Index

I-1

Note: Page numbers followed by f indicate figures; those followed by t indicate tables.

absolute difference, 601, 608
abstractness, 807
Action on Smoking and Health (ASH), 466
actuary, 930
Addition Rule
- for disjoint events, 351
- general, 351, 385
add-on loan, 927–929, 933
adjustable-rate mortgage (ARM), 921, 933
adjusted winner procedure, 540–546, 560
- basic steps in, 541
- properties of, 543
agenda, 430
- manipulation, 448–449, 454
Ahern, Bertie, 714
air pollution, 313
airline scheduling, 61
airline service, 147
Alabama paradox, 582, 608
algebra review
- arithmetic sequences, 884
- combinations, 480
- composite numbers, 717
- formulas, 197, 257
- fractional exponents, 755, 876, 916
- fractions, 304, 315, 344, 871
- function notation, 960
- geometric sequences, 884
- graphs of exponential equations, 877
- linear equations in one variable, 542
- linear equations in two variables, 131, 635–636
- logarithms, 762
- logarithms for solving equations, 952
- midpoint of line, 509, 514
- natural exponents, 755, 876, 916
- percentages, 304, 315, 344, 871
- percents, 304, 315, 344, 871
- permutations, 466
- points on plane, 514
- powers, 104, 322, 361
- prime numbers, 717
- remainders, 670
- roots, 104, 322, 361
- rounding numbers, 320, 373
- scientific notation, 369, 487
- sequences, 781
- significant digits, 748
- slope of lines, 253, 274, 280
- slope-intercept form, 634, 954
- solving for one variable in terms of another, 338, 391, 916
- systems of linear equations and inequalities, 138
algorithms
- bin packing heuristic, 96
- compression, 708, 728
- decreasing-time lists, 94
- fast, 147
- first-fit, 97, 105
- first-fit decreasing, 98, 105
- greedy, 48, 62
- heuristic, 51, 62, 96, 105
- Kruskal’s, 53, 55, 62
- list-processing, 84–85, 89f, 95f, 105
- Luhn, 673–674, 679, 691
- nearest-neighbor, 48, 63
- next-fit, 97
- next-fit decreasing, 98
- sorted-edges, 49–50, 63
- worst-fit, 97, 105
- worst-fit decreasing, 98, 105
Alice’s Adventures In Wonderland (Dodgson), 440
allometric growth, 761–765
American Cancer Society, 311
American Express Travelers Cheque, 678
American Idol, 327
Ammann, Roger, 851
Ammann bars, 852f
amortization, 916, 933
annual percentage rate (APR), 913, 933
annual percentage yield (APY), 878–880, 896
annual rate of inflation, 888, 896
annuity, 884, 896
- in borrowing models, 929–932
- life, 931–933
Appel, Kenneth, 104
apportionment
- 1820 congressional, 590
- 1882, 581
- congressional, 597
- Dean method, 598, 608
- d’Hondt method, 592–593, 608
- divisor methods, 585–597, 608
- equitable, 598, 608
- Hamilton method, 578–585, 608–609
- Hill-Huntington method, 597, 602–608
- Jefferson method, 585–593
- of math classes, 588
- method, 573, 608
- in parliament, 584
- population, 573
- population paradox, 583
- problem, 572–578, 608
- quotient, 585, 608
- Sainte-Laguë method, 596, 609
- of teacher’s assistants, 582, 588
- tentative, 579, 609
- vetoed, 579
- Webster method, 594–597, 600, 607, 609
approval voting, 428–429, 430
approximations, 486
APR. See annual percentage rate
APY. See annual percentage yield
Archaeology of Economic Ideas (Lowry), 552
Archaeopteryx, 764
Archimedean solids, 829
area scaling, 739, 765
area-volume tension, 755, 765
arithmetic growth, 870–872, 896
arithmetic sequences, 884
ARM. See adjustable-rate mortgage
Arrow, Kenneth J., 425–426
Arrow’s impossibility theorem, 424–428, 430
- weak version of, 426
arsenic testing, 358–359
ASH. See Action on Smoking and Health
aspect ratio, 788
association
- causation and, 272
- negative, 247, 274
- positive, 247, 274
associativity, 803
AT&T, 51, 56, 146
Aumann, Robert J., 646
autism, 851
automobile assembly, 127f
average, 199
average-case analysis, 94
Avis, 678
backward induction, 650, 654
Baker v. Carr, 480, 599
Bakuba patterns, 795, 799
balance point, 378f
Balinski, Michel L., 591
Banach, Stefan, 553, 554
Banach–Knaster proportional procedure, 555
bank check, 673f
bank identification numbers, 672–673
bank routing numbers, 672, 679
Banzhaf, John F., 480
Banzhaf model, 474–487
- for film selection committee, 477
Banzhaf power index, 466, 475, 487, 492
- calculation of, 476–477
bar codes, 680–687, 691
- history of, 687
- new applications, 686–687
- new frontier, 686
- UPC, 684–686, 685t
- ZIP code, 681–683
Barlow, Peter, 853
Barlow’s law, 853–855, 856
Barnsley’s fractal fern, 809f
base-10 logarithmic scale, 762, 765
basic combinations formula, 481
basketball poll, 415
Batey, Mavis, 725
Bayes rule, 360
beer, 243, 261f, 264
Bell Labs, 146
Benford’s law, 362, 380
- probability model for, 376
beverages, 139, 143
Bhargava, Manul, 783
bias, 295, 324
bin packing, 97–99
- heuristics, 96
binary code, 681, 691, 699–702, 702t
- UPC, 685t
- weight of, 705, 728
binary linear code, 705, 728
biomass, 960, 976
birthday coincidences, 370
blackjack, 378
Blanquerna (Llull), 409
Bletchley Park, 725

I-2
blood alcohol content, 243, 251, 261f, 264
- scatterplot of, 244
BLS. See Bureau of Labor Statistics
Boer War, 720
bonds, 871, 896
Borda, Jean-Charles de, 409, 440
Borda count, 430
- failure of IIA with, 417–418
- manipulating, 443, 445–447
- rank methods and, 414, 415
Borel, F. E. Émile, 622
Borovcnik, Manfred, 370
borrowing models
- annuities in, 929–932
- compound interest in, 911–914
- conventional loans, 914–923, 933
- discounted loans, 923–927, 933
- simple interest, 910–911
- terminology in, 912–913
Boruvka, Otakar, 55
bottom-up strategy, 560
boxplots, 201–202, 219
- modified, 203
Brams, Steven J., 553
bread delivery, 148, 149–150, 154
Brownell, Blaine, 749
brute force method, 46, 62
Buchanan, Patrick J., 412, 523
Buchmann, Stephen, 684
buckyballs, 829
Buffet, Warren, 894
Bureau of Labor Statistics (BLS), 241
Burj Khalifa, 748, 749
Burkov, Sergei, 854
Bush, George, 514, 518, 522, 523
Bush, George W., 406, 524
butterfly effect, 973, 976
cable TV, 52–53
Caesar cipher, 714, 728
cake-division procedures, 552–555, 560
- envy in, 555–558
California’s quota, 577
Callebotte, Gustave, 787
Canterbury Tales (Chaucer), 57
carbon-14 dating, 958–959
Carroll, Lewis, 440
