Student Projects

 

I’m happy to say that many of my research projects and activities over the years have involved students, both undergraduates from here at W&L and also high-school students from around the world (by way of the Pioneer Academics). If you’re interested in doing the same, this page will give you an idea of the kind of work we do. Not every project leads to publication, but it’s always nice when that does happen.

  • My student Yike Li (Beijing City International School) came up with a delightful formula connecting cosines, Fibonaccis, and binomial coefficients, and that led to an article currently under review at the Journal of Integer Sequences. (pdf).
  • My student Yunqi Liu (Nanjing Foreign Language School) and I just submitted a very nice problem on a variation of Zeckendorf’s Theorem to the College Math Journal. (pdf).
  • In 2022, Michael Tulskikh (Columbia U.) and I finished up a nice article on convolutions of linear recurrence sequences. It’s now in print at the Journal of Integer Sequences volume 25, article 22.3.3. (pdf).
  • In that same volume of the Journal of Integer Sequences is this article on tiling graph compositions by my former student Liam Buttitta, from work we did together over the summer of 2021.
  • High-school student Yichen Wang (now at UCLA) and I just finished an article on convolutions of Fibonacci-type and Lucas-type sequences, and it’s just been accepted by Mathematics Magazine. (pdf).
  • Cheney and I also wrote a nice article on k-bonacci and k-Lucas numbers. It’s now published as article #A56 in the journal INTEGERS (2021, volume 21). (pdf).
  • High-school student Yu Xiao (now at Oxford) and I wrote up a nice paper on Fibonacci and Lucas identities via rainbow tilings. It’s now in print in the Fibonacci Quarterly (May 2022, volume 60, number 2, pages 126-135). (pdf).
  • A few summers ago (2020) I worked with W&L students Kathleen McNeil and Jackson Gazin on matrices and continued fractions. Along the way, we produced this problem (#2120) on the normalizer of a subgroup, which was published in the April, 2021 issue of Mathematics Magazine.
  • High-school student Myanna Nash and I produced a nice problem about gentle diagonals in Pascal’s Triangle. It was published in the March, 2022 issue of Crux Mathematicorum as problem #4721 (English version, French version).
  • In the spring of 2020, my work with high-school student Oluwatobi Alabi (now at Grinnell) led to a nice article on fault-free tilings (pdf).  This article is now in print at the Journal of Integer Sequences, volume 24 (it’s the second article from the top of that link).
  • Oluwatobi and I also worked on another nice problem on tiling squares with long rectangles, which has now appeared in print as problem #1216 in the College Math Journal (January 2022).
  • In 2019, I worked with high-school student Ziqian Alexa Jin (now at U. Chicago) on a nice article on Tetranacci numbers and hexagonal tilings. It’s finally (!!) appeared in print in the Fibonacci Quarterly (May 2022, volume 60, number 2, pages 99-103). (pdf).
  • Also from 2019, high-school student ZhenShu Luan (now at Cornell) and I worked on continued fractions, which led to this problem (#1186) in the College Math Journal (November 2020, solution published November 2021).
  • Another student from 2019, Michael Tulskikh (now at Columbia), worked with me on a really fun article on tiling 2 x n boards with dominos and L-shaped trominos. This article is now in print in the Journal of Integer Sequences (2021, volume 24, issue 4) (pdf).
  • 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 polynomial roots with common tails (here it is, revised in 2019 and published in 2020 in the MAA Monthly vol. 127, number 4). 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. Unless stated otherwise, these are all international high-school students who worked with me through Pioneer Academics.
  • 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 about decimal roots appear in print in Mathematics Magazine (December 2017) and this article about Ramanujan cubics also appear in Mathematics Magazine (December 2019, volume 92, number 5), and this article about 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 4.
  • 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 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.
  • 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.

      • Jiahao Zhang (W&L ’20) is a math PhD student at the University of Washington.
      • 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 Environmental Politics and a Distinguished Scholar at the University of Arizona.

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. Recent graduate Hung Viet Chu (’20) is a graduate student at UIUC and has already published more than 20 articles, including some based on my old papers!