1. Read one of the following books (for the longer ones, a few chapters will do), and write a paper on it. This is not a book report; instead, the goal is to understand and present one or more of the main ideas in your own words.
Chaos: Making a New Science by James Gleick
Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
Instability rules : the Ten Most Amazing Ideas of Modern Science
by Charles Flowers
How to Solve It : A New Aspect of Mathematical Method by G. Polya
Attacking Faulty Reasoning: A Practical Guide to Fallacy-Free Arguments
by T. Edward Damer
With Good Reason: An Introduction to Informal Fallacies by Morris S Engel
Logic Made Easy: How to Know When Language Deceives You by D.J. Bennet
Archimedes’ Revenge: The Joys and Perils of Mathematics by Paul Hoffman
Understanding the philosophy of science by James Ladyman
Scientific method in practice by Hugh G. Gauch, Jr.
Godel: A Life of Logic by John L. Casti and Werner DePaul
Freakonomics: A Rogue Economist Explores the Hidden Side of Everything
by Steven Levitt
Crimes Against Logic by Jamie Whyte
Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart
by Ian Ayres
(Many of these are available in the CLC library)
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2. Write a “mathematical biography” on one of the leading figures of mathematical Logic. Research the life and work of one, and write a paper about him. AT MOST one third of your paper should concern their biography. The remainder should show discuss their contributions to the field, and why it was important. Note that you also should refrain from giving a list of results – rather, the purpose of this paper is to show what you learned about their work. Connections to what we have learned in class should be included. Suggested subjects: Kurt Godel, Bertrand Russell, Aristotle, George Boole, Georg Cantor, Leibniz.
3. Each quarter, the U.S. government issues estimates of economic indicators such as the inflation rate, growth rate of the economy, and unemployment statistics. In recent years, there has been considerable controversy over the government’s calculation of the inflation rate – since many government outlays are directly tied to the inflation rate, small errors in its estimation can have large impacts on federal budgets. Write a report describing how the inflation rate is calculated, and why this method of calculation has been questioned. Be sure to discuss the CPI and how it impacts the economy and federal budget.
4. Imagine that you are a financial consultant. One of your clients is a young lady, age 30. She has recently bought a home for $200,000. The mortgage is for 30 years at a rate of 6%. She also wants to save for retirement. She is able to put $2400 annually into an IRA that earns 5% compounded monthly. The money put into the IRA is pre-tax; assume that she pays 25% of her income as income tax. She is currently weighing two options: either paying an additional $200 per month on her mortgage payment, or paying the same $200 into her IRA. Which would you recommend if she wants to retire at age 60? Draw up a couple of scenarios that would help her make her decision. Give a detailed comparison of the merits of each plan.
5. The following books discuss some of the ways in which statistical data is commonly misused:
– How to Lie with Statistics, by Darrell Huff
– Damned Lies and Statistics by Joel Best
– More Damned Lies and Statistics by Joel Best.
– Standard Deviations: Flawed Assumptions, Tortured Data and Other Ways
to Lie with Statistics by Gary Smith