carrying capacity, 946, 976
Carville, James, 514
casinos, 384
categorical variables, 183
cattle ranching, 966–967
causation, association and, 272
CD. See certificate of deposit
Census Bureau, 599, 690
center
- of data, 190
- mean describing, 196–200
- median describing, 196–200
central limit theorem, 380–385, 396–397
centrosymmetric, 840, 856
certificate of deposit (CD), 887
chair’s paradox, 452–454
chance outcomes, 215
Chandrasekaran, R., 549
chaos
- in biological populations, 974–976
- computers and, 976
- dynamical systems, 971–976, 977
- fractal patterns and, 807
- mathematical, 972–974
- symmetry in, 810–811
Chaucer, Geoffrey, 57
check digits, 669–679, 691
Cheney, Dick, 518
chicken, 641–642, 654
childhood disease epidemics, 975
Chinese postman problem, 14–15, 22
Christy, Howard Chandler, 573f
chromatic number, 101
Chrysler, 540
Churchill, Winston, 725
cipher
- Caesar, 714, 728
- decimation, 716–717, 728
- Jefferson wheel, 724–725
- linear, 718–719, 728
- permutation, 719–720, 728
- Playfair, 720–721, 728
- Vigenère, 722–723, 728
ciphertext, 719, 728
circuits, 6, 22
Civil War, 580
class intervals, 186, 219
climate change, 321
Clinton, Bill, 514, 522, 714
Clinton, Hillary, 505
closure, 803
clothing manufacturers, 131
coalitions
- blocking, 476
- grand, 477, 492
- losing, 474, 492
- minimal winning, 478, 487–488, 492
- winning, 474, 478–479, 487–488, 488t, 493
cobweb diagram, 975f
code tree, 712
code words, 702, 728
- distances, 704t
coin toss, 343, 346
cold-blooded animals, 759–760
college success, 265
college tuition histograms, 192–193
coloring, resolving conflict via, 100–104
column maxima, 624t
combinations, 367, 385, 480, 832
- algebra review, 480
- basic formula, 481
- formulas, 492
- graphing calculators for, 369
- sum formula for, 486
- symbol, 480, 492
- symmetry of, 482
combinatorics, 363, 385
committees
- Banzhaf index of, 477
- film selection, 463, 469, 477
- nine-person, 472
- scholarship, 491
common ancestors, 56
comparative experiments, 307
comparisons, 742
complement of events, 350, 385
complement rule, 350, 385
complete graphs, 45, 62
- vertices in, 45f
- weighted, 49f
composite numbers, 717
compound interest, 872–878, 896
- in borrowing models, 911–914
- formula, 875, 933, 944, 976
- limits to, 880–882
- simple interest vs., 876–877
compounding period, 872, 913, 933
compression algorithm, 708, 728
concentrated solar plant (CSP), 782
conditional probability, 357, 385
- models, 358–359
Condorcet, Marquis de, 408
Condorcet winner, 412, 430
Condorcet winner criterion (CWC), 413, 430
Condorcet’s method, 407–412, 430
- impossibility and, 450–451
- majority rule and, 443–445
- nonmanipulability of, 444
Condorcet’s voting paradox, 411, 430, 445
confidence intervals, 320–321, 324
conflict resolution, 100–104
confounding, 306–307, 324
connected graph, 11, 22
- with Euler circuit, 12f
connectedness, 10
constant dollars, 890, 896
constant-sum games, 635, 654
Constitution, 573
Consumer Price Index (CPI), 780, 785–786, 891–895
continuous compounding, 881, 896
continuous interest formula, 977
continuous probability models, 371–374, 385, 395
continuous uniform model, 373
continuous voter distribution, 515, 527
- median of, 517
control groups, 307, 325
convenience sample, 295, 325
Convention of the Law of the Sea, 551, 560
conventional loans, 914–923, 933
convex polygons, 834, 856
Conway, John H., 841, 845
Conway criterion, 841–842, 856
Cook, Elizabeth, 553
Cook, Thomas, 147
cool, 758
Le Corbusier, 787
corner points principle, 134, 141–144, 160
corporations
- permutations, 471t
- pivotal voters, 471t
correction capacity, 706
correlation, 254–260, 274, 281–282
- calculation, 257
- datasets exploring, 285t
- evaluation, 271
- extrapolation and, 269–270
- formula for, 257
- interpolation and, 270
- interpreting, 268–273
- nonsense, 271
- outliers and, 268–269
- regression and, 265
- scatterplot and, 254–255
CPI. See Consumer Price Index
Cramer, Kathryn, 749
credit card
- data, 726–727
- invalid, 674
credit default swap, 894

I-3
criminal trials, 465, 475
critical path, 58–62
- schedules, 89–93, 92f
critical voters, 475, 492
- probability of, 483
Crowder, Todd, 757
crushing strength, 750, 765
cryptography, 714–727, 728
crystal structures, 796–798
crystallographic notation, 798, 812
crystallographic restriction, 853
CSP. See concentrated solar plant
current dollars, 890, 896
curves
- density, 210, 211, 219, 371, 372, 385
- normal, 212, 213f, 374
- power, 764, 765
- reproduction, 960–961, 977
Cusanus, Nicolaus, 409
customary system, U.S., 743
CWC. See Condorcet winner criterion
cyclic rosettes, 794
da Vinci, Leonardo, 787, 829
Daimler-Benz, 540
dairies, 159
Dantzig, George, 146, 147
data
- center of, 190
- collection of, 179
- compression, 707–714, 728
- correlation exploration, 285t
- credit card, 726–727
- distributions, 184
- entry, 95
- exploratory analysis, 183–184, 219
- individuals and, 182
- outliers in, 190
- real, 214
- regression exploration, 285t
- shape of, 190
- variability in, 190
- variables and, 182
De Morgan, Augustus, 104
deadheaded, 8
Dean, James, 598
Dean method, 598, 608
Debs, Eugene V., 522
decay constant, 955, 956, 977
decimation cipher, 716–717, 728
decoding, 704
- nearest-neighbor, 705, 728
decrease, 740–742
decreasing-time heuristics, 99
- first-fit, 98
- next-fit, 98
- worst-fit, 98
decreasing-time lists, 95
- algorithm, 94, 95f
- nonoptimal schedule from, 95f
- optimal schedule from, 95f
decryption, 714, 728
deflation, 848, 890
delta encoding, 710–711
Democratic Party, 505
density, 747, 765
- curves, 210, 211, 219, 371, 372, 385
- estimation, 215
- traffic, 193–194
dependent events, 354, 357f
depreciation, 890–891
depression, 893
derivatives, 893, 896
deterministic systems, 971, 977
d’Hondt, Victor, 592
d’Hondt method, 592–593, 608
dice, 347
- doubles, 361
- histograms of, 342f
- outcomes, 342f
- rolling two, 352
dictator, 463, 475, 492
difference
- absolute, 601, 608
- percentage, 601, 609
digraphs, 20, 22
- order-requirement, 58, 59f, 63, 86f, 88f, 93f
dihedral rosettes, 794
dimension tension, 754–760
