Ruhlman Conference

Every spring, Wellesley has an annual campus-wide conference to celebrate Wellesley students' achievements. Wellesley's Mathematics students have given talks and presented posters on independent studies and on independent research.

In some years, mathematics classes have put together Ruhlman exhibits: hands-on demonstrations to illustrate the beauty and the challenges of a wide range of mathematical topics, from Graph Theory to Knot Theory to the fourth dimension. In fact, these exhibits have proved to be popular Ruhlman attractions, not just an outlet for math students' creativity.

Here are some more detailed descriptions of past math projects presented at the 2011 and 2012 Ruhlman Conferences:

• Melinda Lanius ('12) presented Universal Cycles for k-subsets of an n-set. Universal cycles address questions in the field of discrete mathematics. They are one of the oldest mathematical objects, arising in diverse contexts: the creation of Sanskrit memory wheels, digital fault testing, pseudo-random number generation, modern public-key cryptography, and even mind-reading illusions. The idea of a universal cycle is to create a compact list of information within a string of characters. Existence results for universal cycles maximize efficiency, particularly in the expanding areas of encryption and data storage. Melinda explored creating universal cycles of size-k subsets of the integers {1, 2, . . . , n}. (Research supported by a Schiff Fellowship)

• Gissell Castellon ('14) presented The Squeky Wheel. Through the use of discourse analysis, she researched her own teaching practices and pedagogical interactions with students from a SAT prep program. The program expands college access to low-income high school students by providing free SAT preparation and college admissions counseling. Through the analysis of quantitative and qualitative data of teacher and student interactions during a math tutoring session, she became acutely aware of the inequitable opportunities students faced as a result of differences of participation that impacted their ability to expand and deepen their mathematical knowledge and skills.
   
• Amanda Curtis and Jane Rieck ('11) presented Creativity in Math: Visualizing Different Forms of Arithmetic. In elementary school arithmetic, you are taught that every math problem has only one answer. Two times six is always twelve. The truth is that this familiar arithmetic is just one of many possibilities. There are other equally valid ways to do arithmetic in which two times six might equal, for instance, zero. Moreover, these “nonstandard arithmetics” have real applications, and are also important objects of study for mathematicians. Studying such a system often involves symbol manipulation, which, while suitable for rigorous proof, can sometimes cloud our intuition about the overall structure of the system. In their research, Amanda and Jane investigated ways of representing these structures visually in order to complement the symbolic approach. In their presentation, they introduced these nonstandard arithmetic  systems and, with the help of the audience, explored several examples.