Quantitative Reasoning 22. Deductive Logic
Catalog Number: 2508
Richard G. Heck, Jr.
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. Students will learn how others think about uncertainty and risk and how better to assess uncertainty in their own lives. The course introduces concepts and the language of probability and statistics with an emphasis on its relationship to quantifying uncertainty for use in daily life. Examples will be drawn from the media, science, law, medicine, and government.
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.
Note: Expected to be omitted in 2003–04.
Quantitative Reasoning 36. Statistics and Public Policy
Catalog Number: 7412
Christopher Winship
Half course (fall 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.
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 43. Introduction to Investments
Catalog Number: 4629
John Y. Campbell
Half course (fall term). Tu., Th., 10–11:30, and a weekly section to be arranged. EXAM GROUP: 12, 13
This course introduces students to the basic mathematical tools and economic concepts needed to analyze financial investments. The course discusses the measurement of asset prices and returns, arbitrage, interest rates and discounting, quantitative measures of risk, portfolio choice, risk management, and derivative securities. Students are asked to apply these ideas to real financial data.
Quantitative Reasoning 44. Greek Geometry and its Aftermath: Euclid for a Digital Age
Catalog Number: 7964
Paul G. Bamberg
Half course (spring term). Tu., Th., 1–2:30, and a weekly section to be arranged. EXAM GROUP: 15, 16
Investigates why Greeks could construct a regular pentagon or bisect an angle with compass and straightedge but had to resort to trickery to trisect an angle or construct the cube root of 2. Reviews elementary calculus and develops the theory of infinite series to explain why the Greeks could not “square the circle,” and presents modern methods for calculating millions of digits of pi by computer. Students will learn to use the interactive programming language Mathematica to replicate the approaches of Archimedes, Newton, Euler, Ramanujan, and other giants of mathematics.
Quantitative Reasoning 46. The Visual Display of Quantitative Information
Catalog Number: 9479
Alyssa A. Goodman
Half course (spring term). Tu., Th., 1–2:30, and a weekly section to be arranged. EXAM GROUP: 15, 16
This course focuses on the insight into quantitative information offered by graphs, tables, charts, maps, and other illustrations. We analyze which of these tools are best for communicating what kinds of data, and why. Ideas about causality, approximation, statistical significance, credibility, and dimensionality will be addressed by analyzing real data, and their display. The data will be drawn from medical, astronomical, social-science, aerospace, financial, and geographic examples. Approximately one-quarter of the course will focus on web and live (e.g. PowerPoint) presentations of data. Much of the course’s philosophy is based on the work of Edward Tufte (edwardtufte.com).
Note: Expected to be omitted in 2003–04.