Dimetrodon, 759
disaster recovery, 90
discounted loans, 923–927, 933
discrete distribution, 509, 527
discrete probability models, 360–362, 392–393
- mean of, 375, 385
- standard deviation of, 379, 385
disingenuous ballot, 439, 454
disjoint events, 350, 385
- Addition Rule for, 351
distance between two strings, 704, 728
distinct items, 365, 368
distributions
- boxplots, 201–203
- continuous voter, 515, 517, 527
- data, 184
- describing, 188
- displaying, 182–188
- five-number summary, 201–203
- frequency, 184–185, 185t, 187t, 189t, 219
- histogram display of, 182–188
- left-skewed, 190, 219
- normal, 208, 209–215, 216–218, 219
- quartiles in, 200–201
- range in, 200–201
- right-skewed, 190, 199f, 219
- sampling, 317, 320, 320t, 382f
- stemplots of, 194–195
- symmetric, 191, 220
- unimodal, 520, 528
- variability, 200–201
district population, 575, 608
dives, 759
divide-and-choose, 551–552, 560
divine proportion. See Golden Ratio
division by 7 schemes, 671
division by 9 schemes, 670–671
divisor methods
- of apportionment, 585–597, 608
- choosing, 598–608
- Dean method, 598, 608
- d’Hondt method, 592–593, 608
- paradoxes and, 589
- Sainte-Laguë method, 596
- Webster method, 594–597, 600, 607, 609
DNA sequences, 363
Dodgson, Charles L., 440
dollars
- constant, 890, 896
- current, 890, 896
- deflation, 890
- purchasing power, 889
- value, 891
dolls, 129, 135t, 136–141
- feasible regions for, 138f
dominant strategies, 640, 654
dominated strategies, 644, 654
dose-response relationship, 313
dotplots, 197, 219
double-blind experiment, 310, 325
driving to work, 356
Dubins, Lester E., 553
dummy voters, 464, 492
dynamical systems, 971–976, 977
e (number), 881, 896
EAN. See European Article Number
Easter Island, 969
edges, 22
- in Euler circuits, 6, 15
- in eulerization, 17
- reusing, 15f
- walkers, 18
- wiggly, 40f, 54f
edge-to-edge, 830, 856
Edison, Thomas, 788
Edwards Lifesciences, 128
effective annual rate, 913, 933
effective rate, 869–870, 878–880, 896
elections. See also presidential elections
- multicandidate, 518–523
- two-candidate, 508–518
electoral college, 465, 467, 484
- primary process, 504–508
- spatial models and, 524–527
Electoral College, 504
Elements (Euclid), 57, 783
Emperor’s Cloak, 811f
encoding personal data, 700, 728
encryption, 728
enigma machines, 724
enlargement, 740–742
entertainment, 382–383
envy, 555–558
envy-free, 543, 556, 560
equally likely outcomes, 363–370, 393–394
equiangular spiral, 761
equilateral triangle, 828, 856
equilibrium, 511, 527
- Nash, 640
- population size, 961, 977
equitability, 543, 560, 600
equitable apportionment, 598, 608
equity, 933
- growth of, 920
- Hill-Huntington, 605
- home, 919
equivalent voting systems, 489, 492
error-detection, 691, 706
Escher, M. C., 836, 841
- tiling and, 837
ethics, 309
Euclid, 57, 783
Euler, Leonhard, 8, 9
Euler circuits, 6–10, 22, 99
- beyond, 14–20
- Chinese postman problem in, 14–15
- connected graph with, 12f
  
  I-4
- edges in, 6, 15
- finding, 10–14
- graphs having, 6
- vertices in, 6
eulerization, 22
- edges in, 17
- good, 19–20
- of graphs, 16
- methods, 17
- odd-valent vertices in, 17f
- of rectangular networks, 18f
Euler’s theorem, 13–14
European Article Number (EAN), 672, 679, 691
even parity, 701, 728
events, 346
- complement of, 350, 385
- dependent, 354, 357f
- disjoint, 350–351, 385
- independent, 354, 385
- mutually exclusive, 350
exam scores, 191f
existence theorem, 622
expected payoff, 632
expected value, 632, 654
experiments, 305
- comparative, 307
- control groups, 307
- double-blind, 310, 325
- ethics in, 309
- flowchart, 314f
- observational studies, 309–314
- randomized comparative, 307–308, 325
- realism in, 313
- statistical significance in, 308
- uncontrolled, 306
explanatory variable, 242–243, 274
exploratory data analysis, 183–184, 219
exponential decay, 889, 896
exponential equations, 877
exponential growth, 896
exponential reserve, 952, 977
exponents
- fractional, 755, 876, 916
- natural, 755, 876, 916
express mail, 42f
extended median, 512, 527
exterior angle, 829, 856
extra votes principle, 476, 492
extrapolation, 269, 270, 274
Exxon, 128
factorial, 385, 470, 492
- formula, 366
- graphing calculators for, 369
fair division, 546–548, 557
fair game, 633, 654
falls, 754–755
family incomes, 270f
family size, 376
fast algorithms, 147
feasible points, 142, 160
feasible region, 140f, 143f, 160
- corners in, 144f
- for dolls, 138f
- drawing, 134
- general shape of, 136
- pictorial method, 137
- representing, 132–134
- for skateboards, 138f
feasible set, 132
feasible solution, 154–157
FF. See first-fit algorithm
FFD. See first-fit decreasing algorithm
Fibonacci numbers, 780–790, 809, 812
Fibonacci sequence, 780
film selection committee, 463
- Banzhaf model applied to, 477
- pivotal voters in, 469
final exam scores, 244t
Fink, A. M., 553
Finn, Ed, 749
first-fit algorithm (FF), 97, 105
first-fit decreasing algorithm (FFD), 98, 105
fish, 280t, 965, 967
Fisher, Irving, 895
Fisher’s effect, 895
five-number summary, 201–203, 219
fixed-length codes, 707, 728
flight, 756
football, 271
Ford, Gerald, 505
formulas
- algebra review, 197, 257
- basic combinations, 481
- combinations, 492
- compound interest, 875, 933, 944, 976
- continuous interest, 977
- for correlation, 257
- factorial, 366
- payment, 884, 896
- profit, 135, 136–137
- savings, 875, 884, 896, 914–915, 933, 977
- sum, for combinations, 486
Four Color Problem, 104
four-letter words, 365
four-person corporation, 470, 471t
four-person inheritance, 544
four-shareholder corporation, 488t
fractal patterns, 807–811
fractional exponents, 755, 876, 916
fractions, 304, 315, 344, 871
free rider, 653, 654
frequency distribution, 184–185, 219
- of COINS, 185t, 187t
- construction of, 186–187
- Hispanic population, 189t
- relative, 186
fruit juices, 139–140
fuel economy, 196t, 747f
Fuller, Buckminster, 829
fundamental principle of counting, 45–46, 62, 363, 385
fundamental region, 845, 856
futures, 894
Galileo, 752
Gallup polls, 323, 339
Galton, Francis, 260
gambling, 341–342, 378
game theory
