## Scholarships

$40,000 Scholarships are available in mathematics and statistics with CPaMS Scholars

Professor of Mathematics, Emerita

410-617-2328

ayoung@loyola.edu

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 (MSU) 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.

At one time or another I have 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.

One of my most rewarding educational experiences was designing and teaching Ciphers and Codes, MA106, a core course on mathematical encryption. Requiring only high school mathematics, each new mathematical topic is motivated by a cipher, which is a scheme for encrypting messages. The course begins with the Caesar cipher, which is a very simple encryption scheme, and ends with the RSA cipher, which is used today to provide security for the Internet and electronic transactions. I wrote the text for the course: Mathematical Ciphers: From Caesar to RSA. It was published by the American Mathematical Society (AMS) in Fall 2006.

My research is in the area of iterative number theoretic functions. I was first introduced to this area of number theory by Dr. Gordon Prichett when we were both faculty members at Hamilton College. Gordon and I worked together on generalizations of the Kaprekar routine. That led me to the study of other number theoretic functions, including 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.

From 2000-08, I was Associate Vice President for Academic Affairs. In this role I oversaw all budgets (personnel, operating, and capital) for the academic division, provided support for department chairs and deans, served as liaison to the University's governance bodies, and prepared the annual report on the strategic plan. The most interesting, and often most challenging part of the position, was the last line of my job description: "and other duties as assigned by the Vice President for Academic Affairs"! I worked on many special projects, including the School of Education Business Plan and the 2005 Periodic Review Report (PRR) for the Middle States Commission on Higher Education (MSCHE).

I was Project Manager for the University's strategic planning process from 2006-2008. Reporting to Fr. Linnane, Loyola's president, this was one of my most rewarding administrative assignments. The resulting Strategic Plan, *Grounded in Tradition, Educating for the Future*, has as its overarching goal that Loyola will be the leading Catholic comprehensive university in the nation. To archive that goal, the Plan lays out several spotlight initiatives, including the establishment of Living Learning Communities for all first-year students and the expansion of services that enable recruitment, retention, and development of graduate students.

Following the adoption of the Strategic Plan by the Board of Trustees in October 2008, I stayed in the President's Office as Special Assistant to the President for Planning. In addition to assisting with the implementation of the Strategic Plan, I also oversaw Loyola's MSCHE decennial reaccreditation process.

Part of what makes Loyola special is its mission to "inspire students to learn, lead, and serve in a diverse and changing world." As noted in the preamble of the University's Strategic Plan, "the Jesuit philosophy strives to educate men and women of competence, imbued with the desire to seek the greater glory of God in all things." Jesuit ideals, which are elucidated in Loyola's Core Values, include an emphasis on academic excellence and a focus on the whole person. Following the Jesuit tradition, the liberal arts play a prominent role in undergraduate education at Loyola.

Of course, educational philosophies would be just words on paper without faculty members to implement them, students to be engaged by them, and administrators and staff to support them. And so, what really makes Loyola special for me is the campus community. Because classes are small, I got to know my students. As an administrator, I had the opportunity to work with many dedicated and talented people from across the entire university. As an Emerita Professor I continue to maintain my connections with Loyola.

I am looking forward to having more time to travel with my husband David, especially during "nice" times of the year such as September and April. I want to identify a volunteer project or two. My motto is "have spreadsheet, will travel"! But I don't want to overextend myself, especially at first. I want to make sure I have time to workout with David at the JCC, to read (during the day!), and to try out many of the recipes that I have been collecting over the last few years. And, I am sure that David and I will continue to take advantage of Baltimore's many special attractions, including excellent restaurants, Center Stage, the Baltimore Symphony Orchestra, and Orioles baseball.

I am also looking forward to increasing my Jewish education. David and I are active members of Chizuk Amuno Congregation, a large conservative synagogue. I am the Immediate Past President of the Congregation. As a synagogue community, Chizuk Amuno is guided by the rabbinic teaching, "The world is sustained by three things: Torah, Avodah (worship), and Gemilut Hasadim (acts of lovingkindness)." The Congregation fulfills this vision of synagogue life through lifelong learning, in celebration and worship, and by community service and programs. I am eager to return to my studies at the Congregation's Stulman Center for Adult Learning.

$40,000 Scholarships are available in mathematics and statistics with CPaMS Scholars