## Girls’ Angle Bulletin, Volume 16, Number 4

This issue’s interviewee is Katharine Ott, who is an Associate Professor of Mathematics at Bates College. In this interview, which was conducted by Ken Fan and Raegan Phillips, Katharine discusses a wide range of topics, including her role as the Director of GirlsGetMath@ICERM as well as her writing/journalism career. The interview contains lots of wonderful advice for students interested in mathematics.

Our cover shows all 196 domino tilings of a 5-by-5 square with its central square removed. This spring, two of our members found a formula for the number of tilings of a family of annuli. Unfortunately, they didn’t know until after they got their results that these results were published by Tauraso in 2004. This material is related to a lesser known algebraic identity called “Candido’s identity”:

$(x^2 + y^2+(x+y)^2)^2 = 2(x^4+y^4+(x+y)^4).$

For details, see Member’s Thoughts.

Robert Donley brings together several ideas from recent installments of his series on counting and partially ordered sets, this time delivering a beautiful bijection between compositions of positive integers into parts of size 1 or 2, into parts of odd size, and into parts of size greater than 1. There’s a lot of math to savor in this topic!

Anna Ma continues her discussion of natural language processing, illustrating language models with a toy example. If you know how to program, it would be easy to scale up the model described in her article.

After resolving the mystery of the rational number romping sequence that they learned through social media, Emily and Jasmine returned to an idea they had in Part 2 of Romping Through the Rationals, finding integer sequences $a_k$ such that $a_k$ is relatively prime to $a_{k+1}$ and every nonnegative rational number is equal to $a_k/a_{k+1}$ for a unique index $k$.

We close with some Notes from the Club where you can read about former Girls’ Angle mentor, now graduate student at the University of Chicago, Karia Dibert’s Support Network presentation after returning from her first trip to the South Pole to prepare for the installation of a cosmic background radiation detector of her own design!

Special thanks to Margaret Lewis for permission to share her wonderful picture of MK the eagle (see page 29).

We hope you enjoy it!

Finally, a reminder: when you subscribe to the Girls’ Angle Bulletin, you’re not just getting a subscription to a magazine. You are also gaining access to the Girls’ Angle mentors.  We urge all subscribers and members to write us with your math questions or anything else in the Bulletin or having to do with mathematics in general. We will respond. We want you to get active and do mathematics. Parts of the Bulletin are written to induce you to wonder and respond with more questions. Don’t let those questions fade away and become forgotten. Send them to us!

Also, the Girls’ Angle Bulletin is a venue for students who wish to showcase their mathematical achievements that go above and beyond the curriculum. If you’re a student and have discovered something nifty in math, considering submitting it to the Bulletin.

We continue to encourage people to subscribe to our print version, so we have removed some content from the electronic version.  Subscriptions are a great way to support Girls’ Angle while getting something concrete back in return.  We hope you subscribe!