- constant-sum, 635, 654
- extensive form, 647
- fair, 633, 654
- history of, 622
- larger games in, 643–651
- mechanism design, 646
- ordinal, 639, 655
- outguessing in, 630–631
- partial-conflict, 637–643, 655
- perfect information in, 622
- practical applications of, 652–654
- solutions, 651–652
- total-conflict, 655
- two-person total-conflict games, 628–637
- using, 651–654
- variable-sum, 637
- zero-sum, 624
game tree, 647, 649f, 654
Gardner, Martin, 851
gasoline, 467
General Addition Rule, 351
general multiplication rule, 357
generation, 806, 812
generic medicines, 742
genetic code, 716
geometric growth, 872–878, 896
geometric mean, 602, 608, 784–785, 812
geometric sequences, 884
geometric series, 883
geometric similarity, 738–742
- area scaling, 739, 765
- volume scaling, 739, 765
gerrymandering, 527
Gibbard, Allan, 451
Gibbard-Satterthwaite theorem, 451, 454
Glaxo Wellcome, 540, 542
glide reflections, 792, 812
global warming, 877
Goldberg, Rube, 503–504
Golden Ratio, 783–790, 812
golden rectangle, 783
The Good, the Bad and the Ugly, 647
Gore, Al, 412f, 523, 526
Graham, Evarts, 311
grand coalition, 477, 492
graphing calculators
- for combinations, 369
- for factorial, 369
- for least-squares regression, 266
- for permutations, 369
- for scatterplots, 249–250
- for simple random samples, 300–301
- for standard deviation, 206–207
graphs, 22
- complete, 45, 45f, 49f, 62
- connected, 11, 12f, 22
- connectedness of, 10
- with Euler circuits, 6
- eulerizing, 16
- of exponential equations, 877
- grid, 41
- line, 294f
- of lines, 253
- with no Hamiltonian circuits, 41f
- not connected, 11f
- parts of, 7
- streetmaps and, 8
- theory, 57, 100f, 148f
- unweighted, 20
- urban graph traversal problems, 20–22
- weighted complete, 49f
Great Depression, 893

I-5
Great Pyramid, 787
greedy algorithm, 48, 62
Green Party, 450
grid graphs, 41
groups
- manipulability, 449–450, 454
- non-number, 804
- of numbers, 803
- symmetry, 802–807, 812
- theory, 804–805
growth
- allometric, 761, 765
- arithmetic, 870–872, 896
- of biological populations, 944–950
- exponential, 896
- geometric, 872–878, 896
- hormone, 272
- human, 760–764
- isometric, 762, 765
- language of, 740–742
- limitations on, 946–950
- linear, 872, 896
- proportional, 760, 765
- real rate of, 895
Guan, Meigu, 15
Guy, Richard K., 553
Haken, Wolfgang, 104
Haken-Appel proof, 104
half-life, 956, 977
half-planes, 137
Hamilton, Alexander, 574
Hamilton, William Rowan, 104
Hamilton method, 578–585
- Alabama paradox, 582, 608
- diamond sharing, 579
- new states paradox in, 585, 609
- paradoxes of, 581–585
- upper and lower quotas and, 578
Hamiltonian circuit, 40, 66–71
- graphs with no, 41f
- minimum-cost, 42–43, 62
Hamming, Richard, 705
Hamming codes, 705
Hammond, E. Cuyler, 311
Hardin, Garrett, 970
Hare, Thomas, 584
Hare method, 584, 608
Hare system, 420, 430
Harrington, James, 552
Harsanyi, John C., 646
Heawood, Percy, 104
Hebert, Paul, 686
Hebrew Bible, 551
height, 381
helping traveling salesman, 48–52
Hesiod, 551
heuristic algorithms, 51, 62, 105
- bin packing, 96
- definition, 96
hexagons, 828
- tiling with, 834, 840
Hill, Joseph, 602
Hill-Huntington method, 597
- apportionment and, 602–608
- equity and, 605
- rounding, 603–604
- trial divisors by, 606
Hispanic populations, 189t
- stemplot of, 195–196
histograms, 219
- college tuition, 192–193
- construction of, 186–187
- density curves and, 210
- of die rolls, 342f
- distribution display with, 182–188
- interpreting, 188–194
- outliers in, 188
- probability, 353f, 385
- of vocabulary scores, 209f
Hjelmstad, Keith, 749
home construction, 83–84
honesty, 304
Horn, Daniel, 311
House of Representatives, 580
Hubbert, M. King, 954
Huffman, David, 711
Huffman coding, 711–714
Huffman tree, 713
human growth, 760–764
human-readable numbers, 685f
Humphrey, Hubert H., 522
Huntington, Edward V., 601, 607
Hurwicz, Leonid, 622
Huygens, Christiaan, 622
identity element, 803
IFS. See iterated function system
IIA. See independence of irrelevant alternatives
imperfect patterns, 800–801
independence of irrelevant alternatives (IIA), 416, 430
- Borda count failure with, 417–418
independent events
- diagram of, 354
- multiplication rule for, 356, 385
independent tasks, 93
- average-case analysis, 94
- decreasing-time lists, 94–95
- worst-case analysis, 94
indicator value, 155, 160
individuals, 219
- data and, 182
inference, 314–324
- 68–95-99.7 rule and, 319
- statistical, 292, 314, 325
inflation, 848, 888–895, 896
- annual rate of, 896
insincere ballot, 439
interest
- compound, 872–878, 880–882, 896, 911–914, 933, 976
- continuous, 977
- nominal rate, 874, 933
- rates, 933
- real rate, 913–914
- simple, 870–872, 876–877, 896, 910–911, 933
interior angle, 830, 856
Internal Revenue Service, 652
International Standard Book Number (ISBN), 669, 674–677, 679, 691
Internet traffic, 148
interpolation, 270, 274
intervals, confidence, 320–321
Introduction to Economic Analysis (MacAfee), 559
inverses, 803
iodine-131, 956
Iowa test scores, 192
IQ test scores, 245t, 246t
irregular polygon, 833–838
irrelevant alternatives, 414
ISBN. See International Standard Book Number
isohedral tilings, 838
isometric growth, 762, 765
isometry, 791–792, 812
isotopes, 956, 977
Israel electric company, 21
iterated function system (IFS), 809, 973, 977
Ivanpah Solar Power Facility, 782
James, Richard, 836
Jefferson, Thomas, 574
Jefferson method, 585–593
- diamond sharing, 587
Jefferson wheel cipher, 724–725
job interview scheduling, 103
Johnson, Gary, 406
Joint Photographic Experts Group (JPEG), 708
Jones, Stephen, 508
JPEG. See Joint Photographic Experts Group
jump transposition, 677
jumps, 756
Karmarkar, Narendra, 146–147
Kempe, Alfred, 104
Kepler, Johannes, 829
Kerry, John, 520
Kershner, R. B., 835–836
Kirkman, Thomas, 40
Knaster, Bronislaw, 553, 554
Knaster inheritance procedure, 544–545
- basic steps in, 546
Kohler, D. A., 549
Koppel, Ted, 648
Kruskal, Joseph, 53
Kruskal’s algorithm, 53, 55, 62
larger games, 643–651
last-diminisher method, 554, 560
Laubach, Lloyd, 757
