Undergraduate Research Projects
If you are an undergraduate curious about applied math research, there are many opportunities to participate. Many professors in the Applied Math department would love to talk to you about potential projects – just send them an email! If you’d like to receive funding for a particular project, Northwestern provides plenty of grants. Check out undergradresearch.northwestern.edu for details.
Past Research Projects:
Louisa Lee ’19 (Applied Mathematics)
Siyu Zhang ’18 (Mathematics & Electrical Engineering/Computer Science)
(2016 Undergraduate Research Assistant Program): Political Party Cluster Analysis Using the Gaussian Mixture Model
Graduate mentor: Vicky Chuqiao Yang
Additional advising by: Doug Downey (Electrical Engineering/Computer Sciences), Daniel Abrams (Applied Mathematics), Adilson Motter (Physics & Astronomy)
Louisa and Siyu’s research aimed to answer the question: is the US public’s political opinion two clustered, like the two US parties would suggest? To address this question, they applied the Gaussian Mixture model, an unsupervised machine learning technique, to the American National Election Studies survey data set, which records hundreds of thousands of individuals’ opinion over political issues for over 60 years. Louisa also used the Akaike Information Criteria to find the optimal number of clusters to represents the data. They found that the political party centers are close to the population cluster centers, when we restrict the population to be two-clustered. The Democrat Party is closer to its corresponding cluster center than the Republican Party. When they relaxed the two-cluster restriction, they find introducing additional clusters would represent the population better, even after penalizing for the additional parameters it introduces. This result suggests a multi-party political landscape can be more representative of the US public than the current two-party one.
Eileen Herbers ‘18 (Applied Mathematics)
Jack Chen ‘18 (Applied Mathematics)
(2016 Undergraduate Research Assistant Program): The Tipping Point: Mathematical Model Predicts Restaurants Will Soon Abandon Tipping En Masse
Graduate mentor: Sara Clifton
Additional advising by: Daniel Abrams (Applied Mathematics)
Eileen and Jack created and analyzed a mathematical model of tipping in American restaurants. The average tip rate for waiters at full-service restaurants has been increasing in America since the convention began the early 1900’s. As the conventional tip rate rises, restaurants have a harder time retaining talented cooks because tipped wait staff make a significantly higher wage. The proposed mathematical model ties restaurant profitability to the conventional tip rate, customer preferences, and minimum wages. The model predicts that as average tip increases over time, there exists a critical threshold at which it will be advantageous for all restaurant owners to eliminate tipping. The model suggests that the threshold when restaurants disallow tipping is strongly dependent on the relative importance customers place on food quality versus service quality. Using statistics compiled by hospitality scholars, it is predicted that American restaurants will abandon tipping when the conventional tip rate exceeds approximately 27%. Jack and Eileen wrote a paper to communicate these results, which they have submitted to the Northwestern Undergraduate Research Journal.
Graduate School Panels
In Fall 2015 and 2016 we spoke with undergraduate students in mathematics at Northeastern Illinois University, about life in graduate school and tips on applying for graduate schools.