*Did you do any research as an undergraduate?*

Continue reading at the AMS Graduate Student Blog.

*John Herrera is a junior math major at Williams. He is a New Yorker who loves watching soccer matches*.

Over Dead Week, Nina Pande and I attended the Nebraska Conference for Undergraduate Women in Mathematics at the University of Nebraska-Lincoln. We had a wonderful experience, and we are grateful to the Clare Boothe Luce Program and the Math Department for providing us with the opportunity to go. Over the course of the three-day conference, we heard talks given by invited speakers and fellow undergraduate women, presented on our own research, went to panels and discussions, and met amazing female mathematicians from across the country.

There were two plenary talks, one by Emina Soljanin of Rutgers University and another by Abigail Thompson of University of California-Davis. Soljanin gave a talk, “How Does Applied Math Become Applicable?” on her experiences working at Bell Labs and her research in coding theory and applied math. Thompson’s talk, “Understanding 3-Dimensional Spaces,” went through key concepts in knot theory and low-dimensional topology while weaving in her own her own experiences through college, graduate school, and beyond. Both speakers gave very engaging and informative presentations. Throughout the conference, there were five sessions of presentations by undergraduate students and two poster sessions. We gave a talk, “The Relationship Between a Ring and its Completion,” on our research this summer at SMALL. It was the largest audience we have presented to so far, which was very exciting.

The conference also offered many opportunities to network and talk with other students and mathematicians. Graduate students and professors facilitated small sessions on a variety of themes, including applying to graduate school and the confidence gap between men and women. It was great to have a space to discuss these issues and topics with women from many different backgrounds at varying points in their career. At a pizza dinner, we got the chance to talk with Sylvia Wiegand, professor emerita at UNL who has made significant contributions to the field of commutative algebra. She has led a fascinating life: her grandmother, Grace Chisholm Young, was the first woman in Germany to receive a PhD in any field, and she has run over 250 marathons across all 50 states. Talking with her was definitely a highlight of the conference.

Overall, NCUWM was a great conference, and I’m glad that I got the chance to participate. It offers invaluable experiences for undergraduate women in math to see examples of successful women in the field and to learn about math research, graduate school, and career paths in math. Many of the graduate students, professors, and other mathematicians there had actually attended the conference as undergrads, and they serve as testaments of its success in encouraging women to continue with math. I would strongly urge students to attend next year.

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Goldmakher tells Ai about the importance of creativity and ownership in mathematics.

*How did you get interested in mathematics? *

When I was in 7th grade, in Boston, I enrolled in an experimental program called The Math Circle, where students discover math on their own. We, the students, came up with all sorts of ideas about number theory, argued with each other, proposed conjectures, shot each other down, and eventually came up with all sorts of proofs. No one told us these things–we made them up. Turns out other people had discovered them earlier, but that wasn’t the point. The point was that we owned them–they were ours because we invented them! This experience showed me that math was creative and could be created by me. From then on, I was totally hooked.

*Do you take this kind of curiosity into your teaching at Williams College?*

For whole interview, see AMS Graduate Student Blog.

]]>Lee, a junior math major at Williams College, engages in problem solving activities.

*How did you get interested in mathematics?*

I took a lot of math courses growing up. There was a positive feedback loop in the classes that I have taken. Taking math courses that I enjoyed made me love math even more. I became more confident in my ability to do higher level mathematics.

*Can you tell me your math career prior to Williams?*

When I lived in San Diego, I took an algebra course during middle school. When I moved to Irvine, however, there were no advanced-level courses for me to take. So I traveled by bus to another school where such courses were offered. I moved once again to Korea and went to an international school. There I took an online course on statistics. I was always interested in taking what seemed to be challenging courses for middle school and high school students.

*What was the moment when you decided to major in math?*

I took a fair amount of math courses during my freshman and sophomore year, so it was natural to pick the major. I like the math department here at Williams. They are friendly and supportive and are the reason why I continued to take more math courses.

*What is the interaction between math students and professors?*

Students can go to the library and see that professors are in their offices waiting for them to come in. The offices are very close to the library so you can’t miss them on your way. There is a strong sense of community building among the students and faculty.

*What was your most difficult math class?*

Abstract Algebra. This class was difficult because some ideas were hard to understand. The class demanded a lot of work and I spent many hours understanding new concepts. Two class meetings were spent on a single chapter. I was used to having more time dealing with one chapter, so it was naturally harder. It didn’t seem like there were topics or classes I took that would build up to that class. This class introduced me to intense proof writing that I have not taken before.

*What was your favorite class?*

Multivariable Calculus was my favorite class. I could grasp the terms better because the class was building up on concepts that I remember. I was able to visualize the terms. The class allowed me to be artistic. I could draw multiple graphs in a plane and color code them.

