- Ph.D., University of Wisconsin-Madison (1980)
- M.A., University of Wisconsin-Madison (1977)
- B.A., Dartmouth College (1976)
- A.M. (honorary), Amherst College (1992)
Awards and Honors
- Carl B. Allendoerfer Award (for the paper "Permutations and combination locks"), 1996
- Lester R. Ford Award (for the paper "Versatile coins"), 1994
- Honorable mention (38th place), Putnam Exam, 1975
Much of my research has been in the field of mathematical logic, particularly set theory. However, I have published papers in a wide range of fields, including combinatorics, topology, analysis, philosophy of mathematics, and foundations of quantum mechanics.
Many high school students view mathematics as a collection of formulas to be used to calculate numerical answers. To succeed in college-level mathematics, they must learn to think of mathematics as involving reasoning, rather than merely calculation. In advanced undergraduate courses, they must learn to express their reasoning in the form of mathematical proofs. In my teaching, I try to help students make this transition from calculation to reasoning to proofs. I put particular emphasis on making sure students understand the meaning of mathematical language and the importance of using that language precisely.