Social Sciences

Mathematics of Crime

Speaker: 
Andrea L. Bertozzi
Date: 
Wed, Sep 19, 2012
Location: 
IRMACS Center, Simon Fraser University
Conference: 
Hot Topics in Computational Criminology
Abstract: 

There is an extensive applied mathematics literature developed for problems in the biological and physical sciences. Our understanding of social science problems from a mathematical standpoint is less developed, but also presents some very interesting problems. This lecture uses crime as a case study for using applied mathematical techniques in a social science application and covers a variety of mathematical methods that are applicable to such problems. We will review recent work on agent based models, differential equations, variational methods for inverse problems and statistical point process models. From an application standpoint we will look at problems in residential burglaries and gang crimes.
Examples will consider both "bottom up" and "top down" approaches to understanding the mathematics of crime, and how the two approaches could converge to a unifying theory.

Class: 
Scientific
Applied
Subject: 
Social Sciences
Applied Mathematics

Hot Topics in Computational Criminology

Conference: 
Hot Topics in Computational Criminology
Date: 
Wed, Sep 19, 2012
Class: 
Scientific
Applied
Subject: 
Applied Mathematics
Social Sciences

Coordination Cascades: Sequential Choice in the Presence of a Network Externality

Author: 
B. Curtis Eaton,
David Krause
Date: 
Fri, Oct 7, 2005
Location: 
University of Calgary, Calgary, Canada
Conference: 
Alberta Conference on Industrial Organization
Abstract: 

In the network externality literature, little, if any attention has been paid to the process through which consumers coordinate their adoption decisions. The primary objective of this paper is to discover how effectively rational individuals manage to coordinate their choices in a sequential choice framework. Since individuals make their choices with minimal information in this setting, perfect coordination will rarely be achieved, and it is therefore of some interest to discern both the extent to which coordination may be achieved, and the expected cost of the failure to achieve perfect coordination. We discover that when it counts, that is when the network externality is large, a substantial amount of coordination is achieved, and although perfect coordination is never guaranteed, expected relative efficiency is large.

Notes: 
PDF icon Eaton_and_Krause.pdf
Class: 
Applied
Subject: 
Econometrics
Social and Information Networks
Social Sciences

"Mathematical Social Sciences;" An Oxymoron?

Author: 
Donald G. Saari
Date: 
Sun, Sep 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

An explicit part of my agenda with these lectures is to encourage more mathematicians to seriously consider issues coming from the social sciences; let me assure you that you will find different and new mathematical issues. In the other direction, I also hope to encourage social scientists to appreciate the important gains that can result by using serious mathematics; I want to encourage the social scientists to seriously consider using this powerful approach. Because of these twin goals, my lectures, and these notes, are explicitly designed to address both audiences. For instance, the beginning of each section consists of examples which are intended to help develop intuition about the issues at hand. Then, toward the end of each section, there is a slightly stronger mathematical emphasis which is intended for the mathematicians. Nevertheless, I encourage the social scientists reading these notes to push on through this somewhat more technical material.

Table of Contents:

1. Mathematical Physical vs. Social Sciences

2. Symmetry galore!

3. Singularity theory and departmental meetings

4. Evolutionary game theory

 5. Adam Smith’s “Invisible hand” — and continuous foliations

Notes: 
PDF icon Saari.pdf

An explicit part of my agenda with these lectures is to encourage more mathematicians to seriously consider issues coming from the social sciences; let me assure you that you will find different and new mathematical issues. In the other direction, I also hope to encourage social scientists to appreciate the important gains that can result by using serious mathematics; I want to encourage the social scientists to seriously consider using this powerful approach. Because of these twin goals, my lectures, and these notes, are explicitly designed to address both audiences.

Class: 
Applied
Subject: 
Social Sciences

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