Lavin, Christine, 260
law of large numbers, 378, 385
least-squares regression, 260–264, 282–283
- equation of line, 265–266
- fitting, 269
- graphing calculators for, 266
- line, 262, 274
- Microsoft Excel for, 267
left-skewed distribution, 190, 219
Leibniz, Gottfried W., 622
Leonardo of Pisa, 787
less, 742
Levine, Don, 854
Libertarian Party, 406
life annuity, 931–933
line graphs, 294f
linear cipher, 718–719, 728
linear equations
- in one variable, 542
- systems of, 138
- in two variables, 131, 635–636
linear growth, 872, 896

I-6
linear inequalities, 138
linear programming, 144–157
- alternative to simplex method, 146–147
- case studies in, 128
- current solutions, 157–159
- feasible solutions, 154–157
- mixture problems and, 126–134
- Northwest Corner Rule, 152–154, 158, 160
- origins of, 146
- simplex method, 145, 160
- stepping stone method, 157–159, 160
linear scaling factor, 738, 765
lines
- graphing, 253
- midpoint, 509, 514
- slope of, 253, 274, 280
- slope-intercept form, 634, 954
- y-intercept of, 253, 274
list-processing algorithm, 84–85, 89f, 105
- optimal schedule from, 95f
living histogram, 191f
Llull, Ramon, 408, 409
logarithmic spiral, 761
logarithms
- algebra review, 762
- for solving equations, 952
logistic map, 811
logistic model, 948, 949, 977
log-log paper, 762, 765
lone divider method, 554, 560
Lorenz, E. N., 973
losing coalition, 474, 492
lottery, 367, 930
lower quota, 578, 609
Lowry, Todd, 552
Lu, Peter J., 855
Luhn algorithm, 673–674, 679, 691
MacAfee, R. Preston, 559
machine-scheduling problem, 82
Magnanti, Thomas, 10
mail delivery, 41f
majority rule, 407–412, 430, 456–457, 485
- Condorcet’s method and, 443–445
Malthus, Thomas Robert, 878
management science, 22, 90
manipulability, 414, 430, 440–442
- agenda, 448–449, 454
- Borda count and, 443, 445–447
- group, 449–450, 454
- May’s theorem for, 444, 454
- of runoff systems, 447–448
margin of error, 321, 325
Mary’s theorem, 408
Maskin, Eric S., 622
matching pennies, 632, 651
mathematical chaos, 972–974
mathematical models, 462
Mathieu, Georges, 622
matrioshka dolls, 807f
matrix, payoff, 623
maximin, 511, 527, 624, 654, 655
maximum sustainable yield, 977
May, Kenneth, 408
May’s theorem, 408, 430
- for manipulability, 444, 454
McCain, John, 507
McEliece, Robert, 701
mean, 219
- in center, 196–200
- of discrete probability, 375, 385
- finding, 197
- geometric, 602, 608, 784–785
- probability, 395
- regression toward, 260
measurement
- metric system, 743–744
- U.S. customary system, 743
- variables, 204f
mechanism design, 643–651, 655
median, 219, 511
- in center, 196–200
- of continuous voter distribution, 517
- extended, 512, 527
- finding, 198–199
- weighted, 525–526, 528
median-voter theorem, 512, 528
medical doctors, 877
mergers, 540
metabolic rates, 758f
meter-reading task, 21
method of trees, 42, 62
metric system, 743–744
Microsoft Excel, 183, 250
- for least-squares regression, 267
- for residual calculation, 263t
midpoint, 509, 514, 528
midterm exam scores, 194–195, 244t
Mill, John Stuart, 420
minimal winning coalitions, 478, 487–488, 492
minimax, 625
- strategy, 655
- theorem, 637, 655
minimum constraints, 131, 160
minimum-cost Hamiltonian circuits, 42–43, 62
minimum-cost spanning trees, 52–57, 63
mixed strategies, 628–637, 655
mixture chart, 129, 138f, 143f, 160
- for dolls, 138f
- fruit juices, 139–140
- making, 130
- for skateboards, 138f
- translating, 130–132
mixture problems, 160
- common features of, 128–130
- linear programming and, 126–134
- objectives in, 129
- products in, 128
- profits in, 129
- recipes in, 129
- resources in, 128
mode, 199, 219
- in right skewed distributions, 199f
modified boxplot, 203
modular arithmetic, 715, 728
money orders, 670f
monohedral tiling, 828, 856
monotonicity, 407, 430
- failure of, 422
more, 742
Morgenstern, Oskar, 646
Morse code, 708
mortgages
- adjustable rate, 921, 933
- amortization, 916, 933
- crisis, 922–923
- points on, 933
Mozart, Wolfgang Amadeus, 787
Mt. Everest, 750
multicandidate elections, 518–523
multiplication by 13 scheme, 677
multiplication rule, 356
- general, 357
- for independent events, 385
musical sequences, 850–853, 856
mutually exclusive events, 350
Myerson, Roger B., 622
Nader, Ralph, 412, 450, 523
NASA, 700
Nash, John F., Jr., 622, 646
Nash equilibrium, 640, 655
National Center for Missing and Exploited Children (NCMEC), 761
National Organ Transplant Act, 546
National Popular Vote law, 524, 528
National rental cars, 678
natural exponents, 755, 876, 916
natural increase, 945, 961, 977
Nautilus pompilius, 760–761
NCMEC. See National Center for Missing and Exploited Children
nearest-neighbor algorithm, 48, 63
nearest-neighbor decoding, 705, 728
negative association, 247, 274
new states paradox, 585, 609
New York City, 22f
- subway system, 90
news, understanding, 323
next-fit algorithm (NF), 97
next-fit decreasing algorithms (NFD), 98
NF. See next-fit algorithm
NFD. See next-fit decreasing algorithms
NIMBY, 513
nine-person committee, 472
Nixon, Richard M., 522
nominal rate, 874, 896, 933
non-number groups, 804
nonoptimal schedules
- decreasing-time-list algorithm and, 95f
- time lengths, 94f
nonperiodic tilings, 845–855, 856
nonrenewable resources, 950–955, 977
nonresponse, 303, 325
nonzero minimums, 142
normal curve
- areas under, 374
- standard deviation of, 213f
- variability of, 212
normal density curve, 210, 219
normal distributions, 208, 209–215, 219
- quartiles of, 214
- 68–95-99.7 rule, 216–218
Northwest Corner Rule, 152–154, 158, 160
NP-complete problems, 51, 63
nuclear waste, 877
numbers
- bank identification, 672–673
- bank routing, 672, 679
- chromatic, 101
- composite, 717
- e, 881, 896
- EAN, 672, 679, 691
  
  I-7
- Fibonacci, 780–790, 809, 812
- groups of, 803
- human-readable, 685f
- ISBN, 669, 674–677, 679, 691
- law of large, 378
- prime, 717
- random, 372f
- rounding, 320, 373
- Social Security, 688, 786
- table of random digits, 298t, 299, 325
- vehicle identification, 678
- of voters assumption, 407
numeric symmetry, 807
1/3-separation obstacle, 520–521, 528
