ARTS 191
Judy Holdener joined the Department of Mathematics 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. More recently Judy has tapped into a life-long interest in art, creating digital artwork that reflects the nature and beauty of mathematics. She has given national and international…
Read MoreJudy Holdener joined the Department of Mathematics 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. More recently Judy has tapped into a life-long interest in art, creating digital artwork that reflects the nature and beauty of mathematics. She has given national and international presentations about this work.
1994 — Doctor of Philosophy from Univ Illinois Urbana
1989 — Master of Science from Univ Illinois Urbana
1987 — Bachelor of Science from Kent State Univ Kent, Phi Beta Kappa
The first-year seminar in mathematics provides an introduction to the rich and diverse nature of mathematics. Topics covered will vary from one semester to the next (depending on faculty expertise) but will typically span algebra and number theory, dynamical systems, probability and statistics, discrete mathematics, topology, geometry, logic, analysis and applied math. The course includes guest lectures from professors at Kenyon, a panel discussion with upper-class math majors and opportunities to learn about summer experiences and careers in mathematics. The course goals are threefold: 1) to provide an overview of modern mathematics, which, while not exhaustive, will expose students to some exciting open questions and research problems in mathematics; 2) to introduce students to some of the mathematical research being done at Kenyon and; 3) to answer whatever questions students might have during their first semester here, while exposing them to useful resources and opportunities that are helpful in launching a meaningful college experience. Open only to first-year students. Prerequisite or corequisite: MATH 112 (or equivalent) and concurrently enrolled in another MATH, STAT or SCMP course or permission of instructor. Offered every fall semester.
The third in a three-semester calculus sequence, this course examines differentiation and integration in three dimensions. Topics of study include functions of more than one variable, vectors and vector algebra, partial derivatives, optimization and multiple integrals. Some of the following topics from vector calculus also will be covered as time permits: vector fields, line integrals, flux integrals, curl and divergence. Prerequisite: MATH 112 or a score of 4 or 5 on the BC Calculus AP exam or permission of instructor. Offered every semester.
This course introduces students to mathematical reasoning and rigor in the context of set-theoretic questions. The course will cover basic logic and set theory, relations — including orderings, functions and equivalence relations — and the fundamental aspects of cardinality. The course will emphasize helping students read, write and understand mathematical reasoning. Students will be actively engaged in creative work in mathematics. Students interested in majoring in mathematics should take this course no later than the spring semester of their sophomore year. Advanced first-year students interested in mathematics are encouraged to consider taking this course in their first year. Students wanting to do so should contact a member of the mathematics faculty. Prerequisite: MATH 213 or permission of instructor. Offered every spring semester.
Patterns within the set of natural numbers have enticed mathematicians for well over two millennia, making number theory one of the oldest branches of mathematics. Rich with problems that are easy to state but fiendishly difficult to solve, the subject continues to fascinate professionals and amateurs alike. In this course, we will get a glimpse at both the old and the new. In the first two-thirds of the semester, we will study topics from classical number theory, focusing primarily on divisibility, congruences, arithmetic functions, sums of squares and the distribution of primes. In the final weeks we will explore some of the current questions and applications of number theory. We will study the famous RSA cryptosystem, and students will read and present some current (carefully chosen) research papers. Prerequisite: MATH 222. Offered every other year.
Individual study is a privilege reserved for students who want to pursue a course of reading or complete a research project on a topic not regularly offered in the curriculum. It is intended to supplement, not take the place of, coursework. Individual study cannot be used to fulfill requirements for the major. Individual studies will earn 0.25–0.50 units of credit. To qualify, a student must identify a member of the mathematics department willing to direct the project. The professor, in consultation with the student, will create a tentative syllabus (including a list of readings and/or problems, goals and tasks) and describe in some detail the methods of assessment (e.g., problem sets to be submitted for evaluation biweekly; a 20-page research paper submitted at the course's end, with rough drafts due at given intervals, and so on). The department expects the student to meet regularly with his or her instructor for at least one hour per week. All standard enrollment/registration deadlines for regular college courses apply. Because students must enroll for individual studies by the end of the seventh class day of each semester, they should begin discussion of the proposed individual study preferably the semester before, so that there is time to devise the proposal and seek departmental approval before the registrar's deadline. Permission of instructor and department chair required. No prerequisite.\n\n
This course will consist largely of an independent project in which students read several sources to learn about a mathematical topic that complements material studied in other courses, usually an already completed depth sequence. This study will culminate in an expository paper and a public or semi-public presentation before an audience consisting of at least several members of the mathematics faculty as well as an outside examiner. Permission of department chair required. Prerequisite: Senior standing and at least one "depth sequence" completed.
"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