The Numbers Behind NUMB3RS: Solving Crime with Mathematics

✍ Scribed by Keith Devlin, Gary Lorden

• Publisher: Plume
• Year: 2007
• Tongue: English
• Leaves: 258
• Category: Library

✦ Synopsis

The companion to the hit CBS crime series Numb3rs presents the fascinating way mathematics is used to fight real-life crime

Using 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.

✦ Table of Contents

Cover
Copyright page
Acknowledgments
Contents
List of Figures
1 Total deaths at the hospital, by shift and year
2 A simple neural network with a single hidden layer and one output node
3 Many facial recognition systems are based on measurements of and between key locations on the face called nodal points
4 Is an anomalous datapoint just a blip or a sign of a change?
5 Mathematically enhanced aerial photograph of the Reginald Denny beating, with feature enlargement showing a blurred mark on the assailant's left arm
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
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
8 Wavelets. The one on the left is called, for obvious reasons, the "Mexican hat."
9 Graph of the Al Qaeda group behind the September 11 attacks
List of Tables
1 The data for the statistical analysis in the Gilbert case
2 Mortality rates per 1,000 people per year
3 Mortality rates per 1,000 people per year, adjusted for age
4 Admission figures from the University of California at Berkeley on a program-by-program basis
5 The relationship between average run length and speed of detection
Introduction: The Hero Is a Mathematician?
1 Finding the Hot Zone: Criminal Geographic Profiling
Fact or Fiction?
Rossmo's Formula
2 Fighting Crime with Statistics 101
The Angel of Death
The Science of State
Hypothesis Testing
Figure 1. Total deaths at the hospital, by shift and year
Table 1. The data for the statistical analysis in the Gilbert case
Table 2. Mortality rates per 1,000 people per year
Table 3. Mortality rates per 1,000 people per year, adjusted for age
Statistics in the Courtroom?
Policing the Police
Table 4. Admission figures from the University of California at Berkeley on a program-by-program basis
How Do You Determine Bias?
3 Data Mining: Finding Meaningful Patterns in Masses of Information
Brutus
Finding Meaning in Information
Link Analysis
Geometric Clustering
Software Agents
Machine Learning
Neural Networks
Figure 2. A simple neural network with a single hidden layer and one output node
Training a Neural Network
Crime Data Mining Using Neural Networks
I Know That Face
Figure 3. Many facial recognition systems are based on measurements of and between key locations on the face called nodal points
The Case of the Suspicious Conference Calls
More Data Mining in Numb3rs
Further Reading
4 When Does the Writing First Appear on the Wall?: Changepoint Detection
The Baseball Numbers Genius
Changepoint Detection
Out of Industry
Figure 4. Is an anomalous datapoint just a blip or a sign of a change?
Mathematics Gets Into the Act
Table 5. The relationship between average run length and speed of detection
Early Detection of a Bioterrorist Attack
5 Image Enhancement and Reconstruction
The Reginald Denny Beating
The Rose Tattoo
Figure 5. Mathematically enhanced aerial photograph of the Reginald Denny beating, with feature enlargement showing a blurred mark on the assailant's left arm
What the Eye Cannot See: The Math of Image Reconstruction
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
Image Enhancement: The Inside Scoop
Math in Court
And on Into the Future
6 Predicting the Future: Bayesian Inference
Manhunt
Predicting the Future
How Mathematics Predicted the 9/11 Attack on the Pentagon
Site Profiler
Thomas Bayes and the Probabilities of What We Know
Bayes' Method
The (Fictitious) Case of the Hit-And-Run Accident
How Charlie Helped Track Down the Escaped Killer