Obama, Barack, 406, 465, 505, 527
observational studies, 305, 309–314, 325
- flowchart, 314f
odd parity, 701, 728
oil production, 954f
online polls, 295
operations research (OR), 5, 22
optimal production policy, 128, 134–141, 160
- finding, 135–136
optimal schedules, 85–87, 91f
- decreasing-time-list algorithm and, 95f
- from list-processing algorithm, 95f
- order-requirement digraphs and, 93f
optimal solution, 5, 22, 156
OPTN. See Organ Procurement and Transplantation Network
OR. See operations research
ordered collections, 365
order-requirement digraph, 58, 59f, 63, 86f, 88f
- optimal schedule and, 93f
orders of magnitude, 762, 765
ordinal game, 639, 655
Organ Procurement and Transplantation Network (OPTN), 546
organ transplant policies, 427
- fair division and, 546–548
outliers, 188, 197f, 219, 274
- beware of, 268
- correlation and, 268–269
- in datasets, 190
- identification of, 245
- regression and, 268–269
- in scatterplot, 245
paper ballots, 445f
paradoxes
- Alabama, 582, 608
- chair’s, 452–454
- Condorcet’s voting, 411, 430, 445
- divisor methods and, 589
- of Hamilton method, 581–585
- new states, 585, 609
- population, 583
parallelogram, 833, 839–840, 856
parameters, 315, 325
Pareto, Vilfredo, 543
Pareto condition, 418–420, 430
Pareto-optimal, 543, 560
par-hexagon, 840, 856
parity-check sums, 702–707, 728
Parthenon, 787
partial-conflict games, 637–643, 655
Pascal, Blaise, 345
path, 6, 22
- critical, 58–62
patterns
- Bakuba, 795, 799
- fractal, 807–811
- imperfect, 800–801
- notation for, 798–801
- preserving, 792–793, 812
- Pueblo pottery, 800–801
- rosette, 790–798
- strip, 790–798, 805–806, 812
- symmetry groups of, 793, 802–807, 812
- symmetry of, 793, 812
- wallpaper, 793, 797, 812
payment formula, 884, 896
payoff matrix, 623, 655
payoff surface, 626f
penalty kick, 629, 636
Penrose, Roger, 846
Penrose tiles, 845–847
- nonperiodic, 849
- symmetry of, 849
- on toilet paper, 850f
pentagon, 828
percentages
- algebra review, 304, 315, 344, 871
- difference, 601, 609
percents, 304, 315, 344, 871
periodic tilings, 844, 856
perishables, delivery of, 148–157
permutations, 365, 385, 492
- algebra review, 466
- cipher, 719–720, 728
- computing, 366
- corporations, 471t
- graphing calculators for, 369
- pivotal voters and, 471t
- presidential election, 468t
- voting, 466
Perot, Ross, 508, 522
PERT. See program evaluation and review technique
Pew Research Center, 303, 316
photocopy shop, 95
phyllotaxis, 782, 812
pictorial method, 137
pigeonhole principle, 811
pivotal voter, 467, 492
- in corporations, 471t
- film selection committee, 469
- permutations and, 471t
placebo effect, 310, 325
plaintext, 719, 728
planes, 302
- points on, 514
- turning, 59
Playfair, Lyon, 720
Playfair cipher, 720–721, 728
Pledged Party Leaders and Elected Officials (PLEO), 508
plurality runoff, 423, 430
plurality voting, 412, 430
- CWC failure with, 413
- group manipulability and, 449–450
point ratio, 561
points, 933
- balance, 378f
- on plane, 514
- problem of, 345
policy positions, 509, 528
politics, mathematics and, 607
polling, truth in, 324
polygons
- convex, 834, 856
- irregular, 833–838
- regular, 828–833, 856
population, 292, 325
- chaos in, 974–976
- district, 575, 608
- dynamics, 964–969
- equilibrium, size, 961
- food and, 877
- growth models, 944–950
- logistical model, 974
- paradox, 583, 609
- proportion, 321
- structure, 946, 977
positive association, 247, 274
post delivery companies, 42f
postal money orders, 678
postnet code, 691
power curve, 764, 765
power index, 462
- Banzhaf, 466, 475–477, 487, 492
- of scholarship committee, 491
- Shapley-Shubik, 466, 469–473, 487, 492
powers, 104, 322, 361
preference list ballot, 406, 430, 550, 561
present value, 886–891, 896
presidential elections
- electoral college and, 484
- permutation resulting from, 468t
pressure, 747, 765
primary process, 504–508
- delegate awarding in, 505–506
prime numbers, 717
principal, 896, 910, 933
priority list, 83
Prisoners’ dilemma, 638, 652, 655
probability, 343–348
- area under normal curve as, 374
- Benford’s law, 376
- conditional, 357, 358–359
- continuous, models, 371–374, 385, 395
- discrete, 360–362, 375, 379, 385, 392–393
- for driving to work, 356
- histogram, 353f, 385
- mean, 395
- mean of, 375–380
- means of transportation, 348
- models, 345, 346, 353, 385
- outcomes, 348
- psychology and, 349
- for random number generation, 372f
- rules, 348–360, 390–392
- standard deviation, 375–380, 395
problem of points, 345
problem of scale, 754, 765
processors, 82
profit
- formula, 135–137
- at four corner points, 139t
- line, 141, 142f
- maximizing, 137, 140
program evaluation and review technique (PERT), 62
proportional growth, 760, 765

I-8
proportional procedure, 553
proportionality, 552–555, 561
prospective studies, 312, 325
psychology, probability and, 349
Pueblo patterns, 800–801
Pukelsheim, Friedrich, 409
Pulp Fiction, 647
purchasing power, 889, 896
pure strategies, 623–628, 631, 655
QR code, 686
quadrilaterals, 833, 856
- tiling with, 834
qualitative variable, 183
quartiles, 219
- of normal distributions, 214
- in variability, 200
quasicrystals, 853–855
quasiexperiments, 307
quasiperiodic, 856
- tilings, 848–850
Quetzalcoatlus northropi, 756
quotas, 462, 492, 528, 576
- California, 577
- conditions, 590, 609
- lower, 578, 609
- upper, 578, 609
radioactive decay, 955–959
radioisotopes, 956
rain rate, 280t
Ramphastos toco, 760
RAND Corporation, 425
random digits, table of, 297, 298t, 325
- using, 299
random numbers, 372f
random phenomena, 343–348
randomized comparative experiments, 307–308, 325
randomness, 343, 385, 389–390, 845
range, 219
- in variability, 200
rank methods, 414, 415
rational choice, 623, 655
reading test scores, 245t, 246t
Reagan, Ronald, 505
real data, 214
recounting ballots, 524f
rectangles
- golden, 783
- symmetry of, 802
rectangular networks, eulerization of, 18f
recursion, 812
Reed-Solomon codes, 701
reflection symmetry, 792, 794, 812
Reform Party, 508
regression
- correlation and, 265
- datasets exploring, 285t
- equation, 252f, 253
