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- Bicycle or Unicycle? (with Stan Wagon), MAA Press, 2020, sample chapters
- How To Prove It, Cambridge University Press, 1994; 2nd ed., 2006; 3rd ed., 2019
- Calculus: A Rigorous First Course, Dover Publications, 2016
- Philosophies of Mathematics (with Alexander George), Wiley-Blackwell Publishers, 2001
- Which Way Did The Bicycle Go? (with Stan Wagon and Joe Konhauser), MAA Press, 1996
- Differences of bijections (with Daniel H. Ullman), American Mathematical Monthly 126 (2019) 199-216
- On Gauss's first proof of the fundamental theorem of algebra (with Soham Basu), American Mathematical Monthly 124 (2017) 688-694
- Anonymity in predicting the future (with Dvij Bajpai), American Mathematical Monthly 123 (2016) 777-788
- The fundamental theorem of algebra: A visual approach, Mathematical Intelligencer vol. 37 no. 4 (Dec. 2015) 12-21
- A drug-induced random walk, American Mathematical Monthly 121 (2014) 299-317
- What to expect in a game of memory (with Gregory Warrington), American Mathematical Monthly 120 (2013) 787-805
- The even-odd hat problem, Fundamenta Mathematicae 219 (2012) 105-110
- If the IRS had discovered the quadratic formula..., Math Horizons, April 2007, p. 21
- Variable declarations in natural deduction, Annals of Pure and Applied Logic 144 (2006) 133-146
- The generalized Simpson's rule, American Mathematical Monthly 112 (2005) 342-350
- Simpson symmetrized and surpassed, Mathematics Magazine 77 (2004) 31-45
- The mean value theorem in second order arithmetic (with Christopher Hardin), Journal of Symbolic Logic 66 (2001) 1353-1358
- Multivariable calculus and the plus topology, American Mathematical Monthly 106 (1999) 733-740
- Probability and quantum mechanics, American Journal of Physics 66 (1998) 967-969
- Two conceptions of natural number (with Alexander George), in Truth in Mathematics, Garth Dales and Gianluigi Oliveri (eds.), Oxford University Press, 1998, pp. 311-327
- Characterizing continuity, American Mathematical Monthly 104 (1997) 318-322
- Another proof of the fundamental theorem of algebra, Mathematics Magazine 70 (1997) 216-217
- Fermat's last theorem and Hilbert's program, Mathematical Intelligencer vol. 19 no. 1 (Winter 1997) 64-67
- Permutations and combination locks (with Gregory Call), Mathematics Magazine 68 (1995) 243-253
- Pascal's matrices (with Gregory Call), American Mathematical Monthly 100 (1993) 372-376
- Constructivism liberalized, Philosophical Review 102 (1993) 59-84
- Versatile coins (with István Szalkai), American Mathematical Monthly 100 (1993) 26-33
- Partitioning pairs of countable sets of ordinals, Journal of Symbolic Logic 55 (1990) 1019-1021
- Gap-2 morasses of height omega, Journal of Symbolic Logic 52 (1987) 928-938
- Simplified gap-2 morasses, Annals of Pure and Applied Logic 34 (1987) 171-208
- Omega-Morasses, and a weak form of Martin's axiom provable in ZFC, Transactions of the American Mathematical Society 285 (1984) 617-627
- Simplified morasses, Journal of Symbolic Logic 49 (1984) 257-271