The companion to the hit CBS crime series Numb3rs presents the fascinating way mathematics is used to fight real-life crimeUsing the popular CBS prime-time TV crime series Numb3rs as a springboard, Keith Devlin (known to millions of NPR listeners as "the Math Guy" on NPR's Weekend Edition with Scott Simon) and Gary Lorden (the principal math advisor to Numb3rs) explain real-life mathematical techniques used by the FBI and other law enforcement agencies to catch and convict criminals. From forensics to counterterrorism, the Riemann hypothesis to image enhancement, solving murders to beating casinos, Devlin and Lorden present compelling cases that illustrate how advanced mathematics can be used in state-of-the-art criminal investigations.
Author(s): Keith Devlin, Gary Lorden
Edition: First Printing
Publisher: Plume
Year: 2007
Language: English
Pages: 258
Tags: Юридические дисциплины;Криминалистика;
Cover......Page 1
Copyright page......Page 6
Acknowledgments......Page 7
Contents......Page 9
List of Tables......Page 0
Figure 1. Total deaths at the hospital, by shift and year......Page 30
Figure 2. A simple neural network with a single hidden layer and one output node......Page 54
Figure 3. Many facial recognition systems are based on measurements of and between key locations on the face called nodal points......Page 60
Figure 4. Is an anomalous datapoint just a blip or a sign of a change?......Page 69
Figure 5. Mathematically enhanced aerial photograph of the Reginald Denny beating, with feature enlargement showing a blurred mark on the assailant's left arm......Page 81
Figure 6. The result of the segmentation algorithm run on the photograph of the left arm of the Reginald Denny assailant, showing a mark entirely consistent with the rose tattoo on Damian Williams' left arm......Page 84
Figure 7. Fourier analysis of a wave (such as the sound wave shown above) represents it as an infinite sum of sine waves (such as the one shown below) of different frequencies and amplitudes......Page 147
Figure 8. Wavelets. The one on the left is called, for obvious reasons, the "Mexican hat."......Page 148
Figure 9. Graph of the Al Qaeda group behind the September 11 attacks......Page 155
Statistics in the Courtroom?......Page 32
Table 2. Mortality rates per 1,000 people per year......Page 33
Table 3. Mortality rates per 1,000 people per year, adjusted for age......Page 34
Table 4. Admission figures from the University of California at Berkeley on a program-by-program basis......Page 36
Early Detection of a Bioterrorist Attack......Page 73
Introduction: The Hero Is a Mathematician?......Page 11
1 Finding the Hot Zone: Criminal Geographic Profiling......Page 15
Fact or Fiction?......Page 19
Rossmo's Formula......Page 24
The Angel of Death......Page 27
The Science of State......Page 28
Hypothesis Testing......Page 29
Policing the Police......Page 35
How Do You Determine Bias?......Page 37
Brutus......Page 39
Finding Meaning in Information......Page 41
Link Analysis......Page 42
Geometric Clustering......Page 43
Software Agents......Page 49
Machine Learning......Page 50
Neural Networks......Page 53
Training a Neural Network......Page 55
Crime Data Mining Using Neural Networks......Page 58
The Case of the Suspicious Conference Calls......Page 61
Further Reading......Page 64
The Baseball Numbers Genius......Page 65
Changepoint Detection......Page 67
Mathematics Gets Into the Act......Page 70
The Reginald Denny Beating......Page 77
The Rose Tattoo......Page 80
What the Eye Cannot See: The Math of Image Reconstruction......Page 82
Image Enhancement: The Inside Scoop......Page 85
Math in Court......Page 86
And on Into the Future......Page 88
Manhunt......Page 91