- extrapolation and, 269–270
- interpolation and, 270
- interpreting, 268–273
- least-square, 260–267, 269, 274, 282–283
- least-square, equation, 265–266
- least-square, line, 262, 274
- line, 251–253, 274, 280–281
- toward mean, 260
- outliers and, 268–269
- slope of line, 253
regular polygon, 828–833, 856
regular tiling, 830–833, 856
Reinhardt, Karl, 834–835
relationships
- dose-response, 313
- scatterplots, 242–250
- straight-line, 255
- variables, 256f
relative frequency distribution, 186
- of COINS, 187
remainders, 670
renewable resources, 977
- elimination of, 969–971
- harvesting, 960–971
representative share, 609
- Webster method and, 600
representative shares, 599
reproduction curves, 960–961, 977
Republican Party, 507
Reservoir Dogs, 647
residential neighborhoods, 22f
residual, 261
- Excel for calculation of, 263t
- graphical representation of, 262f
resources
- constraints, 131, 160
- in mixture problems, 128
- nonrenewable, 950–955
- renewable, 960–971, 977
response variable, 242–243, 274
retirement, 885–886, 931, 953
retrospective studies, 312, 325
rhombus, 847, 856
Rice, Marjorie, 835–836
right-skewed distributions, 190, 219
- mode in, 199f
rigid motions, 791–792, 812
rim conditions, 160
road construction costs, 55f
Robertson, Neil, 104
Rodenhizer, Bill, 61
Romney, Mitt, 406, 465
Roosevelt, Theodore, 522
roots, 104, 322, 361
rosette patterns, 790–798
- cyclic, 794
- dihedral, 794
rotational symmetry, 796
Roth, Alvin, 646
roulette, 378
rounding numbers, 320, 373
roundoff error, 373
routing problems, 21f
row minima, 624t
Rule B, 366
running, 271
runoff systems, 420–424
- manipulation of, 447–448
68–95-99.7 rule, 216–218, 220
- inference and, 319
saddlepoint, 626, 655
Sainte-Laguë method, 596, 609
salt-spreading route, 21f
sample space S, 345, 385
sampling, 292–293, 325
- bias, 295
- convenience, 295
- distribution, 317, 320, 320t, 382f
- events in, 315
- methods, 294–296
- proportions, 317
- songs, 299
- voluntary response, 296, 325
Sanders, Daniel, 104
SAT scores, 217, 248
Satterthwaite, Mark, 451
savings formula, 875, 884, 896, 914–915, 933, 977
savings models, 882–888
- arithmetic growth, 870–872, 896
- for retirement, 885–886
- simple interest, 870–872, 896
scale
- economy of, 967, 977
- problem of, 754
scalene triangle, 833, 856
scaling
- area, 739, 765
- linear, factor, 738, 765
- volume, 739–740, 758, 765
scatterplot, 274
- of BAC, 244
- correlation and, 254–255
- differing, 256f
- examining, 245
- graphing calculators for, 249–250
- of heights and weights, 242f
- outliers in, 245
- relationships displayed with, 242–250
- technology for creation of, 249
Schechtman, Daniel, 855
Schechtman’s alloys, 854
scheduling tasks, 82–89
- airline, 61
- assumptions, 83–84
- bin packing, 96–99
- critical-path, 89–93, 92f
- examinations, 100–101
- goals, 83–84
- hospital use of, 82f
- independent tasks, 93–95
- job interviews, 103
- list-processing algorithm in, 84–85
- machine-scheduling problem, 82
- nonoptimal, 94f, 95f
- optimal, 85–87, 91f, 93f, 95f
- priority list in, 83
- processors in, 82
- strange happenings, 87–89
- two processors, 91–92
Schelling, Thomas C., 646
scholarship committees, 491
scientific notation, 369, 487
Selfridge, John L., 553
Selfridge-Conway envy-free procedure, 556, 561
Selten, Reinhard, 646
semilog paper, 762, 765
semiregular tiling, 832, 856
Senechal, Marjorie, 851, 853
September 11, 2001, 90
sequences
- algebra review, 781
- arithmetic, 884
- DNA, 363
- Fibonacci, 780
  
  I-9
- geometric, 884
- musical, 850–853, 856
sequential pairwise voting, 418–420, 430
- agenda manipulation and, 449–450
Seurat, Georges, 787
Seymour, Paul, 104
Shapley, Lloyd, 466, 646
Shapley-Shubik power index, 466, 469, 487, 492
- computing, 470–473
shareholders, 462
Shubik, Martin, 466
Sierpiinski triangle, 810f
significant digits, 748
simple interest, 933
- borrowing models, 910–911
- compound interest vs., 876–877
- savings models, 870–872, 896
- on student loans, 871
simple random samples, 297–302, 325
- graphing calculators for, 300–301
simplex method, 145, 160
- alternative to, 146–147
simplified Chinese postman problem, 15
simulation results, 318
sinking fund, 884, 896
six-voter system, 464
skateboards, 129, 135t, 136–141
- feasible region for, 138f
skewness, 190
Sloane, Neil, 703
slope of lines, 274, 280
- regression, 253
slope-intercept form, 634, 954
smart cards, 727
SmithKline Beecham, 540, 542, 543
smoking, 311
social choice, 406–407
Social Security Numbers, 688, 786
solar system, 973
Solomon, Gustave, 701
songs, 364
sorted-edges algorithm, 49–50, 63
Soundex Coding System, 689, 691
Spanier, Edwin H., 553
spanning trees, 53
- minimum-cost, 52–57, 63
spatial models
- electoral college and, 524–527
- for multicandidate elections, 518–523
- for two-candidate elections, 508–515
- for two-candidate elections with continuous distributions, 515–518
spinners, 371f
spirals, 761
spoiler problem, 523
spreadsheets, 888
St. John’s wort, 309
standard deviation, 204, 220
- calculating, 205–206
- of discrete probability models, 379, 385
- graphing calculators for, 206–207
- of normal curve, 213f
- probability, 375–380, 395
- in sampling distribution, 320, 320t
- variability and, 203–208
standard divisor, 575, 609
Stanford University, 146
static reserve, 951, 977
statistical inference, 292, 314, 325
statistical significance, 308, 325
statistics, 315
Steinhardt, Paul, 554, 854–855
Steinhaus, Hugo, 553, 554
stemplots, 220
- of Hispanic populations, 195–196
- making, 194
- of midterm scores, 194–195
Stephenson, Neil, 749
stepping stone method, 157–160
straight-line relationship, 255
strange happenings, 87–88
strategies, 454
- dominant, 640, 654
- dominated, 644, 654
- minimax, 655
- mixed, 628–637, 655
- pure, 623–628, 631, 655
strip patterns, 790–798, 805–806, 812
Stromquist, Walter R., 553
student grades, 271
student loans, 871, 917, 926
student questionnaire, 182–183
subway system, 90
summaries, 208
Super Bowl XLVIII, 291
supply-and-demand transportation problem, 148f
surface area, 758
surveys, sample, 293
- cautions about, 302–305
