P605 | 4087 | J. Townsend

Course Description: Psychology 605—INTRODUCTION TO MATHEMATICAL PSYCHOLOGY 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 MULTI-DIMENSIONAL THEORIES OF SIGNAL DETECTION, IDENTIFICATION 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 ARCHITECTURE AND PROCESSING CAPACITY. Whereas TOPIC 1 emphasizes 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 theories.