## Rose-Hulman Hosts 18th Annual Undergraduate Mathematics Research Conference

**June 10, 2001**

Invited speakers at this year's Rose-Hulman Undergraduate Mathematics Conference (left to right): Back row---students Ben Harwood, William Cuckler, David Blair, Stephen Young, John Slewitzke, and Brad Berron. Middle row---students Jessamy Ofcarcik, Robin DeGracia, Gabe Shaughnessy, and Daniar Hussain, and faculty members Suzanne Lenhart (University of Tennessee, Knoxville, and Oak Ridge National Laboratory) and Linda Petzold (University of California, Santa Barbara). Front row---students Randy Tanner and Sylvain Hallé. Not pictured are student speakers Robert Clark, Hanna Wagner, and David Aukerman.

**David Finn and Tanya Leise**

The 18th Annual Rose-Hulman Institute of Technology Undergraduate Mathematics Conference was held March 16 and 17, 2001. Traditionally, the conference showcases research done by undergraduates, giving students the opportunity both to present their work and to network with other young mathematicians. The only non-undergraduate speakers at the conference each year are two invited faculty speakers, chosen for the broad appeal of their research and their ability to communicate mathematical research at a level accessible to strong undergraduate math majors. We also hope that the invited speakers, as successful mathematicians, will act as role models and mentors to this up-and-coming generation of mathematicians.

The invited faculty speakers at this year's conference were Suzanne Lenhart of the University of Tennessee, Knoxville, and Oak Ridge National Laboratory and Linda Petzold of the University of California, Santa Barbara. Both are highly successful applied mathematicians and wonderful role models; Lenhart is the current president of the Association for Women in Mathematics, and Petzold is SIAM's vice-president-at-large.

Each of the invited speakers addressed various aspects of optimal control, with both small- and large-scale applications. In a talk titled "Parking Your Car with Lie Brackets," Lenhart discussed the idea of controllability and the use of Lie brackets in conditions that guarantee the controllability of certain ordinary differential equations. Parallel parking, for example, is possible (for the coordinated among us) because of the non-commutativity of the operations involved (e.g., backing, turning, pulling forward).

In another talk, Lenhart discussed real-world applications of her research, such as determining the optimal dosage of a "drug cocktail" for treating HIV infection, using a system of ordinary differential equations, and finding the best soil-venting strategy to promote optimal degradation of a pollutant via bacterial action, using a parabolic partial differential equation coupled with an ODE.

Petzold outlined current work in computational science and engineering, an area that lies at the intersection of applied mathematics, computer science, and engineering, and was recently the focus of a very successful SIAM conference. She discussed the development of software for very large optimization problems, such as finding the optimal path for the insertion of a solar wind sampling probe into a desired orbit (under strict budget restrictions from NASA). In her talk, Petzold emphasized the overall effort of building a problem-solving environment for the dynamic optimization of physical, chemical, and biological processes.

The remaining speakers---all undergraduates---described their own mathematical research on a diverse array of problems, in both pure and applied areas. A few of the applied talks from this year's conference are briefly considered here.

In "Improving Solar Car Strategy," Brad Berron, a chemical engineering major at Rose-Hulman, demonstrated how mathematical modeling has contributed to the success of the Phantom solar car. Using data from previous Phantom solar cars and the efficiency curve for the current engine, he analyzed the energy cost of running the car at various speeds up different hill grades. His conclusions: For moderately steep hills, the speed should be held at about 30 mph---going either slower or faster resulted in greater energy costs; on flat ground, by contrast, lower speeds usually led to lower energy costs.

Public-key cryptography was a popular research topic among the undergraduates who spoke this year. Ben Harwood of Northern Kentucky University discussed the application of elliptic curves to public-key cryptography, with the goal of developing a harder-to-break coding system. An alternative method for attacking an RSA public-key cryptosystem, discussed by Stephen Young of Rose-Hulman, avoids the difficulty of factoring the modulus of the RSA public key. David Aukerman of Taylor University explored the number theory-based process that allows RSA cryptography to work, as well as the properties of the patterns that emerge.

The following are a few other examples of the applied undergraduate research presented: Robert Clark and Hanna Wagner, physics majors from Ohio Northern University, explained how they had used Maple to develop numerical solutions to a complicated mechanics problem; John Slewitzke of the College of Mount St. Joseph discussed randomized tournament seeding as a way to avoid favoritism; and Sylvain Hallé of l'Université Laval discussed the use of Boolean similarity measures to search for computer programs close to some desired specifications.

Additional details and a full list of the speakers, along with their abstracts, can be found at the conference Web site http://www.rose-hulman.edu/class/ma/web/mathconf/

For readers who like to plan ahead, the 19th Annual Rose-Hulman Undergraduate Mathematics Conference will be held March 29 and 30, 2002.

*David Finn and Tanya Leise are assistant professors of mathematics at Rose-Hulman Institute of Technology.*