Psychology | Introduction to Mathematical Psychology
P605 | 4087 | J. Townsend

Course Description:  Psychology 605—INTRODUCTION TO MATHEMATICAL

When:  Fall, 2003

Where:  PY 115

Instructor:  Jim Townsend

Prerequisites: 1.  Working knowledge of calculus (a semester might
suffice; a year is better).  2. Familiarity with elementary
probability theory and stochastic processes would help, but these can
be picked up, perhaps with some ancillary reading, during the course.

Tests:  None

Homework:  Important:  Turned in weekly.

Papers:  One term paper based on modeling interests of the student.

Description:  This course does not survey math modeling in cognition.
It does develop the ability to construct simple, but rigorous
cognitive/perceptual mathematical models.  It also aims to lead the
student to understand at a fairly deep and fundamental level two major
avenues in elementary psychological modeling: TOPIC 1. UNI- AND
CATEGORIZATION.  This theory is ubiquitous in cognitive and perceptual
science, being employed in a huge spectrum of perception and
psychophysics as well as many regions of memory and categorization.
In this class, the student learns the fundamentals of the main and
some alternative theories and many basic results are proven and/or
discussed.  We begin with the simple 1-dimensional case and end with
multi-dimensional generalizations that are applied to such important
areas as perceptual independence of features, dimensions, channels, or
objects.  This broad approach is also appropriate studying similarity
and decision rules in various spheres of research such as
identification and categorization.  TOPIC 2. RESPONSE TIMES, MENTAL
patterns of accuracy and confusion in data, the second primary topic
focuses on how long it takes a person to respond to various kinds of
stimuli and situations.  In addition to teaching students to build
models that predict response times in various psychological
situations, they will learn basic meta-modeling strategies permitting
the experimental assessment of fundamental aspects of human
information processing. It turns out that using response times alone,
it is feasible to determine whether people are processing various
kinds of items, channels, etc., in a parallel (simultaneously) or
serial (one at a time) fashion.  In addition sensitive measures of
capacity have been developed and it is possible to specify when mental
tasks cease, despite the fact that some of them consume only a few
hundredths of a second in their fulfillment.  At the end of the
course, I will show how to put the accuracy and response times
together to construct even more powerful types of mathematical