I’ve worked on research projects with a number of students over the years. If you’re interested in doing the same, this page will give you an idea of the kind of work we do.
- This summer (2020) I’ll be working with W&L students Kathleen McNeil and Jackson Gazin on continued fractions.
- For the summer of 2018, I worked with W&L students Saimon Islam (we also worked together in 2016) and Eric Zhang (likewise, in 2017) on a nice article about polynomials with common tails (here it is, revised in 2019 and recently accepted by the MAA Monthly). We also had this problem (on the Galois group of a degree-six polynomial) appear in print in Mathematics Magazine (December 2018).
- Over the years, I’ve helped many students add or edit entries in the Online Encyclopedia of Integer Sequences. W&L students Saimon Islam, Aaron Schmitt, and Yue Pan are credited in A272069. High-school student Shaoxiong Yuan (from China) contributed to many entries (see for example A049669), as did high-school students Eldin Sijaric (from Wales; A326369 and others), Michael Tulskikh (New Mexico; A052980, etc), Shuer Jiang (Maryland; A003269), Shahreer Al Hossain (New York; A000129), Ruijia Liu (China; A001644), ZhenShu Luan (Canada; A048879), Ziqian Jin (China; A000078), Advika Srivastava (India; A000078 and A001591), Rana Urek (Turkey; A030186), Miles Wu (China; A316726), Yu Xiao (China; A004146 and A005248), Kengbo Lu (China; A015518), Areebah Mahdia (Bangladesh; A179070), Qianyu Guo (China; A335559), and Oluwatobi Alabi (Kenya; A335560 and A335747) . My thanks to Pioneer Academics for creating these research opportunities with so many talented high-school students!
- Pioneer student Ziqian Jin was able to develop her 2019 work with me into an article on Tetranacci numbers, which was just accepted for publication in Fibonacci Quarterly!
- Pioneer student ZhenShu Luan and I had this problem (on continued fractions) accepted in the College Math Journal (to appear, November 2020).
- In 2017, I worked with W&L students Prakriti Panthi (rising sophomore), Anukriti Shrestha (rising junior), and Eric Zhang (rising sophomore) on a number of different topics. We had this problem (on decimal roots) appear in print in Mathematics Magazine (December 2017) and this article (on Ramanujan cubics) also appear in Mathematics Magazine (December 2019, volume 92, number 5), and this article (on finite subgroups of the modular group) was published by the Rocky Mountain Journal of Mathematics (2019, volume 49, number 4). Thanks to this collaboration, Prakriti, Anukriti, and Eric now have an Erdös number of 4.
- Oh, and the December 2019 cover of Mathematics Magazine was inspired by our article on Ramanujan cubics (which we did in 2017)! (Artwork by David Riemann).
- Oh, and Anukriti was featured in this article on the W&L home page!
- In 2016, I worked with W&L students Saimon Islam (rising sophomore), Aaron Schmitt (rising junior), and Yue Pan (rising sophomore) on a nice little problem concerning the sum of two squares. We collaborated with another professor/undergraduate team from Wake Forest and ended up with this 21-page article which has now been published in Involve (2019, volume 12, issue 4, page 585-605). Thanks to this paper, Saimon, Aaron, and Pan now have an Erdös number of 3.
- Back in 2015, exchange student Gabriella Iwasaki, rising W&L senior Luke Quigley, and I worked on a lovely project involving graphs associated with rings modulo 16. This picture here shows one of the problems we worked on, demonstrating that the digraph associated with multiplication by 6 modulo 16 will be of genus 2.
- In the summer of 2013, I worked with W&L student Wenda Tu (rising senior) on a nifty problem involving digraphs. This work continued with Wenda’s honor thesis in the academic year 2013-14, and that led to a joint paper which, after a few revisions, has appeared in print in the undergraduate math journal Involve (2018, volume 2, pages 181-194) . I also worked with Ginger (Qiuchi) Sun that same summer on her interesting ideas involving the Goldbach Conjecture with polynomials.
- Back in 2012, W&L students Ginny Huang (rising sophomore) and Cathy Wang (rising junior) worked with me on a very nice problem involving Fibonacci numbers.
- Kuan Si and I did a year-long independent study course on Fibonacci identities, during the academic year 2011-12.
- Elizabeth Twentyman wrote her honors thesis “Finding Factors of Factor Rings” with me over 2005-06; she graduated with honors in 2006.
- My colleague Wayne Dymacek and I worked with Elizabeth Townsend on her honors thesis on the inverse Galois problem; Liz graduated with honors in 2003.
- My first research student was Adam Henry; back in the summer of 1999, we did a nice project on Gaussian integers.
Where are they now? My research and honors students have done lots of different things after graduating W&L! But for those who went on a bit further in academia, here’s what they did.
- Anukriti Shrestha (W&L ’19) went to UVa for a PhD program in engineering.
- Yue Pan (W&L ’19) went to Univ. of Iowa for a PhD in statistics.
- Gabriela Iwasaki (transfer student 2014-15) returned to Brazil and changed her major to mathematics!
- Wenda Tu (W&L ’14) attended graduate school in statistics at the University of Iowa.
- I think that Qiuchi Sun (W&L ’13) went to grad school in economics.
- Kuan Si (W&L ’12) went to graduate school in math at Georgia Tech.
- Elizabeth Twentyman (W&L ’06) went on to math graduate school at the University of Michgan.
- Elizabeth Townsend (W&L ’03) went on to graduate school in math at the University of Chicago; after a post-doc at Michigan and some time at Williams, she is now a math professor at Haverford.
- Adam Henry (W&L ’00) got his PhD in Transportation Technology and Policy at UC Davis, and went on to posts at Harvard, Boston University, and the University of West Virginia. Adam is now a professor of government and public policy at Arizona State University.
Plenty of other W&L students have also gone on to graduate school and to careers as math professors. For example, Jonathan Graber (’08) is a math professor at Baylor University, and both Matt Morena (’05) and Neville Fogarty (’10) teach at Christopher Newport University.