Mathematical Mayhem: The “Crime Wave” Continues
[July, 2015] On May 4, 2015, DIMACS Associate Director Eugene
Fiorini 
was a
central figure in what turned out to be a multi-state “crime wave.”
The “crimes” were completely staged, but they were serious business
for students participating in two different classes on mathematical
forensics.
In Ayer, MA, high school teacher Jessie Yackel worked with Detective
Andrew Kularski of the Ayer Police Department to teach her students
the mathematics behind crime scene investigations. Meanwhile, in
Piscataway, NJ, Fiorini was doing the same thing with his honors
seminar at Rutgers. Both classes ended on May 4 with students
conducting investigations into the untimely (unsubstantiated and
completely untrue) demise of unpopular faculty members. Fiorini
taught a course
in 2013 that also ended with a tale of murder and deceit in
service of teaching mathematical forensics. 
Evidence
suggests that he was at it again.
Mathematical forensics is the application of mathematics in forensic
science, which, broadly speaking, is the application of scientific
methods to gather and analyze evidence for use in a court of law. It
turns out that forensic science is fertile territory for
mathematical analysis. Basic statistical principles are used in
computing body size and gender from measurement of bone fragments or
stride length. Time of death estimates can make use of simple
algebraic calculations to estimate body temperature over time or can
employ more sophisticated methods that apply differential equations
based on Newton’s Law of Cooling. Trigonometry and vector analysis
are the central tools of blood spatter and ballistic evidence
analysis. They help to determine the position of the victim and
assailant at the time an attack occurred.
Because of popular television shows like CSI: Crime Scene
Investigation many of these 
techniques
are already familiar and interesting to students. Most students
readily relate to the search for fingerprint matches to a national
database, but until they take Fiorini’s class, they probably don’t
know that graph theory is applicable to fingerprint analysis.
Fingerprints formed by the ridge patterns on fingertips are unique
to each individual, making their identification a workhorse in
criminal forensics. A coarse classification based on prominent ridge
features allows investigators to winnow the database to a smaller
set of 
candidate
matches, but it is not enough to make a definite match. To confirm a
match they have to rely on a detailed analysis of finer
characteristics within the ridge patterns. Fiorini applies concepts
from graph theory to identify such characteristics and the relations
between them in a “module”
on fingerprint analysis that he coauthored as part of the
DIMACS project on the Integration
of Mathematics and Biology. The module is one of 20 modules in
mathematical biology that have been developed through DIMACS
projects for use in high school mathematics and science classrooms.
More recently, Fiorini has developed another module on blood spatter
analysis and time-of-death calculation. The modules are part of a
growing portfolio of activities and materials in mathematical
forensics that Fiorini has been building and sharing with teachers.
In so doing, he has inspired teachers, like Jessie Yackel at
Ayer-Shirley High School, to bring the topic to their students.
Violeta Vasilevska, a professor of mathematics at Utah Valley
University (UVU), is also helping to spread the word about
mathematical forensics following an encounter with Fiorini.
Vasilevska attended the 2014 Reconnect
Workshop on Forensics in which Fiorini was the primary
speaker. Inspired by the topic, she and her colleagues organized a
conference, “Math and
Forensics: Whodunit, Howdunit, Whendunit,” for high school
students and teachers held at UVU in May 2015. With 150 registered
participants, the conference illustrates the enthusiasm for the
topic.
Fiorini’s students are not the only ones to be immersed in the
murder-mystery drama of his final exams. 
DIMACS staff have
contributed to the “script”, the fingerprint database, the suspect
pool, and alas, played the victim – all in service of education.
The crime wave at DIMACS will likely end soon, and the students may
have played a role. At the end of the summer, Fiorini will step down
as DIMACS Associate Director to return to the classroom. He will
join Muhlenberg College as a Professor of Mathematics, where he will
inspire students and (most likely) launch future waves of crime and
mathematical mayhem. All of us at DIMACS wish him well in this new
endeavor and thank him for all he has done during his time at
DIMACS. We will miss having him here at DIMACS full-time, but we
look forward to continuing to work with him as an active DIMACS
member in his new role!
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