Tom Ramsey
Emeritus Professor

Computing Angular Kronecker Constants (joint work with Kathryn Hare)

Papers about Kronecker Constants (updated Jan. 7, 2016)
co-authored with Kathryn Hare (University of Waterloo)

A New Paper in Statistics (July, 2011)

Two recent papers co-authored with Colin C. Graham:

CitizenshipLogic | Credit by Exam 
International Student Service | Math Department


Shark Attacks in Hawaii (posted 12/12/2013)
(Traditional) Exact Confidence Intervals for the Binomial Distribution
(posted 4/5/2005, pdf format; revised very slightly, 5/6/2011; mahalo to Hong Zhang for a careful reading)
Convexity of the Binomial Distribution
(posted 4/5/2005, pdf format)
How Not To Define Surface Area:   an 1890 Example Due to H. A. Schwartz   (posted 11/08/2004, in pdf format). I learned this example from T. W. Korner's book, "A Companion to Analysis", page 218. Schwartz produced a simple triangulation of a cylinder for which the sum of the areas of the triangles converges to any chosen number greater than the true surface area, or even converges to infinity.
New!  How many people have ever lived?  Keyfitz's computation is updated. This page on demography was written at the behest of Prof. Glen Paige for his new book, "Non-Killing Political Science."


Youth Economics

Relative to male high school graduates, the college wage premium soared from 35 percent to 93 percent between 1973 and 1992 (page 177, The Future of Capitalism, by Lester Thurow).

However, the standard deviations are also quite large:

"During the peak earning years of forty-five to fifty-four years of age, 26 percent of all white males with bachelor's degrees will earn less than the median white male high school graduate and 21 percent of al white male high school graduates will earn more than the median white male with a bachelor's degree (page 282, The Future of Capitalism, by Lester Thurow).

Social Security Reform

Perhaps the most responsible review of social security issues is "The Coming Generational Storm" by Laurence J. Kotlikoff and Scott Burns. Here is an outline of their proposal, from page 156:
  • The accrual of additional Social Security retirement benefits is eliminated. Ramsey's paraphrase: immediately stop making new unfunded promises but keep all the old promises.
  • Current retirees and current workers receive their accrued Social Security retirement benefits. Ramsey's paraphrase: old promises are kept.
  • Social Security's Old Age Insurance (OAI) payroll tax is eliminated and replaced with equivalent compulsory contributions to PSS accounts. Ramsey's paraphrase: mandatory personal savings accounts are set up to take care of new retirement needs of new workers, with no change in take-home pay.
  • A new federal retail sales tax is used to pay off the accrued retirement benefits owed under the old system. Ramsey's paraphrase: the money to keep the old promises must come from somewhere.
  • Workers' PSS contributions are shared fifty-fifty with their spouses.
  • The government contributes to PSS accounts on behalf of disabled and unemployed.
  • The government matches PSS contributions on a progressive basis.
  • All PSS balances are invested in a single market-weighted global index fund of stocks, bonds and real estate.
  • The government guarantees the real principle that workers contribute to their PSS accounts. Ramsey's note: real means growing enough to match inflation.
  • Between ages 57 and 67, workers' PSS balances are gradually sold off and transformed into inflation-protected pensions.
  • If a worker dies prior to age 67, any remaining PSS balances would be transferred to PSS accounts of the worker's heirs.

Kotlikoff and Burns personally believe that there is no chance that Congress will implement a reform plan such as this, but they offer the plan as proof that we don't have to let a financial crisis happen.