Dr. Anne L. Young

  Associate Vice President for Academic Affairs
  Professor of  Mathematical Sciences
  Office: JH 120
  Phone: 410-617-2400
  e-mail: ayoung@loyola.edu

What's your educational background?
My undergraduate degree is from Wheaton College, a small liberal arts institution in Illinois. I went to college planning to major in mathematics and wavered in that decision only once, while taking Calculus III. I couldn't picture any of the 3-dimensional figures then and I still can't today! I stayed with mathematics when I discovered the beauty of pure mathematics, particularly abstract algebra and number theory.

After Wheaton I went to graduate school at Michigan State University where I earned an MS and a Ph.D. I concentrated in commutative ring theory, an area of abstract algebra. My dissertation was entitled "Higher Derivatives of a Plane Algebraic Curve over a Field of Prime Characteristic." 

It was at MSU that I discovered my love for teaching. Like most graduate students in mathematics, I was a Teaching Assistant. In my first year I conducted problem sessions for large lecture courses; after that I taught my own sections. Much to my great surprise I found that I really enjoyed teaching.

What courses do you teach?
At one time or another I've taught almost every course in the undergraduate curriculum. As a pure mathematician two of my favorite upper level courses are Number Theory and Algebraic Structures. I also enjoy conducting the Honors Seminar, which gives students the opportunity to work individually and in small groups pursuing topics of interest.

Now that I'm an administrator, teaching only one course a year, I usually teach Ciphers and Codes, MA106, my core course on mathematical encryption. I designed and wrote the text for this course. It's a liberal arts course that's taken primarily by humanities majors to satisfy Loyola's core mathematics requirement. Since the course requires only high school mathematics, it begins slowly. Each new mathematical topic is motivated by a cipher. A cipher is a scheme for encrypting messages. While a few years ago, only governments and some big businesses needed encryption, we all need it now because of the use of e-mail and the Internet. The text for this course, Mathematical Ciphers: From Caesar to RSA will be published by the American Mathematical Society (AMS) in Fall 2006.

What are your research interests?
My research is in the area of iterative number theoretic functions. I was first introduced to this area of number theory by Gordon Prichett when we were both faculty members at Hamilton College. Gordon and I worked together on generalizations of the Kaprekar routine. In the last few years I have written several papers on Ducci sequences. For more information, see the list of my publications.

Here is a brief description of the kind of questions that interest me. Suppose f is a function whose domain and range are the finite set S. Now we can compose f with itself; denote the resulting function (f o f ) by f2. Similarly, if we compose f with itself n times, we get fn. Now let s be an element in S. Then applying the iterations of f to s gives us a sequence of elements from S:

f(s), f2(s), f3(s), ... , fn(s) ...

Since the set S is finite, eventually this sequence must repeat, resulting in a cycle. Among the interesting questions are:

• What elements of S are in a cycle?
• How many elements are in a cycle?
• How many different cycles are there?
• For a given s , how many steps does it take until we reach a cycle?

I am a member of the AMS and MAA. I occasionally referee articles for various journals, most frequently the Fibonacci Quarterly. In addition, I am on the editorial board of the Fibonacci Quarterly.

What's special about being at Loyola?
Part of what makes Loyola special is its educational philosophies: the Jesuit idea of "cura personalis" or "care for the whole person" and the Sisters of Mercy tradition of "men and women for others." Following the Jesuit tradition, the liberal arts play a prominent role at Loyola. I am proud to teach mathematics at an institution where students take nineteen core courses including two courses in philosophy, two courses in theology, and one course in ethics.

Of course, educational philosophies would be just words on paper without faculty to implement them, students to be engaged by them, and administrators to support them. And so, what really makes Loyola special for me are the people. Because classes are small, I get to know my students. Within the department there are many opportunities for majors and the faculty to interact informally. And now with the widespread use of e-mail, it's easier than ever for former students to keep in touch.

What do you do when you're not at Loyola?
I spend evenings and weekends with my husband David. We enjoy taking advantage of Baltimore's many special attractions, including excellent restaurants, Center Stage, the Baltimore Symphony Orchestra, and Orioles baseball.

David and I are active members of Chizuk Amuno Congregation, a large conservative synagogue. I am First-Vice President of the Congregation.

I am a past chair of the Krieger Schechter Day School (KSDS) Board of Directors. KSDS is a conservative Jewish day school which offers an outstanding education for grades K through 8. Open to the entire Baltimore community, KSDS is affiliated with Chizuk Amuno.

In my "free" time, I read best seller fiction. I enjoy cooking, especially Chinese.