*What do you do outside of math?*

I really enjoy rock climbing. It connects me to math because rock climbing deals with problem solving. At first, going up is not so challenging. You can pick any colored rock that you would use to go up. Given the multiple rocks above you at any given moment, it is not a difficult task to make it to the top. When you get enough practice, you can decide to rock climb using rocks of a single color. This is a more difficult, yet fun challenge. The problem solving in rock climbing is figuring out how to bend your body in a way to keep climbing forward. I always look forward to a new path to take. The possibilities are endless.

*Any advice for students?*

For potential math majors, I would say, like doing proofs. If you are not enjoying coming up with a proof, then you will not like math. For current math students, working with others is crucial. By collaborating with others, you are helping each other out. New ideas can come out and challenging math problems become easier to do. Just make sure to do the math by yourself afterwards. This is helpful when preparing for an exam. A final thing I would say is don’t be afraid to branch out from mathematics. There are many applications of math. Just go out there and try new things.

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Klingenberg (right) tells Nguyen about his recently published textbook, “Statistics: The Art and Science of Learning from Data.”

*When did you discover your passion for mathematics?*

I was really bad at math in middle school. In 11th grade, all of a sudden, I understood what the textbook said. The best moment was when my teacher got stuck when trying to find the volume of a body generated by revolving a graph about the x-axis. Meanwhile, I knew exactly how to do it. So I volunteered to solve the problem, to the surprise of my peers. From then on, I knew that I loved math and wanted to study it..

*What is your favorite mathematical theorem?*

I would say The Central Limit Theorem. It is really powerful in predicting the behavior of averages or “means.” Basically the theorem states that the arithmetic mean of a large number of independent variables will always be normally distributed, regardless of the distribution these variables came from.

*What are you currently researching?*

My research focuses on exact confidence intervals. This concept is applied when you have two success counts and try to look for a parameter called the difference in success proportions. For instance, let’s assume that you want to compare a drug to a placebo in a clinical trial. To say which treatment works better, you need to look at the success probability of both. Using an exact confidence interval allows us to compare success probabilities of the two treatments and come to a conclusion. The advantage of the exact approach is that it provides guaranteed 95% confidence in the interval without the need for a large amount of data.

*What is your plan for the near future?*

I am trying to finish my research and publish the result. Besides that, I’m designing a web-interface program that utilizes and presents my research to find confidence intervals without heavy computation. Additionally, I’m putting finishing touches on a textbook on introductory statistics. I also plan to have a publication on medical statistics, a field that I have been working in for a long time.

*Why did you choose University of Florida for your PhD research?*

It was quite difficult for me to continue my research on statistics in Austria because post-graduate study there focuses more on theoretical side of mathematics. Therefore, I decided to seek my PhD in the US. My last year at graduate school in Austria, I studied a book on categorical data analysis and was especially intrigued by an analysis of alligators’ food choices. Subsequently, I ended up with a Fulbright scholarship at the University of Florida to do research with the author of the book and to meet all the alligators there.

*Do you have any hobbies?*

Definitely! One of them is scuba diving because I like to explore space and the underwater world in 3D. I also love to swim and play a few sports such as basketball and tennis. Besides all of that, I also spend a significant amount of my free time on photography.

*What do you think of a liberal arts college like Williams?*

I actually did not know anything about liberal arts education and college before coming to Williams. I also had no ideas about residential life in a small college like Williams; I grew up in a town which just had three big universities. However, as I understood more about liberal arts, I considered it a great model of education. During my free time, I often go to dining halls with students or enjoy some sports events. I really love it here and hope to get more attached to this community in the years to come.

*Do you have any advice for aspiring statistics majors?*

Get involved in as many applied projects as you can. Get familiar with data analysis and statistical modelling. Hands-on experience is necessary to advance in statistics. It gives you ideas of what classes to take or what research to pursue.

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Sarria explains to Ariyibi his goal of finding a mathematical link to the physical properties of pressure in fluids.

*What’s your favorite part of math?*

I work in nonlinear partial differential equations, and the main reason I like partial differential equations is that they’re wild. There isn’t much theory for how to deal with many of them. You have to figure it out yourself. It’s not always about applying methods already in the literature. In most cases you have to come up with the tools to study a problem.

*What are you working on right now?*

Right now, I’m working with a student assistant on the incompressible Euler equations, which model ideal fluid flow. We incorporated damping into the system. We’re studying the impact of this damping term on the behavior of solutions to these equations.

*Do you have some overarching goal for your mathematics research?*

When you model fluids, there is something called the pressure. For example, in the sea, when you go very deep, the pressure can actually kill you. Unfortunately, this pressure term is not very well understood from a mathematical perspective, so I would like very much to understand it better. That would be really nice.

*Do you have any advice for aspiring math students?*

Keep an open mind. Don’t restrict yourself to studying just one area of math and one methodology or theory, because later on you may find yourself at a disadvantage if new theories are developed using tools from different fields. Just keep an open mind. Keep on researching. Keep on studying other areas of math, and stay up with new developments through attending conferences and workshops.

