Quantitative Reasoning 22. Deductive Logic
Catalog Number: 2508
Warren Goldfarb
Half course (fall term). M., W., (F.), at 10, and a weekly section to be arranged. EXAM GROUP: 3
The concepts and principles of symbolic logic: valid and invalid arguments, logical relations of statements and their basis in structural features of those statements, the analysis of complex statements of ordinary discourse to uncover their structure, the use of a symbolic language to display logical structure and to facilitate methods for assessing arguments. Analysis of reasoning with truth-functions (“and”, “or”, “not”, “if...then”) and with quantifiers (“all”, “some”). Attention to formal languages and axiomatics, and systems for logical deduction. Throughout, both the theory underlying the norms of valid reasoning and applications to particular problems will be investigated.
Quantitative Reasoning 24. Health Economics
Catalog Number: 4667
David M. Cutler
Half course (fall term). Tu., Th., 10–11:30, and a weekly section to be arranged. EXAM GROUP: 12, 13
Analysis of the medical care system is integral to a number of disciplines, including economics, philosophy, sociology, demography, and statistics, as well as four professional schools (medicine, public health, law, and public policy). This course uses quantitative methods to examine the organization and operation of the medical system. The course will cover the medical and non-medical determinants of health; markets for medical care services and health insurance; and proposed reforms of medical care. Methods of analysis will include graphical analysis, algebra, survey design, and use of secondary data. Techniques will be developed in class and section. Use of a computer spreadsheet is required and will be demonstrated in class and section.
Quantitative Reasoning 26. Decisions, Games, and Negotiation
Catalog Number: 4123
Daniel L. Goroff and Howard Raiffa (Business School)
Half course (spring term). M., W., (F.), at 1, and a weekly section to be arranged. EXAM GROUP: 6
This course develops quantitative reasoning skills that help individuals and groups make better choices. We study decisions whose results are perfectly predictable as well as situations with incomplete information, uncertainty about the future, or outcomes that depend on other people’s actions. Based on examples that range from everyday career conundrums to the politics of public policy, and from household financial strategies to professional school cases, our discussions cover: the mathematics of ideal rationality; the pragmatic use of spreadsheets, data, heuristics, and other tools; and behavorial research on surprising ways that people estimate, wager, and bargain in practice.
Note: High school algebra and willingness to think hard are prerequisites.
Quantitative Reasoning 28. The Magic of Numbers
Catalog Number: 4764
Benedict H. Gross and Joseph D. Harris
Half course (fall term). M., W., F., at 10, and a weekly section to be arranged. EXAM GROUP: 3
This course will explore the beauty and mystery of mathematics through a study of the patterns and properties of the natural numbers 1, 2, 3, .... We will discuss various special classes of numbers, like Fibonacci numbers, factorials, and binomial coefficients, and the many ways they arise in mathematics. We’ll also investigate the distribution of prime numbers and discuss coding systems based on modular arithmetic.
Note: We will assume no mathematical background beyond high school algebra. Emphasis will be placed on discovery through conjecture and experimentation.
[Quantitative Reasoning 32. Uncertainty and Statistical Reasoning]
Catalog Number: 2228
Carl N. Morris
Half course (fall term). Tu., Th., 10–11:30, and a weekly section to be arranged. EXAM GROUP: 12, 13
Individuals continually must make decisions under uncertainty in their personal and in their professional lives. This course develops probability as the appropriate language for describing uncertainty, and it shows how statistical data and planned studies can be crucial when evaluating probabilities and associated risks. It will help students understand and discover how people think about uncertainty and risk. The course will improve each student’s ability to handle uncertainty, and so to make better decisions. It introduces concepts and the language of probability and statistics. Students will review and assess probabilities and statistics developed for and reported in the media, science, industry, law, medicine, and government.
Note: Expected to be given in 2002–03.
Quantitative Reasoning 33. Causal Inference
Catalog Number: 0424
Donald B. Rubin
Half course (spring term). Tu., Th., 11:30–1, and a weekly section to be arranged. EXAM GROUP: 13, 14
Do private schools do a better job than their public counterparts? Does the existence of the QRR improve the quantitative literacy of the undergraduates at Harvard? Such questions dominate many decision-making processes, but only rarely are their “answers” based on the careful collection and analysis of empirical data. This course confronts such causal questions and how to reach inferentially valid answers that summarize uncertainty using formal probabilistic statements.
[Quantitative Reasoning 36. Statistics and Public Policy]
Catalog Number: 7412
Christopher Winship
Half course (spring term). M., W., F., at 11, and a weekly section to be arranged. EXAM GROUP: 4
Data, or more accurately statistics calculated from data, are used ubiquitously in the support of various public policy claims. The purpose of this course is to examine the statistical methods used in making such claims and understand their potential strengths and weaknesses. The course examines Sampling, Characteristics of Distributions, Basic Probability, Statistical Reference, Measurement and Scaling, Measures of Association, Experiments, and Quasi-Experiments. The last part of the course will focus on the problem of making causal inferences from empirical data. The goal of the course is to acquire a clear, conceptual understanding of methods as opposed to the ability to manipulate formulas.
Note: Expected to be given in 2002–03.
[Quantitative Reasoning 37. Surveys and Statistics in Sociology]
Catalog Number: 8610
Peter V. Marsden
Half course (fall term). Hours to be arranged.
Introduces quantitative analysis in social research, including principles of research design and the use of empirical evidence, particularly from social surveys. Descriptive and inferential statistics, contingency table analysis, and regression analysis. Emphasis on analysis of data and presentation of results in research reports.
Note: Expected to be given in 2002–03.
Quantitative Reasoning 38. The Strategy of International Politics
Catalog Number: 7119
Lisa L. Martin
Half course (spring term). Tu., Th., 10–11:30, and a weekly section to be arranged. EXAM GROUP: 12, 13
International politics is often about strategic interaction among states. When governments make choices about economic, military, or environmental policies, they take into account the likely responses and actions of others. This course introduces the logic of strategic interaction by way of game theory. The principles of game theory are introduced, and students learn how to solve simple games. Mathematical topics covered include probabilities, set theory, linear equations, and quadratic equations. The games are motivated and illustrated with examples drawn from international politics. The logic and techniques developed in this class have wide applications outside the field of international relations.
[Quantitative Reasoning 42. Powerful Habits of Mind]
Catalog Number: 4786
Eric Mazur
Half course (spring term). Hours to be arranged.
Future decision-makers—politicians, executives, scientists, and citizens—must analyze the arguments of others and develop their own. This course is intended to teach quantitative analysis and exploration as habits of mind—as automatic approaches to the certainty of oneself and others—and to develop comfort with numbers and rough estimates. Techniques of analysis: developing reasoning tools that can be applied to scientific and social arguments, and techniques of exploration: how to create new ideas will be studied. The tools developed will be applied to issues reported in the media, to advertisements, to policy documents, and to students’ thinking and writing.
Note: Expected to be given in 2002–03.