Five major classes of requirements must be fulfilled. Since a number of options are
available, the student will, in consultation with an advisor, submit a plan of study
to the Graduate Committee of the program.

## Mathematical Requirement

To be completed by the end of the third year:

(1) One course in each of analysis beyond calculus, abstract algebra beyond linear
algebra, and logic and (2) Two quarters of mathematical statistics, with calculus
as a prerequisite and covering the fundamentals of probability and random variables.

Most advanced undergraduate or graduate courses in the Mathematics Department qualify
for the completion of the requirement. In Philosophy, the following courses will be
eligible:

PL230 A-B Intermediate Logic (4-4)

PL232 Topics in Mathematical Logic (4)

PL233 Philosophical Logic (4)

In the Department of Information and Computer Science, the following courses are
eligible to satisfy the mathematics requirement.

ICS 231 Formal Analysis Techniques (4)

ICS 233 Analysis of Algorithms (4)

ICS 264 Advanced Analysis of Algorithms (4)

ICS Automata Theory

Typically, the mathematical statistics requirement will be met by taking PSYCH203B
Introduction to Mathematical Statistics (4).

Examples of additional coursework in statistics are as follows:

SS201D Introduction to Biostatistics (4)

SS201C Survey Techniques and Estimation Methods (4)

SS213 B-C Econometrics I, II (4-4)

SS213D-E Econometrics Laboratory

SS213 H Time Series Econometrics (4)

SS241 B Experimental Design (4)

SSXXX Introduction to Stochastic Processes (4)

(Currently taught under a special topics number)

M203A-B-C Topics in Mathematical Statistics (4-4-4)

M204 A-B Multivariate Statistical Analysis (4-4)

M204 LA-LB Multivariate Statistical Laboratory (2-2)

M270 A-B-C Probability (4-4-4)

M271 A-B-C Stochastic Processes (4-4-4)

M271 A-B-C Topics in Probability (4-4-4)

## Computer/Language Requirement

Students must be sufficiently familiar with various computer programs and languages
to be able to conduct serious research in their field of interest and must submit
either proposed courses or some demonstration of competency as part of their plan
of study. In addition, students must either attain proficiency in reading social science
technical publications in one foreitn language or, demonstrate proficienty in computer
programming considerably beyond that of the standard computer requirement. Because
of the continually changing nature of computer languages and software, the conditions
for fulfilling this additional computer expertise will be left to the judgment of
the faculty sub-committee on computers of the Ph.D. program.

## Substantive Major

Students are expected to develop considerable expertise in some substantive field
of social science and in the application of models to it. This requires the completion
of three courses at the upper-division or graduate level that do not necessarily entail
extensive modeling and three courses or seminars in which the primary thrust is mathematical
modeling.

Some examples of courses in the first group are:

SS212 A-B-C Microeconomic Theory I, II, III (4-4-4)

SS213 G Discrete Choice Econometrics (4)

SS214 N Public Choice (4)

SS215 A-B-C Macroeconomic Theory I, II, III (4-4-4)

SS233 A-B Mathematical Athropology I, II, III (4-4-4)

SS243 M Social Psychology of Networks (4)

SS250 C-D-E Spatial Representation in Cognitive Sciences (4-4- 4)

SS253 A-B-C Visual Perception I, II, III (4-4-4)

SS255 A-B Artificial Intelligence and Human Vision I, II (4-4)

The following courses are more intensive in the use of modeling:

SS201 J Statistical Methods in Network analysis (4)

SS204 Algebraic Theories in Social Sciences (4)

SS285A Topics in Graph Theory (4)

(The above courses are being integrated into a series.)

SS241 C Computational Models of Language and Cognition (4)

SS243 G-H-I Observer Theory (4-4-4)

SS251 A-B Mathematical Models of Cognitive Processes I, II (4-4)

SSXXX A-B Game Theory (4-4)

SSXXX A-B Foundations of Measurement (4-4)

SSXXX A-B-C Mathematical Modeling in the Behavioral Sciences

## Research Papers and Colloquia

At the end of the second year, a 10-20 page paper either reporting original research
or a penetrating analysis of some subtopic of mathematical behavioral science is expected.
A 15-20 minute oral presentation will be given to faculty and graduate students. Two
faculty members will be assigned to read and evaluate the paper and the talk.

## Dissertation

The dissertation entails two steps:

**Advancement to Candidacy**

Usually at the end of the third year or the beginning of the fourth, the candidate
submits a prospectus proposal of at least 20 pages. A three-person dissertation committee
is formed to read and comment on the proposal. When it is deemed ready, an oral examination
will conducted by four faculty from the School of social Science and one from elsewhere
in UCI. It will cover not only the prospectus, but also related background material.

**Dissertation Defense**

After the written dissertation is submitted and evaluated by the dissertation committee
to be eligible for presentation, an oral examination will be held on the dissertation.

Students are expected to regularly attend the Colloquium in Mathematical Behavioral
Science.

For paper application and information contact:

John Sommerhauser

School of Social Sciences

University of California

Irvine, CA 92697-5100

(949) 824-4074

E-mail: jdsommer@uci.edu