*Throughout graduate school, what was the most difficult point for you?*

Coming up with the topic for my dissertation. There was this Millennial problem on fluid flow. It kinda sounded interesting to study a problem whose solution is worth a million bucks. Of course I didn’t solve the problem, but I was able to find some related problem that I could work on. So coming up with the topic was probably the most difficult part in graduate school. The next most difficult part was managing my time. I found myself reading tons of papers and attending all these conferences. I would do a little bit over here and a little bit over there. At the end, you have to be very well-organized and have some sort of structure. Know what it is that you want to do and what it is that you actually can do.

*What else do you like outside of Mathematics?*

Physics. I like physics a lot. Outside of the office, I like to go hiking and running. I play soccer whenever I find people to play with. I like exercising in general. I like the outdoors a lot.

*What exactly brought you to Williams?*

I wanted to work on my teaching skills as well as interact and work with students. At Williams the interaction between faculty and students is fantastic. There are lots of workshops for teaching. The professors are top tier, some of the best teachers in the country when it comes to math. You can get very good advice from them. It is a good opportunity to keep on doing research while working on my teaching skills.

*You’ve mentioned the million-dollar “Millennial” problem on fluid flow. Are there any others you are interested in?*

The Poincaré conjecture. It already got solved using, in part, differential equations. That would have interested me if I would have known that was the method to solve it, but it has already been solved, so actually, I think I’ll stick with the fluid problem.

*Sarria is Visiting Assistant Professor at Williams College. Ariyibi is in the Class of 2019 studying mathematics and economics; he likes multivariable calculus and playing the saxophone.*

Friends of Williams gathered 5-6 pm January 8, followed by humorous math theater by Prof. Colin Adams and the Mobusibandaid players, now available on YouTube.

The meeting featured the AMS Colloquium Lectures by the Fields Medalist W. Timothy Gowers, as well as AMS Invited Addresses by Marta Lewicka, Steve Zelditch, Alex Eskin, and Panagiota Daskalopoulos, MAA Invited Addresses by T. Christine Stevens, Katherine D. Crowley, Steven Brams, Alan Schoenfeld, and Charles R. Hadlock, and many other exciting talks.

9 am *Frechet Differentiability in Optimal Control of Free Boundary Problems for the Second Order Parabolic PDE.* **Dylanger S Pittman**

2:15 pm Etudes of Questions: A New Approach for Writing Mathematics **Thomas Garrity**

9:30 pm AWM Reception (**Sarah Tammen** as Schafer prize runner-up at 10)

9:30 pm AWM Reception (

8:45 am *The Fibonacci Quilt Sequence: A Generalization of Zeckendorf Decompositions with Non-Uniqueness.* **Dawn C. Nelson***, **M. Catral**, **P. Ford**, **P. Harris**, **S. J. Miller**

9:30 am *Dimensions of Formal Fiber Rings.* **Sarah Fleming**,**Lena Ji**,**Susan Loepp***, **Peter McDonald**, **Nina Pande**, **David Schwein**

5 pm Friends of Williams gathering, Sheraton Lobby

10:30 am *Rings, Completions, and Strange Formal Fibers.* **Sarah Fleming**,**Lena Ji**,**Susan Loepp**, **Peter McDonald**, **Nina Pande***, **David Schwein**

1 pm *Centrality Properties of Graphs with an Application of Functional Connectivity of the Brain.* **Roger Vargas***, **Abigail Waldron**, **Anika Sharma**

1:30 pm *Centers of endomorphism rings of modules.* **Haydee M Lindo**

]]>3:30 pm *Peak Sets of Classical Coxeter Groups.* **Alexander Diaz-Lopez**, **Pamela Estephania Harris***, **Erik Insko**, **Darleen Perez-Lavin**

5:45 pm *The Convex Body Isoperimetric Conjecture.* **Matthew J Dannenberg***, **John Berry**, **Jason Liang**, **Yingyi Zeng**

At the first meeting this fall, four officials were unanimously elected: Roger Vargas (President), Gabriel Ngwe (Vice President), Xixi Edelsbrunner (Treasurer), and David Moon (Secretary). From these positions, they have successfully organized many events this fall including biweekly meetings aimed at GRE prep and math puzzles. In addition they planned a special event called Lightning Talks where students presented short (5-10 min) talks on their own research or other topics of interest. The next big event – the Putnam Prep Pizza Rally – will be on Tuesday, December 1st in collaboration with SMASAB and will include free pizza from Hot Tomatoes. This event is to help Williams students prepare for the upcoming nationwide Putnam Math Competition, which will be held on Saturday, December 5th at 9:45 AM in Griffin 3. Everyone is welcome to participate. We hope to see you at future AMS activities.

Update: The Putnam Prep Pizza Rally was a big success. Here are a few pictures from the event.

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