*By: **Sarah Blackwell, mathematics major, Saint Louis University; **Rose Kaplan-Kelly, mathematics major, Bryn Mawr College; and **Lilly Webster, mathematics major, Grinnell College*

*Editor’s note: The editorial board believes that in our discussion of teaching and learning, it is important to include the authentic voices of undergraduate students reflecting on their experiences with mathematics. We thank Ms. Blackwell, Ms. Kaplan-Kelly, and Ms. Webster for contributing their essay. The American Mathematical Society maintains **a list of summer mathematics programs for undergraduates** and has published **Proceedings of the Conference on Promoting Undergraduate Research in Mathematics** as a resource for mathematicians interested in similar programs.*

We were participants in the Summer Math Program for Women Undergraduates (SMP) at Carleton College, a program with the goal of encouraging and supporting women undergraduates in their study of mathematics during their first two years of college. For four weeks we took math classes, listened to math talks, went to problem sessions, and talked about math for fun. We had the opportunity to meet many mathematicians from across the country. The people we met did not fit into the mold of the solitary eccentric that popular culture would have us believe. We met mathematicians who defied negative stereotypes often attributed to people in STEM areas and especially to women who are interested in math. Learning about their projects and interests helped us to see ourselves as capable of becoming mathematicians as well. In talking to them, we started to see what our lives could be like if we pursued math as a career and learned that there was no single “correct” type of person we would need to become. SMP was also an opportunity to meet mathematicians who worked outside of academia, mainly in applied math, which was not an area many of us had been exposed to before. This expanded our view of what being a mathematician might be like and what we could achieve.

This program helped shape our view of mathematics in many different ways. SMP gave us an idea of what upper level math classes could look and feel like. We encountered abstract algebra in our Lie Theory course, and our Topology course presented an entirely new branch of math for most of us. For instance, in Topology, we covered topics such as how to play tic-tac-toe or chess on a torus and klein bottle, which was fun and not something we had seen before. In addition to experiencing upper level math classes, we attended math talks by visiting professors and current graduate students on different areas of math such as a lecture on Knot Theory, a presentation that included a demonstration with a Ruben’s tube, and a lecture given by a professor who studies the history of math. We saw how math was used in different ways and could overlap with other subjects. These talks expanded our mathematical knowledge and also showed us how we could fit into the math community by showing more of what was possible.

SMP provided us with a great introduction to the collaborative math world. In the courses we took, there was much more emphasis placed on collaboration than many of us had been used to in previous math classes. In our Topology class we were assigned to work in groups for homework problems. These homework groups became the first way many of us got to know fellow participants, and we bonded quickly over attempting new problems such as designing a digestive system for a two-dimensional square in Flatland. In Lie Theory, we turned in partner homework assignments and presented tough problems on the board in class. In both classes we also worked on final projects in the form of group presentations. Though the research was tough, we immensely enjoyed putting together the presentations with our group mates. Some groups showed their enthusiasm through added touches like origami demonstrations and knot models. Working in groups helped us improve our collaboration skills and our ability to communicate mathematically, but most importantly it showed us how math can be a social activity.

SMP gave us the chance to become part of a new close-knit math community. We were excited to meet other math students who were passionate about math for its own sake, rather than just as a means to do physics or computer science. At first, most interactions at SMP were facilitated by group homework, but these interactions quickly became friendships centered on a wonderful common interest. Since we all lived in the same dorm, we constantly had opportunities to build on these relationships. Even casual conversations over meals or in the lounge helped strengthen our community. One such conversation about gender in mathematics stretched long past the end of dinner and would have gone hours longer if we hadn’t needed to work on homework.

We were encouraged to meet women who were attending or had completed graduate school for math, and to learn from their experience. The people we met made a point of telling us all the “secrets” of being a mathematician – what courses to take as an undergraduate, how to find summer opportunities, how to apply to and succeed at graduate school, and much more. For example, we learned about how to apply and what to expect at REU programs from current REU participants at the University of Minnesota, and we attended information sessions given by math professors on declaring a math major and applying to graduate school. SMP also made it possible for us to meet former participants who are now professors. At the SMPosium, a two-day conference of former SMP participants who have since earned their PhDs, we heard talks from professional mathematicians working in a wide variety of fields. Many of the talks were in applied math, covering topics such as acoustics or using topology for data analysis. We also heard several talks in pure math, including talks about hyperbolic spaces and a complicated type of algebra. Hearing about the accomplishments of graduate students who were only a few years older than ourselves helped us think about what exciting discoveries we could make in the near future. In addition to learning math, SMPosium allowed us to expand our mathematical community. Through these connections we learned that working on mathematics does not have to be an isolating experience, despite common stereotypes to the contrary.

By combining classroom work, problem solving, and lectures with a community of people who are all invested and enthusiastic about math, SMP provided a holistic math experience. Many of us came into SMP viewing graduate school as an unreachable goal, and thoughts of a future in mathematics were unclear. Rather than leaving SMP burnt out, we left wanting to do more math. While we were at SMP, we had the opportunity to talk to many mathematicians and clarify our goals for the future. In particular, our professors were helpful in making plans to achieve our goals. Many of us met one-on-one with our professors to discuss our individual career options and future plans. We now know what is necessary to continue into graduate level work. We believe we are capable of succeeding in graduate school and we are starting to figure out what types of math interest us most. We left SMP with confidence in our ability to have a future in the mathematical community.