Thesis Abstract

Abstract
The application of mathematics in crime detection has become increasingly prevalent in modern law enforcement efforts. This research explores the various mathematical models and algorithms used to analyze crime data, predict criminal activities, and optimize resource allocation for effective crime detention strategies. By leveraging mathematical principles such as probability theory, statistics, and network analysis, law enforcement agencies can enhance their capabilities in identifying crime patterns, understanding criminal behavior, and ultimately preventing and detaining criminal activities. One key area of focus is predictive policing, where mathematical algorithms are employed to forecast when and where crimes are likely to occur. These predictive models utilize historical crime data, geographical information, and other relevant variables to generate forecasts that guide law enforcement in deploying resources proactively to prevent crimes before they happen. Additionally, mathematical models are used to analyze social networks and connections among criminals, aiding in the identification of crime syndicates and key individuals involved in criminal activities. Furthermore, mathematics plays a crucial role in optimizing patrol routes, resource allocation, and response times for law enforcement agencies. Through the application of optimization algorithms, such as linear programming and integer programming, law enforcement can determine the most efficient allocation of resources to maximize crime detention rates within budget constraints. By incorporating mathematical models into decision-making processes, law enforcement agencies can enhance their operational efficiency and effectiveness in combating crime. Moreover, mathematical techniques are also applied in criminal profiling and forensic analysis to assist in identifying suspects and solving criminal cases. By analyzing patterns in crime data, forensic evidence, and behavioral characteristics, mathematicians and law enforcement professionals can develop profiles of potential suspects and narrow down the search for perpetrators. This data-driven approach to criminal profiling has proven to be instrumental in aiding investigations and improving the accuracy of suspect identification. In conclusion, the application of mathematics in crime detention is a multifaceted and evolving field that continues to advance law enforcement capabilities in combating crime. By harnessing the power of mathematical modeling, analysis, and optimization, law enforcement agencies can enhance their proactive and reactive strategies, leading to more effective crime prevention and detention outcomes. This research underscores the importance of integrating mathematical techniques into law enforcement practices to address the complex challenges posed by criminal activities in contemporary society.

Thesis Overview

Introduction

Mathematics is mental activity which consists in carrying out, one after the other, and those mental constructions which are inductive and effective. Meaning that by combining fundamental ideas, one reaches a definite result.

The importance of math in the administration of justice has risen with the growth of identification forensics and its influence continues to permeate questions of proof and judgment. For example, statistics (evidence) and

Mathematics is fast becoming one of the most important techniques in crime detection. Where once a Sherlock Holmes would have had to be content with a magnifying glass, or a jury with gut instinct and rational discussion, now a range of methods from probability and statistics are available to help. Today, mathematics lies behind expert conclusions on a hundred forensic matters from fingerprints to DNA.

1.1           Background of the Study

The application of mathematics to crime detection has proved rather successful in many ramifications.

Another area which can involve rather subtle mathematics is DNA identification. For detection purposes, thirteen particular pairs of genes are identified, amongst the many thousand that make up our DNA, and these thirteen pairs are so varied from person to person that the estimated chance of two people (not identical twins) having the same thirteen is just one in 400 trillion, far greater than the population of the world. Thus, when forensic biologists have a good quality sample to work with, they can make an unchallenged identification. But they often have to work with crime scene samples that are very tiny, mixed, or degraded. In these cases, identification can be made to a given individual only with a certain probability, and it is essential to be able to interpret this probability correctly.

