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“The Sky Is Not the Limit”

Julia Baumgarten is a recent graduate of Jacobs University Bremen in Germany. She came to Columbia for its 2022 Summer Session to take math courses she couldn’t fit into her undergraduate schedule and just before she starts a Master of Science in Physics program at Freie University of Berlin in October. She talked about her summer at Columbia and why she’s captivated by the New York Mets. 

What interested you in the Linear Algebra and Intro to Modern Analysis II courses?

As a physics major, I rarely had the chance to take any non-required mathematics courses. Linear Algebra is probably the math course I have wanted to take the most because I love the topics it covers. What really made the Linear Algebra class stand out was how collaborative it was. I loved that the professor encouraged student-to-student interactions. I was a bit hesitant at first to consider Intro to Modern Analysis II, since it is a graduate-level course—and I did not attend the first part of the course held in Summer Session A. But I contacted the instructor, Dr. Peyam Tabrizian, and after hearing back, I felt confident enough to take on the challenge.

Both of these courses helped prepare me for graduate studies in physics. I now have a foundation in linear algebra to build upon. Especially in fields like quantum mechanics, it is very important to have a good grasp of matrix operations. Modern Analysis II focuses more on proofs than on the result of certain theorems. Being able to derive formulae and prove certain relationships is of utmost importance in physics as well, but historically it hasn’t been one of my strengths. Over the course of my undergraduate studies, I worked on building that skill, and this class at Columbia helped me to further strengthen it.

What was your favorite part of the class?

For Modern Analysis, Dr. Tabrizian’s YouTube channel is a lot of fun to follow. In my Linear Algebra class, I especially appreciate the interesting and diverse topics as well as the extra-credit paper or presentation. “Markov Chains and Linear Algebra” proved to be a lot of fun to write about. The paper was a group project; I worked with two other students. We gave a general introduction to Markov chains before taking a three-state Markov chain and finding its transition matrix. Then the general t-step transition matrix is derived. The paper concluded by deriving the stationary matrix of the three-state Markov chain example.

Tell us a little about your love of sports. Have you been able to participate in anything sports-related while at Columbia?

Ever since I was in elementary school, I’ve had this urge to engage in sports and the community that comes with it. I competed in gymnastics, tennis, aikido, field hockey, and archery, and I have earned every German swimming badge I could. Nine years ago, I started air rifle shooting, and it’s become one of my most deep-running passions in sports. I went to a Mets game organized by the Summer Session, and I might just have a new sport I would like to try. I already purchased a ticket for the next Mets game. Let’s go, Mets!

What are your favorite things to do on and/or off campus?

The day I arrived, I just strolled down Fifth Avenue, and I fell in love with New York. I live right next to Riverside Park, and I’ve explored Central Park; both are truly beautiful and calming. Columbia’s campus is so stunning. Butler Library and the area around the mathematics building are peaceful. The architecture and elements of green in the middle of bustling New York make the campus feel like a safe haven.

What advice would you give to students who are similar to you?

If you want to explore the universe as I do, know that the sky is not the limit. With hard work, honesty, and a bit of support, you can achieve whatever you set your mind to! It will always be amazing to watch someone follow their passion. I believe Columbia has a community where people are following their passions. You can see people’s eyes light up when they’re talking about what they love. Most importantly, and this has always been true for me: Concentrate on what you can influence, and do not worry about what is out of your control.

Explore options for visiting students during the Columbia University Summer Session.