Dan Flath’s Professional Experience


  • B.S., Electrical Engineering, Southern Methodist University, 1972
  • M.S., Electrical Engineering, Southern Methodist University, 1972
  • M.A., Mathematics, Harvard University, 1974
  • Ph.D., Mathematics, Harvard University, 1977
  • Data Science, a 10 course specialization, Johns Hopkins University/Coursera, 2014

Research Positions


Winner of  2014 MAA North Central Section Award for Distinguished College or University Teaching of Mathematics (Mathematical Association of America)


  1. Decomposition of representations into tensor products, Automorphic Forms, Representations, and L-Functions, Proceedings of Symposia in Pure Mathematics 33, Part I, American Mathematical Society,
    Providence, R.I., 1979, pp179-183.
  2. Atkin-Lehner operators, Mathematische Annalen 246 (1980), 121-123.
  3. A comparison of the automorphic representations of GL(3) and its twisted forms, Pacific Journal of Mathematics 97 (1981), 373-402.
  4. The Clebsch-Gordan formulas, L’Enseignement Mathématique 29 (1983), 339-346.
  5. On the structure of tensor operators in SU(3) (with L.C.Biedenharn), Communications in Mathematical Physics 93 (1984), 143-169.
  6. On so(8) and the tensor operators of sl(3), Bulletin of the American Mathematical Society 10 (1984), 97-100.
  7. Tensor operators as an extension of the universal enveloping algebra (with L.C.Biedenharn), Group Theoretical Methods in Physics, Lecture Notes in Physics 201, Springer, New York, 1984, pp486-493.
  8. Beyond the enveloping algebra of sl(3) (with L.C.Biedenharn), Canadian Journal of Mathematics 37 (1985), 710-729.
  9. An analogue of the Weyl algebra, Algebraic Geometry Seminar (Proceedings of the Algebraic Geometry Seminar, Singapore, 1987) (M.Nagata and T.A.Peng, eds.), World Scientific, Singapore, 1988, pp1-4.
  10. Decomposition of the enveloping algebra of sl(3), Journal of Mathematical Physics 31 (1990), 1076-1077.
  11. Remarks on tensor operators, Journal of Mathematical Physics 31 (1990), 1605-1609.
  12. Tensor operators I, the concept of a coherent tensor operator (with J.Towber), Communications in Algebra 18 (1990), 4047-4086.
  13. How to pick out the integers in the  rationals: an application of number theory to logic (with S.Wagon), American Mathematical Monthly 9 (1991), 812-823.
  14. A carry theorem for rational binomial coefficients (with R.Peele), Applications of Fibonacci Numbers 4 (1991), 109-120.
  15. Generators and relations for the affine rings of the classical groups (with J.Towber), Communications in Algebra 20 (1992), 2877-2902.
  16. Tensor operators II, the algebra of tensor operators (with J.Towber), Communications in Algebra 20 (1992), 2903-2917.
  17. Fractal patterns derived from rational binomial coefficients (with R.Peele), Applications of Fibonacci Numbers 5 (1993), 221-228.
  18. Tensor operators III, some fundamental tensor operator identities (with J.Towber), Journal of Mathematical Physics 34 (1993), 1523-1547.
  19. Hausdorff dimension in Pascal’s triangle (with R.Peele), Applications of Fibonacci Numbers 5 (1993), 229-244.
  20. Coherent tensor operators, Lie Algebras, Cohomology and New Applications to Quantum Mechanics, Contemporary Mathematics 160, American Mathematical Society, Providence, R.I., 1994, pp75-84.
  21. Review of (Resources for Calculus, vol. 1-5, Roberts, A.Wayne, Project Director, Mathematical Association of America, Washington, D.C., 1993), The UMAP Journal 15 (1994), 86-89.
  22. Does the Moebius function determine multiplicative arithmetic? (with A.Zulauf), American Mathematical Monthly 102 (1995), 354-356.
  23. A Combinatorial Problem in the Representation Theory of SL(n) (with J.Towber), Annals of Combinatorics 4 (2000), 257-268.
  24. Rocket Math (with S.Wagon and C.Stoll), College Journal of Mathematics 35 (2004), 262-273.
  25. Finding a Hidden Coin (with S.Wagon), The UMAP Journal 27 (2006), 469-490.
  26. The Planar Rook Algebra and Pascal’s Triangle (with T.Halverson and K.Herbig), l’Enseignement Mathématique (2) 54 (2008), 1-16.
  27. The First Year of Calculus and Statistics at Macalester College (with T.Halverson, D.Kaplan, K.Saxe), Undergraduate Mathematics for the Life Sciences: Models, Processes, and Directions, (G.Ledder, J.P.Carpenter, and T.D.Comar, eds.), MAA Notes, MAA, 2013.
  28. Gravity-driven instability of a thin liquid film underneath a soft solid (with S.H.Lee, K.L.Maki, S.J.Weinstein, C.Kealey, W.Li, C.Talbot, S.Kumar), Physical Review E, 90 (2014), 053009.
  29. A role for engineering at a liberal arts college, Engineering Studies 7 (2015), 203-205.
  30. Thinking Like an Engineer: Responding to the Engineering Blind Spot at Liberal Arts Colleges (with D.Michelfelder), 2017 ASEE Annual Conference. online link 
  31. Kremer’s Model Relating Population Growth to Changes in Income and Technology, CODEE Journal 12 (2019). online link

  32. Derivatives are multipliers, College Mathematics Journal 51 (2020), 260-270. online link



  1. Introduction to Number Theory, Wiley, New York, 1988.  Republished, American Mathematical Society, 2018.
  2. Calculus, (with the Calculus Consortium based at Harvard), Wiley, New York, First ed. 1993, Second ed. 1998, Third ed. 2001, Fourth ed. 2004, Fifth ed. 2008, Sixth ed. 2012, Seventh ed. 2017.
  3. The classical and quantum 6j-symbols, (with J.S.Carter and M.Saito), Princeton University Press, Princeton, 1995.
  4. Multivariable Calculus, (with the Calculus Consortium based at Harvard), Wiley, New York, 1995.
  5. Brief Calculus, Preliminary Edition, (with the Calculus Consortium based at Harvard), Wiley, New York, 1997.
  6. Applied Calculus, (with the Calculus Consortium based at Harvard), Wiley, New York, First ed. 1999, Second ed. 2002, Third ed. 2005, Fourth ed. 2009, Fifth ed. 2013, Sixth ed. 2017.
  7. Conceptests for Calculus, (with the Calculus Consortium based at Harvard), Wiley, New York, 2002.
  8. Functions Modeling Change, (with the Calculus Consortium based at Harvard), Wiley, New York, Second ed. 2004, Third ed. 2007, Fourth ed. 2010, Fifth ed. 2014.
  9. Conceptests for Applied Calculus, (with the Calculus Consortium based at Harvard), Wiley, New York, 2006.