A man was recently tried in San Francisco for a 30-year-old rape and murder, on the grounds that a DNA match was found between a semen sample stored in the cold-case files and an entry in a database of California sex offenders. Furthermore, the crime sample was degraded, so that it would actually match about one person in a million, roughly 300 people in the general population. There was virtually no other evidence against the defendant. The defense held that with a chance in a million of a match in the general population, running the sample through a database containing about one-third of a million individuals led to a chance of 1 in 3 of finding a random match to an innocent person. As for the prosecution, they cited the one in a million figure, which runs the risk of being misinterpreted as the defendant’s chance of being innocent (the “prosecutor’s fallacy”). The trouble is that both conclusions are wrong. The defense argument ignores two essential facts: firstly, that the 300 matching individuals are evenly distributed in age and geography around the country, not concentrated in a database of California sex offenders, and secondly the non-negligible probability that the original murderer may actually have been in the database for other offenses. For the prosecution, when using the one in a million figure, they must specify that the DNA alone only narrows the pool of potential murderers down to about 300 individuals, and must then use the facts that the unique database match turned out to be to a man who shared several characteristics with the original murderer, namely age, race (according to an eyewitness statement), location, and being a sex offender (whether registered or not), to narrow the field. Using these factors, the probability of the defendant’s innocence can be assessed as being less than about one in seventy. The fate of defendants can hinge on such calculations being made rigorously. It is essential to examine the errors that are most

Frequently made, learn to avoid them, and to establish controlled mathematical procedures that will be valid in a court of law.

Coralie Colmez (2013).The research seek to investigate the application of mathematics in crime detection

1.2           Statement of the Problem

Crime detection and investigation used to depend mostly on witnesses, hearsay or forced confessions. The first modern crime detection organization was Scotland Yard, established in the 19th century. Crime detection begins with the discovery of a crime scene, and proceeds through the process of evidence collection, identification and analysis. Crime scene investigation employs many forensic techniques, examining hairs or fibers, firearms, anatomy, bodily fluids and chemistry. Crime detection and investigation used to depend mostly on witnesses, hearsay or forced confessions. The first modern crime detection organization was Scotland Yard, established in the 19th century. Crime detection begins with the discovery of a crime scene, and proceeds through the process of evidence collection, identification and analysis Crime scene investigation employs many forensic techniques, examining hairs or fibers, firearms, anatomy, bodily fluids and chemistry. Surveillance is used when there is a high probability of a crime taking place at a specific place and time. Detectives are bound by all privacy laws, and must obtain a court order to intrude on privacy. Interrogation is probably the oldest crime detection and investigation technique. Detectives interview all known victims or witnesses and interrogate suspects to further their investigation. However the application of mathematics to crime detection seems not to have been fully utilized. Hence the problem confronting this research is to determine the application of mathematics on crime detection.

1.3           Objective of the Study

1 To determine the nature of mathematics

2 To determine the application of mathematics in the detection of crime.

1.4           Research Questions

1 What is the nature of mathematics?

2 What is the nature of the application of mathematics in the detection of crime?

1.5           Significance of the Study

The study provides a framework of reference for the application of mathematics in the detection of crime.

1.6           Statement of Hypothesis

1 Ho The level of crime is low

  Hi The level of crime is high

2 Ho Mathematics is not significant

    Hi Mathematics is significant

3 Ho The application of mathematics in crime detection is low

  Hi The application of mathematics in crime detection is high

1.7           Scope of the Study

The study focuses on the application of mathematics in the detection of crime

1.8           Definition of Terms

CRIME SCIENCE DEFINED

The study of crime in order to find ways to prevent it. Three features distinguish crime science from criminology: it is single-minded about cutting crime, rather than studying it for its own sake; accordingly it focuses on crime rather than criminals; and it is multidisciplinary, notably recruiting scientific methodology rather than relying on social theory.

MATHEMATICS DEFINED

Mathematics is mental activity which consists in carrying out, one after the other, and those mental constructions which are inductive and effective. Meaning that by combining fundamental ideas, one reaches a definite result.

CRIME DETECTION

Crime detection begins with the discovery of a crime scene, and proceeds through the process of evidence collection, identification and analysis.

CRIME INVESTIGATION

 Crime scene investigation employs many forensic techniques, examining hairs or fibers, firearms, anatomy, bodily fluids and chemistry