tree-growing Procedure, 144

Tree Shortcut Algorithm, 162

triangle inequality, 162

Twin Paradox, 37

twin primes, 94

uniform probability space, 78

union of sets, 6

unlabeled tree, 147, 153

Venn diagram, 6

vertex, 126

walk, 132, 136

closed, 132

Eulerian, 136