Predicting the Future......Page 92
How Mathematics Predicted the 9/11 Attack on the Pentagon......Page 93
Site Profiler......Page 94
Bayes' Method......Page 96
The (Fictitious) Case of the Hit-And-Run Accident......Page 97
How Charlie Helped Track Down the Escaped Killer......Page 99
United States of America v. Raymond Jenkins......Page 103
DNA Profiling......Page 105
The FBI's CODIS System......Page 106
Back to the Jenkins Case......Page 107
The Math of DNA Profiling......Page 109
Using DNA Profiling......Page 110
Cold Hit Searches......Page 112
NRC I and NRC II......Page 113
Numbers in Court: The Statistical Options......Page 116
The Database Match Calculation......Page 118
Prime Suspect......Page 119
www.cybercrime.gov......Page 120
Keeping Secrets......Page 122
Public Key Cryptography......Page 124
Digital Signatures......Page 130
What Keeps Your Password Safe?......Page 131
The Wrong Guy?......Page 135
The Myth of Fingerprints......Page 136
How Does an Expert "Match" Fingerprints?......Page 139
Fingerprint Experts Versus the Likes of Charlie Eppes......Page 140
An FBI Fingerprint Fiasco: The Brandon Mayfield Case......Page 142
What's a Poor Mathematician to Do?......Page 144
Fingerprints Online......Page 145
Protest......Page 151
A New Kind of War, A New Kind of Math......Page 152
The 9/11 Attacks As a Case Study......Page 153
Basic Graph Theory and "Measures of Centrality"......Page 156
Random Graphs: Useful Tools in Understanding Large Networks......Page 159
Six Degrees of Separation: The "Small World" Phenomenon......Page 161
An Example of Successfully Connecting the Dots......Page 164
11 The Prisoner's Dilemma, Risk Analysis, and Counterterrorism......Page 167
How Mathematicians Define a Game......Page 168
Play It Again, Sam......Page 171
Risk Assessment......Page 172
Real-World Risk Assessment Versus Terrorism......Page 174
Operations Research Versus Nuclear Weapons in Shipping Containers......Page 177
Airline Passenger Screening Systems......Page 183
Two MIT Students Use Mathematics to Analyze Capps......Page 184
The Blonde with the Ponytail......Page 189
Was the Court's Math Correct?......Page 194
Famous Nineteenth-Century Mathematicians Demonstrate a Forgery......Page 199
Using Mathematics in Jury Selection......Page 202
Jury Profiling......Page 205
Double Down......Page 207
The Problem with Blackjack......Page 209
Card Counting: A Mathematician's Secret Weapon......Page 211
Lorden's Story......Page 213
Teams Take on the Casinos......Page 214
A Footnote: Mathematicians and the Games They Choose to Play......Page 217
Lorden Again: Caltech Students Take on the Casinos......Page 218
Is the Math in Numb3rs Real?......Page 221
2.4.05 – "Vector"......Page 224
2.18.05 – "Prime Suspect"......Page 225
4.1.05 – "Identity Crisis"......Page 226
4.22.05 – "Dirty Bomb"......Page 227
5.6.05 – "Noisy Edge"......Page 228
9.30.05 – "Better or Worse"......Page 229
10.21.05 – "Assassin"......Page 230
11.11.05 – "Convergence"......Page 231
12.16.05 – "Scorched"......Page 232
1.27.06 – "Harvest"......Page 233
3.3.06 – "Protest"......Page 234
4.7.06 – "Dark Matter"......Page 235
5.5.06 – "Backscatter......Page 236
9.29.06 – "Two Daughters"......Page 237
10.20.06 – "Traffic"......Page 238
11.10.06 – "Hardball"......Page 239
11.24.06 – "Brutus"......Page 240
2.2.07 – "Take Out"......Page 241
2.16.07 – "Contenders"......Page 242
3.30.07 – "Pandora's Box"......Page 243
5.11.07 – "Money for Nothing"......Page 244
5.18.07 – "The Janus List"......Page 245
B......Page 247
C......Page 248
D......Page 249
H......Page 250
L......Page 251
N......Page 252
R......Page 254
S......Page 255
U......Page 256
Z......Page 257
Credits......Page 258