7 DNA Profiling
United States of America v. Raymond Jenkins
DNA Profiling
The FBI's CODIS System
Back to the Jenkins Case
The Math of DNA Profiling
Using DNA Profiling
Cold Hit Searches
NRC I and NRC II
Numbers in Court: The Statistical Options
The Database Match Calculation
8 Secrets---Making and Breaking Codes
Prime Suspect
www.cybercrime.gov
Keeping Secrets
Public Key Cryptography
Digital Signatures
What Keeps Your Password Safe?
9 How Reliable Is the Evidence?: Doubts about Fingerprints
The Wrong Guy?
The Myth of Fingerprints
How Does an Expert "Match" Fingerprints?
Fingerprint Experts Versus the Likes of Charlie Eppes
An FBI Fingerprint Fiasco: The Brandon Mayfield Case
What's a Poor Mathematician to Do?
Fingerprints Online
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
Figure 8. Wavelets. The one on the left is called, for obvious reasons, the "Mexican hat."
10 Connecting the Dots: The Math of Networks
Protest
A New Kind of War, A New Kind of Math
The 9/11 Attacks As a Case Study
Figure 9. Graph of the Al Qaeda group behind the September 11 attacks
Basic Graph Theory and "Measures of Centrality"
Random Graphs: Useful Tools in Understanding Large Networks
Six Degrees of Separation: The "Small World" Phenomenon
An Example of Successfully Connecting the Dots
11 The Prisoner's Dilemma, Risk Analysis, and Counterterrorism
How Mathematicians Define a Game
Play It Again, Sam
Risk Assessment
Real-World Risk Assessment Versus Terrorism
Operations Research Versus Nuclear Weapons in Shipping Containers
Airline Passenger Screening Systems
Two MIT Students Use Mathematics to Analyze Capps
12 Mathematics in the Courtroom
The Blonde with the Ponytail
Mathematics: Evidence or Sorcery?
Was the Court's Math Correct?
Famous Nineteenth-Century Mathematicians Demonstrate a Forgery
Using Mathematics in Jury Selection
Jury Profiling
13 Crime in the Casino: Using Math to Beat the System
Double Down
The Problem with Blackjack
Card Counting: A Mathematician's Secret Weapon
Lorden's Story
Teams Take on the Casinos
A Footnote: Mathematicians and the Games They Choose to Play
Lorden Again: Caltech Students Take on the Casinos
Appendix: Mathematical Synopses of the Episodes in the First Three Seasons of NUMB3RS
Is the Math in Numb3rs Real?
First Season
1.23.05 – "Pilot"
1.28.05 – "Uncertainty Principle"
2.4.05 – "Vector"
2.11.05 – "Structural Corruption"
2.18.05 – "Prime Suspect"
2.25.05 – "Sabotage"
3.11.05 – "Counterfeit Reality"
4.1.05 – "Identity Crisis"
4.15.05 – "Sniper Zero"
4.22.05 – "Dirty Bomb"
4.29.05 – "Sacrifice"
5.6.05 – "Noisy Edge"
5.13.05 – "Manhunt"
Second Season
9.23.05 – "Judgment Call"
9.30.05 – "Better or Worse"
10.7.05 – "Obsession"
10.14.05 – "Calculated Risk"
10.21.05 – "Assassin"
11.4.05 – "Soft Target"
11.11.05 – "Convergence"
11.18.05 – "In Plain Sight"
11.25.05 – "Toxin"
12.9.05 – "Bones of Contention"
12.16.05 – "Scorched"
1.6.06 – "The O.G."
1.13.06 – "Double Down"
1.27.06 – "Harvest"
2.3.06 – "The Running Man"
3.3.06 – "Protest"
3.10.06 – "Mind Games"
3.31.06 – "All's Fair"
4.7.06 – "Dark Matter"
4.21.06 – "Guns and Roses"
4.28.06 – "Rampage
5.5.06 – "Backscatter
5.12.06 – "Undercurrents"
5.19.06 – "Hot Shot"
Third Season
9.22.06 – "Spree"
9.29.06 – "Two Daughters"
10.6.06 – "Provenance"
10.13.06 – "The Mole"
10.20.06 – "Traffic"
10.27.06 – "Longshot"
11.3.06 – "Blackout"
11.10.06 – "Hardball"
11.17.06 – "Waste Not"
11.24.06 – "Brutus"
12.15.06 – "Killer Chat"
1.5.07 – "Nine Wives"
1.12.07 – "Finders Keepers"
2.2.07 – "Take Out"
2.9.07 – "End of Watch"
2.16.07 – "Contenders"
2.23.07 – "One Hour"
3.9.07 – "Democracy"
3.30.07 – "Pandora's Box"
4.6.07 – "Burn Rate"
4.27.07 – "The Art of Reckoning"
5.4.07 – "Under Pressure"
5.11.07 – "Money for Nothing"
5.18.07 – "The Janus List"
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
Credits