Mathematician Theresa Anderson Receives NSF CAREER Award

Carnegie Mellon University mathematician Theresa Anderson has received a Faculty Early Career Award (CAREER) from the National Science Foundation. One of the most prestigious awards for young faculty, CAREER awards recognize and support those who exemplify the role of teacher-scholars through their outstanding research and teaching.

Anderson, an assistant professor of mathematical sciences, received the five-year grant to build bridges between number theory and harmonic analysis, two areas of mathematics often viewed as separate. Number theory, which deals with properties of whole numbers, such as quickly factoring large numbers into primes, underpins computer security and analysis of the behavior of black holes. Harmonic analysis, which takes a complicated function and breaks it up into simple pieces, is central to medical imaging and quantum states. Anderson's goal is to create new connections between these seemingly disconnected areas.

"In my work, I tend to connect areas of mathematics, pulling techniques from a variety of fields to go out of my comfort zone and explore new things," Anderson said.

Under the grant, Anderson will explore areas broadly in analysis or number theory. First, she is working to develop the infrastructure to travel between number theory and analysis in order to analyze discrete sets that encode curved surfaces. She also plans to explore hidden number theoretic properties in the building blocks of harmonic analysis. And, as a third bridge across the two fields, Anderson will be integrating Fourier analysis to better predict the behavior of a random object of algebraic interest.

The award will also support Anderson's teaching and mentoring. She is creating a class on a topic involving analysis and number theory, where she will develop the needed number theory along the way. According to Anderson, this approach makes it accessible to more students and motivates by example, not by drowning them in technical machinery. The grant also will enable Anderson to continue to involve undergraduates in research, including during the semester and at Carnegie Mellon's Summer Undergraduate Applied Mathematics Institute (SUAMI), an eight-week summer research program for undergraduate students.

"My goal is to teach a hands-on, example-motivated, non-traditional approach to be able to do real, significant research in a short period of time," Anderson said. "The approach of introducing new perspectives, bridging non-traditional areas and approaching problems from different angles permeates the whole NSF proposal." 

Anderson is also collaborating with Carnegie Mellon's Diversity, Equity and Inclusion office to develop the graduate class, "Widening the margins: the experience of underrepresented minorities in the mathematical sciences." Anderson plans to invite several national experts to class to enhance the articles and books they will read with meaningful dialogue. She also hopes to bring in drama students to help the class engage in ways to improve public perception of mathematics, such as by improving the sometimes impromptu "elevator speeches" of their research that they may give to a lay audience.

"These 'elevator speeches' have so much impact on how others view scientists," Anderson said. "Hopefully this multidisciplinary, hands-on activity can help make this sometimes-stressful task fun."