David J. Sprows, Professor
Mathematical Sciences
St. Augustine Center 377
(610) 519-7339

Curriculum Vitae
Publications

CURRICULUM VITAE

EXPERIENCE
Current position: Professor of Mathematics, Villanova University.
Faculty member at Villanova University since 1962.
Spent 1969-1970 as an NSF Faculty Fellow at the University of Pennsylvania.
Villanova Faculty Research Grant Recipient in 1979.

EDUCATION
Ph.D. , University of Pennsylvania, 1971.
(Thesis advisor: Herman Gluck. )
M.A., Villanova University, 1962.
B.A., West Chester University, 1960.

UNIVERSITY ACTIVITIES
Director of Graduate Programs in Mathematics (1985 - ).
Associate Dean for Sciences Search Committee (2003-2005).
University Rank and Tenure Committee (1991 - 2000 ).
Academic Policy Committee (1981 - 1994).
University Planning Committee ( 1975 - 1981).
Chairman of Honors Curriculum Committee ( 1982 - 1984).
Middle States Self-Study Committees on Sciences (1979) and Faculty (1989).                 
 

PROFESSIONAL ACTIVITIES
Member of the American Mathematical Society and the Mathematical Association of America.
Charter member and former moderator of the Villanova Chapter of Pi Mu Episilon .
Referee for the College Mathematics Journal , the Journal of Mathematics and Computer Ed. and PRIMUS.
Problem Author and Consultant for the Bucks County Interscholastic Math League (1976-1991). Reviewer for Zentralblatt fur Mathematik and several textbook publishers.
Member of the Mathematical Association of America Distinguished University and College Teaching Award Committee (1994 - 1996) Member of the Editorial Board of the Mathematical Association NOTES  series (2005) -                                                                                                                    

TEACHING
Taught a full spectrum of courses at both the undergraduate and graduate levels. Developed a new course (Foundations of Mathematics) and two new seminars on the undergraduate level. On the graduate level was responsible for a number of curriculum changes and developed several new courses and seminars.

Finalist for the Lindbach Award for Distinguished Teaching (twice).

Lindbach Award Honorable Mention (seven times).

One of twenty-four mathematicians nationwide to receive a Mathematical Association Regional Award for Distinguished College or University Teaching of Mathematics (1993).
(This annual award was first given in 1992.)

RESEARCH INTERESTS
1. Low dimensional topology. Particular interest in isotopy groups of homeomorphisms of bounded manifolds.

2. Mathematics education. Special interest is developing materials involving iterated functions and number systems.

OTHER ACTIVITIES
Formerly served as Judge of Elections for the Third District of the Borough of Narberth (10 years) and as a member of the governing council of the Narberth Civic Association. Served as a member of the coaching staff of the Narberth Neutrons Soccer team. Currently an area captain and member of the governing board for the Narberth Improvement Community Endeavor (N.I.C.E.).

PUBLICATIONS

1. Homeotopy groups of compact 2-manifolds, Fundamenta Mathematicae, 90, 1 (1975).

2. Problem #977, Mathematics Magazine, 49, 2 (1976). (Reprinted as the Impossible Problem in Scientific AmericanDecember, 1979.)

3. Ozometry, MATYC Journal, 13, 2 (1979) .

4. Subhomeotopy groups of the 2-sphere with n-holes, Fundamenta Mathematicae, 93, 1 (1980).

5. Census-Taker Numbers, MATYC Journal, 15,2 (1981).

6. Nearly Impossible Problems, Mathematics and Computer Education, 17, 3(1983).

7. Isotopy groups of bounded 2-manifolds, Kumamoto Journal of Science, 15, (March)(1983).

8. Homeotopy groups of punctured spheres with holes, Fundamenta Mathematicae, 115, 3(1983)

9. Computer problems involving iterates of functions, Mathematics and Computer Education, 18, 3(1984).

10. Isotopy groups of circle-bounded manifolds, Kumamoto Journal of Science, 17, 1(1986).

11. Sociable sequences and diminishing functions, Mathematics and Computer Education, 23, 1(1989).

12. Irrationals and the Fundamental Theorem of Arithmetic, American Mathematical Monthly, 96, 9(1989).

13. A note of the presentation of isotopy groups of bounded 2-manifolds, Kumamoto Journal of Math 2, (March)(1989).

14. Reiterating an ASHME problem, Mathematics and Computer Education, 25, 1(1991).

15. Iterating Sawtooth Functions, Mathematics and Computer Education, 28, 3(1994).

16. Oscillating Sawtooth Functions, with F.W. Hartmann, Mathematics Magazine, 68, 3(1995).

17. What can happen when the second derivative vanishes, PRIMUS, 6, 4(1996).

18. Digitally determined periodic points, Mathematics Magazine, 71, 4 (1998)

19. Prime triplets and Pythagorean doubles, PRIMUS, 9, 1 (1999)

20. Simx and the Fundamental Theorem of Calculus, Mathematics and Computer Ed.,33,3 (1999).

21. Subhomeotopy groups of bounded surfaces, International Journal of Math .,24,4 (2000).  

22. The Uniqueness of the Fundamental Theorem of Arithmetic , PRIMUS  11,3       (2001).

23. Investigating Possible Boundaries Between Convergence and Divergence  with F. Hartmann, College Mathematics Journal, 33 , 5 (2002).

24. Periodic Point of the Tent Function, College Mathematics Journal, 35, 2 (2004).

25. Taking the Tricks Out of Mathematics, PRIMUS 14,1 (2004).

26. Using Linear Algebra to do an Integration by Parts Example, PRIMUS 15, 4 (2005)

27. The Dynamics of Odd Sawtooth Functions, International Journal of Math Ed. in Science & Technology, 38, 5 (2007).

28. A Tricky Linear Algebra Example, College Mathematics Journal, 39, 1 (2008).

29. Trig Integrals Without Trig Identities, PRIMUS 18, 2 (2008).

30. Constructing Easily Iterated Functions with Interesting Properties, International Journal of Math Ed. Science & Technology         40,3 (2009)

31.   Antiderivatives as Inverse Linear Transformations, Mathematics & Computer Education (in press).

32.   Using the Chain Rule as the Key Link in Deriving Rules for Differentiation, PRIMUS ( to appear).

OTHER JOURNAL ITEMS

The following items were used as filler material.

1. Subset ( a mathematical rebus), American Mathematical Monthly ,92, 6 (1985).

2. What's Hot and What's Not (a poem comparing catastrophe theory to fractals), Mathematical Intellegencer, 12, 1 (1990).

3. More Mathematical Double Entendres, American Mathematical Monthly,104, 7 (1997).

4. Russell's Pair of Ducks (a mathematical cartoon), American Mathematical Monthly, 106, 6 (1998).

5. Another proof that Pi is irrational (a math cartoon), American Mathematical Monthly, 105,9(1998).

6. A Reality Check for Mathematicians, American Mathematical Monthly, 107,5 (2000).