- nonresponse in, 303
- truthfulness and honesty in, 304
- undercoverage in, 302–303
- wording in, 304–305
sustainable-yield harvesting, 962–964, 977
swimming times, 245t, 246t
symmetric distribution, 191, 220
symmetry
- in chaos, 810–811
- of combinations, 482
- distributions, 191, 220
- groups, 802–807, 812
- numeric, 807
- of patterns, 793, 812
- of Penrose tiles, 849
- of rectangles, 802
- reflection, 792, 794, 812
- rotational, 796
- translation, 794, 812
2/3-separation opportunity, 520–521, 528
table of random digits, 297, 298t, 325
- using, 299
tableau, 151, 160
tacks, 344f
Taft, William Howard, 522
Taylor, Alan D., 553
Taylor, Jean, 853
teacher’s assistants, 582
tentative apportionment, 579, 609
tessellation, 828, 856
Theogony (Hesiod), 551
Thomas, Robin, 104
three-voter systems, 489
TI-84, 249–250
tic-tac-toe, 627
tie-breaking power, 452, 454
Tilden, Samuel J., 597
tiling, 827, 856
- Escher and, 837
- with hexagons, 834, 840
- with irregular polygons, 833–838
- isohedral, 838
- monohedral, 828, 856
- nonperiodic, 845–856
- from parallelogram, 833, 839–840
- Penrose, 845–847
- periodic, 844, 856
- with quadrilaterals, 834
- quasiperiodic, 848–850
- regular, 830–833, 856
- with regular polygons, 828–833
- semiregular, 832, 856
- translations and, 838–840
- with triangles, 833, 842–843
total-conflict games, 655
- mixed strategies, 628–637
- pure strategies for, 623–628
Toyota Prius, 197f, 198, 202
traffic density, 193–194
translations, 791, 856
- criterion, 839
- plus half-turns, 840–845
- symmetry, 794, 812
- tiling and, 838–840
transportation problem, 149, 160
- solutions, 151f, 154f
- supply-and-demand, 148f
traveling salesman problem (TSP), 47–48, 63
trees
- branchings of, 42
- code, 712
- diagram, 359f
- game, 647, 649f, 654
- Huffman, 713
- method of, 42, 62
- minimum-cost spanning, 52–57, 63
- spanning, 53
trial divisors, 606
triangles
- equilateral, 828, 856
- scalene, 833, 856
- Sierpiinski, 810f
- tiling with, 833, 842–843
Trouten, Liz, 757
truthfulness, 304
TSP. See traveling salesman problem
Tukey, John Wilder, 184
Turing, Alan, 726
turn taking, 548–551, 561
two-candidate elections
- with continuous distributions, 515–518
- spatial models for, 508–515
Ukraine, 956
undercoverage, 302–303, 325
unemployment, 293
unilateral change, 442, 454
unimodal distribution, 520, 528
United Nations Security Council, 490
United States
- gross annual income in, 215f
- heights of women in, 211, 214, 216
Universal Product Code (UPC), 671–672, 679, 691
- bar code, 684–686, 685t
- binary code, 685t
I-10
unordered collections, 368
unweighted graphs, 20
UPC. See Universal Product Code
upper quota, 578, 609
urban graph traversal problems, 20–22
urban services, 5–21
U.S. customary system, 743
U.S. Department of Commerce v. Montana, 599
vacation planning, 41–44
valence, 10, 22
- of vertices, 10f
value, 626, 633, 655
- expected, 632
Vanderburgh, Paul, 757
variability
- describing, 200–201
- measuring, 204f
- of normal curve, 212
- quartiles in, 200
- range in, 200
- standard deviation, 203–208
variable-length code, 707, 728
variables, 220
- categorical, 183
- confounding, 306–307
- data and, 182
- explanatory, 242–243, 274
- linear equations in one, 542
- linear equations in two, 131, 635–636
- measurement, 204f
- qualitative, 183
- relationships, 256f
- response, 242–243, 274
variable-sum games, 637, 655
vehicle identification number (VIN), 678
vertex coloring, 101
vertices, 22
- in complete graphs, 45f
- in Euler circuits, 6
- in eulerization, 17f
- types, 832, 856
- valences of, 10, 10f
veto power, 464, 492
Vickrey, William, 559
Vickrey auctions, 558–561, 643, 655
- bidding strategy, 559
Vigenère cipher, 722–723, 728
Vigenère square, 723t, 728
VIN. See vehicle identification number
Vinton, Samuel, 590n
VISA Travelers Cheques, 678
vocabulary scores, 209f
volume scaling, 739–740, 758, 765
voluntary response sampling, 296, 325
von Neumann, John, 622
voting
- approval, 428–429, 430
- Condorcet’s, paradox, 445
- continuous voter distribution, 515, 517, 527
- critical, 475, 483, 492
- discrete distribution of, 509, 527
- disingenuous ballot, 439
- dummy, 464, 492
- extra votes principle, 476, 492
- ideal point, 509, 528
- ideal position, 509
- insincere ballot, 439
- median-voter theorem, 512, 528
- number of voters assumption, 407
- permutation, 466
- pivotal, 467, 469, 471t, 492
- plurality, 412, 430, 449–450
- sequential pairwise, 418–420, 430, 448–450
- strategies, 452
- three or more candidates, 412–424
- weak domination in, 452, 454
- weight, 462
voting systems
- equivalent, 489, 492
- manipulability of, 414, 440–443, 445–450, 454
- mathematical models of, 462
- runoff, 420–424, 447–448
- six-voter, 464
- three-voter, 489
- weighted, 462–465, 493
- without weights, 487–492
Wallace, George, 522
wallpaper patterns, 793, 797, 812
warm-blooded animals, 758–759
Washington, George, 574
weak domination, 452, 454
Webster, Daniel, 594f, 598
Webster method, 594–597, 607, 609
- apportioning classes, 595
- population bias and, 596
- representative share and, 600
weight, 42, 63, 691, 747–753, 765
- of binary code, 705, 728
weighted complete graphs, 49f
weighted median, 525–526, 528
weighted voting systems, 462–465, 493
- notation for, 463
Wesberry v. Sanders, 599
WF. See worst-fit algorithm
WFD. See worst-fit decreasing algorithms
Wheatstone, Charles, 720
White, Carlina, 761
wiggly edges, 40f, 54f
Willcox, Walter F., 607
Wilson, Woodrow, 522
wing loading, 756, 765
winning coalition, 474, 479, 493
- four-shareholder corporation, 488t
- minimal, 478, 487–488
Winslet, Kate, 725
Wolf, Naomi, 793
wording of questions, 304–305
World Trade Center, 61, 90
World War II, 146, 150, 724
worst-case analysis, 94
worst-fit algorithm (WF), 97, 105
worst-fit decreasing algorithms (WFD), 98, 105
Wright, Frank Lloyd, 749
Wynder, Ernst, 311
yields, 878–880, 896, 962–964, 977
y-intercept, 253, 274
Young, Peyton, 547, 548, 591
Zermelo, Ernst, 622
zero-sum games, 624, 655
ZIP code, 679–680, 691
- bar coding, 681–683
ZIP + 4 code, 680, 691
Zwicker, William S., 553