## Judy Holdener

Professor of Mathematics (On Sabbatical 2012-2013)

Judy Holdener joined Kenyon's Mathematics Department in 1997, after spending three years at the U.S. Air Force Academy in Colorado Springs, CO. Although her primary research interests are in the areas of algebra and number theory, she has been known to work in other areas when an interesting question arises... especially if the question is accessible to undergraduates. Judy has collaborated with students on research projects relating to algebra, number theory, dynamical systems, and mathematical biology; their work has culminated in research publications and presentations at national math conferences. In 2008, Judy was awarded the Mathematical Association of America Ohio Section Distinguished Teaching Award and in 2003, she was awarded Kenyon's Tomsich Science Award as well as the Board of Trustees Junior Teaching Award.

### Education

Ph.D. University of Illinois
M.S. University of Illinois
B.S. Kent State University

### Selected Publications

"Generalized Thue-Morse sequences and the von Koch Curve," to appear in the International Journal of Pure and Applied Mathematics (co-authored with Kenyon students Lee Kennard '07 and Matthew Zaremsky '07)

"Abundancy 'outlaws' of the form $(\sigma(N)+t)N$," The Journal of Integer Sequences, 10 (2007), Article 07.9.6 (co-authored with Kenyon student William Stanton '07)

"A Cryptographic Scavenger Hunt," Cryptologia, 31 (2007) 316-323 (co-authored with Eric Holdener)

"Conditions Equivalent to the Existence of Odd Perfect Numbers," Mathematics Magazine, 79(5) (2006) 389-391

"Product-free Sets in the Card Game Set," PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies .15(4) (2005) 289-297

"Visualizing Patterns in the Integers relating to the Abundancy Index," Proceedings of the `Art and Math = X' Conference, University of Colorado, Boulder, CO. (2005)

"When Thue-Morse meets Koch," Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society,13 (2005) 191-206 (co-authored with Kenyon student Jun Ma, Class of 2005)

"Art and Design in Mathematics," The Journal of Online Mathematics and its Applications,4 (2004)

"Parametric Plots: A Creative Outlet," The Journal of Online Mathematics and its Applications,4 (2004) (co-authored with Keith Howard of Mercer University)

"A Classification of Periodic Turtle Sequences," The International Journal of Mathematics and Mathematical Sciences,34 ( 2003) 2193-2201 (co-authored with Kenyon student Amy Wagaman, Class of 2003)

"A Theorem of Touchard and the Form of Odd Perfect Numbers," The American Mathematical Monthly,109 (2002) 661-663

### Courses Taught

MATH 108: Models of Life
MATH 111: Calculus A (Differential Calculus)
MATH 112: Calculus B (Integral Calculus)
MATH 213: Calculus C (Multivariable Calculus)
MATH 232: Vector Analysis
MATH 222: Foundations
MATH 327: Number Theory Seminar
MATH 335: Abstract Algebra I (Group Theory)
MATH 352: Complex Functions
MATH 435: Abstract Algebra II (Ring and Field Theory)