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Mathematics and Social Sciences

Professors H. S. Alverson (Anthropology), J. C. Baird (Psychology, Emeritus), K. R. Baker (Tuck), K. P. Bogart (Mathematics), J. L. Campbell (Sociology), T. H. Cormen (Computer Science), A. J. Friedland (Environmental Studies), G. C. Jernstedt (Psychology), J. H. Levine (Mathematics and Social Sciences), R. D. Masters (Government, Emeritus), R. Z. Norman (Mathematics and Social Sciences, Emeritus), D. N. Rockmore (Mathematics and Computer Science), J. T. Scott (Economics), D. G. Sullivan (Government, Emeritus), R. A. Wright (Geography); Associate Professors K. A. Korey (Anthropology), L. Polansky (Music); Assistant Professor P. C. Christesen (Classics); Senior Lecturer R. L. Welsch (Anthropology).

Mathematics and Social Sciences (MSS) is an undergraduate honors major combining mathematical training with one or more of the social sciences. From the social sciences, MSS is for students interested in Anthropology, Economics, Education, Geography, History, Political Science, or Sociology, as a quantitative science. From mathematics, MSS is for students interested in statistics, data analysis, mathematics, or computer sciences directed toward application in social science.

THE MAJOR IN MATHEMATICS AND SOCIAL SCIENCES

 Prerequisite: Honors standing (see pages XXX) and Mathematics 13 (or, with permission, Mathematics 3 and 6 or equivalent), plus introductory work in several social sciences; or permission.

 Minimum Requirements: 1) Four (non-introductory) courses in Mathematics or Computer Science, including Mathematics 36; 2) Four (non-introductory) courses in one social science area. The four courses should form a coherent whole, although they need not fall within the same social science department; 3) Two additional courses, including one or more of the courses offered by the Program, to be approved by the Program committee; 4) Completion of a senior thesis, which may be done under the course Topics in Mathematics and Social Sciences, Mathematics and Social Sciences 88.

Where needed topics are not available in the existing curriculum, students may petition for special study under Mathematics and Social Sciences 88. Mathematics and Social Sciences 88 may be taken for credit more than once.

For further details, consult the Program Chair.

COURSES

7. First-Year Seminar in Mathematics and Social Sciences

Consult special listings

15. Introduction to Data Analysis

04F, 05S, 05F, 06S: 9L

Methods for transforming raw facts into useful information. The course includes basic techniques for detecting relations among events and assessing trends. Topics include exploratory data analysis. With permission from the responsible department, MSS 15 may be used to satisfy some pre-medical, natural science, and social science departmental requirements in mathematics and statistics. Limited enrollment. May be used in some departments in place of introductory methodology requirements.

Prerequisite: Math 3 or higher. Directed toward students with an aptitude for mathematics. Dist: QDS. Satisfies the Interdisciplinary requirement (Class of 2004 and earlier). Welsch.

36. Mathematical Models in the Social Sciences (Identical to Mathematics 36)

05W: 10 06W: Arrange

The mathematical methods of Mathematics 6 and 7, or Mathematics 20, are extended and applied to the study of mathematical models developed for use in such fields as anthropology, biology, economics, sociology, psychology, and linguistics. The role the mathematical models play in scientific study is discussed, as well as the methods by which a model may be validated.

Prerequisite: Mathematics 6 and 7, or 20, and 13. Dist: TAS.

41. Analysis of Social Networks

04F, 05F: Arrange

Students will gather and analyze data on a variety of networks (institutions, communities, elites, friendship systems, kinship systems, trade networks, and the like). Techniques of analysis may include graph theory, text analysis, multidimensional scaling and cluster analysis, and a variety of special models. Not limited to students in the major.

Prerequisite: Mathematics 3 or 6 and some knowledge of statistics, or permission of the instructor.

43. Mathematical Psychology

Not offered in the period from 04F through 06S

A course in mathematical models in psychology with emphasis on psychological foundations, applications, and testing. Topics will be chosen from information theory and its applications in memory, learning, language, and identification under uncertainty; probabilistic learning models; bargaining and its relation to n-person game theory; decision making under uncertainty; and thresholds and signal detectability.

Prerequisite: Psychology 1, and Mathematics 3 or 6. Permission required.

44. The Meaning of Mathematical Models: Careers, Stratifications, and Mobility

Not offered in the period from 04F through 06S

The existence or non-existence of class structure in America, the opportunities for and the degree of upward mobility, and the relation between ability and success are central issues for sociology.

Students will be responsible for understanding both social theory and technical methodology. They will complete a hands-on project, applying the theories of techniques of their choice (or of their invention) to detailed available data on the careers of American men and women of various ages, races, and family backgrounds.

45. Data Analysis

05S, 06S: Arrange

Examination of the assumptions and interpretation of basic quantitative methods in the social sciences. Methods examined may include linear models, tabular analysis, and Tukey- Mosteller exploratory data analysis. Applications will be wide-ranging and customized to student research. Prior knowledge of elementary data analysis or elementary statistics is assumed.

Prerequisite: Mathematics 13, or permission of the instructor.

46. Models of Voting and Decision Making

05W, 06W: Arrange

Is there a fair method of voting to elect a candidate for political office or to apportion representation in Congress among the States? We examine the benefits and problems of traditional plurality voting. Seeking criteria for fairness leads us to Arrow’s axioms for a social welfare function and his ‘impossibility’ theorem. Alternatives to his assumptions are explored as are weighted voting schemes and approval voting, evaluating their advantages and drawbacks. We also explore the concept of fairness in apportionment of congressional districts. Throughout the course both mathematical and political concepts are used to analyze consequences, benefits, and costs.

Prerequisite: By permission only. Government 6 or other introduction to the U.S. political system, and Mathematics 3 or 6 recommended. Norman.

80. Seminars in Mathematics and Social Sciences

All terms: Arrange

88. Topics in Mathematics and the Social Sciences

All terms: Arrange

We call attention to the following courses which include some of the more quantitative and mathematical courses in the curriculum of various social science disciplines.

Anthropology 41: Hominid Evolution

Economics[1]

Engineering Sciences 51: Principles of System Dynamics

Engineering Sciences 52: Introduction to Operations Research

Government 72: Human Nature and Politics

Philosophy 27: Philosophy of Science

Psychology 21: Perception

Psychology 22: Learning

Psychology 28: Cognition

Psychology 68: Experimental Study of Human Perception and Cognition

Sociology 17: Survey Methods and Analysis


[1] Economics courses are quantitative in nature and the advanced sequential courses quite highly so. Mathematics and Social Sciences students are encouraged to speak with the professors of the courses that are of substantive interest to the student so that the student can ascertain whether the mix of quantitative technique and substantive economic issues is right for him.