Quantitative Reasoning 22. Deductive Logic
Catalog Number: 2508
Peter Koellner
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 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 discuss various special classes of numbers, such as prime numbers, factorials, and binomial coefficients, and the many ways they arise in mathematics. We will discuss questions in probability (such as: the likelihood that two people in a class of 25 have the same birthday). We also study modular arithmetic and secret codes based on it.
Note: No mathematical background beyond high school algebra assumed. Emphasis is 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 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 2008–09.
[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.
Note: Expected to be given in 2008–09.
Quantitative Reasoning 46. The Visual Display of Information: The Art of Numbers
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 presentations of data. Much of the course’s philosophy is based on the work of Edward Tufte.
Note: Expected to be omitted in 2008–09.
[Quantitative Reasoning 48. Bits]
Catalog Number: 2793
Harry R. Lewis
Half course (spring term). M., W., F., at 11, and a weekly section to be arranged. EXAM GROUP: 4
Information as quantity, resource, and property. Application of quantitative methods to understanding how information technologies inform issues of public policy, regulation, and law. How are music, images, and telephone conversations represented digitally, and how are they moved reliably from place to place through wires, glass fibers, and the air? Who owns information, what forms of regulation and law restrict the communication and use of information, and does it matter? How can secrets and personal privacy be protected at the same time as society benefits from communicated or shared information?
Note: Expected to be given in 2008–09. Mathematical methods will be developed in the context of the course material. No mathematical background beyond high-school algebra is required.
Quantitative Reasoning 50. Medical Detectives
Catalog Number: 5707
Karin B. Michels (Medical School, Public Health)
Half course (fall term). M., W., F., at 9, and a weekly section to be arranged. EXAM GROUP: 2
Why is there confusion in the scientific community as to whether butter or margarine is worse for your health? How do epidemiologists find out whether cell phone use increases your risk for brain cancer? What is your risk of contracting diabetes? Discover how researchers draw on quantitative skills to detect causes of acute disease outbreaks and chronic diseases. This course introduces the techniques and methods for empirically based analyses, decisions, and actions in the context of current public health problems.