## Syracuse University Honors Program Capstone Projects

#### Title

Mathematics in Forensic Firearm Examination

3

#### Document Type

Honors Capstone Project

#### Date of Submission

Spring 5-1-2015

Prof. Matthew Kurimsky

Prof. Michael Sponsler

Mathematics

Arts and Science

no

no

no

#### Honors Categories

Sciences and Engineering

#### DOI

Forensics, ballistic evidence, firearms

#### Subject Categories

Forensic Science and Technology | Other Applied Mathematics

#### Abstract

Forensic Science encompasses many disciplines that employ the scientific method to examine, analyze, and interpret physical evidence in the courtroom. The discipline of Forensic Firearm Examination involves the examination and comparison of ballistic evidence components to determine if they came from the same source. In other words, firearm examiners are tasked with determining whether spent cartridge cases or bullets were fired through the same gun. Examination of ballistic evidence can involve the employment of automated matching systems, comparison microscopy, and mathematical analysis. The comparison microscope is the tool of the firearm examiner and allows for the simultaneous view of ballistic components. Through examination and comparison, the examiner determines if the components are an identification or an elimination, or are inconclusive. The use of automated matching systems is often a precursor to an examination and comparison, to determine possible matches with evidence stored in large databases. These systems employ mathematical techniques such as matching algorithms, transforms, and cross-correlation functions. Mathematical analysis involves the application of probabilistic thinking and statistical methods to articulate and support the conclusions of the firearms examiner. There is concern in the court system about the prominent presence of subjectivity in firearm examination. Mathematical methods can help decrease subjectivity, and they are unquestionably valuable for concepts of the discipline, such as consecutively matching striations. However, math does not eliminate the subjectivity of Forensic Firearm Examination and only proves valuable when utilized appropriately. The discipline deals with the comparison of individual characteristics that indicate if markings come from one tool and one tool alone. Fitting this idea into a statistical model is possibly an unsuitable course of action.