Daniel Berkowitz, Ph.D.

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I completed two separate dissertations: one with Professor George Fleming on the development of a new method for formulating lattice field theories on Riemannian manifolds, called Quantum Finite Elements (QFE), and another with Professor Vincent Moncrief on a new mathematical method for solving Lorentzian signature problems in terms of their Euclidean signature analogs, called the Euclidean-Signature Semi-Classical Method.

In accordance with my belief that, to truly understand something, you must be able to explain it in a way that someone with significantly less experience in that subject can comprehend, I worked as a teaching assistant for 20 hours a week while completing my two dissertations. As a TA, I provided personalized educational, behavioral, and emotional support to approximately 34 students per semester. I graded their homework, left informative comments to help them develop a deeper understanding of the subject, and advised them on study habits. During the pandemic, I increased my availability and put even more effort into the feedback I provided to students to minimize the detrimental effects that the absence of in-person instruction had on their physics education.

I was a Teaching Assistant for a graduate-level course in General Relativity. I was expected to be able to deliver a graduate-level lecture on a given subject in the course if the professor was unable to teach on a particular day. On the final day of class, I gave a lecture on loop quantum gravity.

I organized the day-to-day operations of a class with over 300 students. My responsibilities included determining how much homework each TA had to grade, handling disputes from students who disagreed with the initial grades assigned by their TA, assisting the instructor with office hours, and organizing the grading of exams so that students could receive their grades within three days. While doing so, I ensured that the workload was manageable for the graduate student graders, who had their own exams and heavy workloads. Additionally, I kept both TAs and students informed of any updates in a timely manner, managed various student-related issues to ensure everyone had the opportunity to succeed regardless of their circumstances, and, most importantly, fostered a safe, engaging, productive, and intellectually stimulating learning environment where students could reach their full potential.

Since my first day working at the PTC, I have always wanted to become the team leader of physics tutoring. When my only responsibility was tutoring, I would ask students about their overall experiences at the PTC and how the tutoring experience could be improved. The most common feedback I received was that tutors should be better able to assign additional problems for students to solve and effectively derive equations. That is why the first thing I did upon becoming team leader was to redesign the qualifying exam that prospective tutors had to take, placing a greater emphasis on derivations. I also introduced tutors to a variety of physics textbooks beyond the one officially used in the introductory physics sequence and taught them how to use these books, which varied in rigor, to assign additional problems to students. To incorporate feedback, I also redesigned the physics mock exams administered by the PTC, ensuring that the questions were somewhat more challenging than those on the actual midterm and final exams. Since proctors would later work out the solutions in front of students, this provided a valuable opportunity for them to observe how difficult physics problems are solved. Seeing the positive impact the PTC had on students in the introductory physics sequence, I wanted to expand the number of courses we tutored. Therefore, I introduced tutoring for two mid-level physics classes: Analytical Mechanics and Mathematical Physics. Doing so required training tutors on how to effectively convey sophisticated concepts while ensuring that students retained them until test day.

I studied systems which have chaotic regions in their phase space such as the double pendulum and the Henon Heiles model to better understand how chaos emerges in them.

At the time, acquiring this job was a dream come true. Physics was my life back then—and to an extent, it still is today—so I jumped at the chance to share the subject I loved most with my peers. I tutored mechanics, electricity and magnetism, and thermodynamics. Another part of my job involved proctoring mock exams with up to 100 students and later reviewing the solutions with them. The Polytechnic Tutoring Center (PTC) offers drop-in tutoring, meaning tutors stay in a room while students from various majors come in with questions. I loved how this allowed me to meet so many new students, especially those from majors I wouldn’t typically interact with in my other classes, and learn about their perspectives. It was particularly illuminating to see how business majors approached physics problems compared to mechanical engineering majors, for example. Given the academic and welcoming atmosphere at the PTC, some students would come not just to study but also to relax or talk to someone they considered a peer about something that was troubling them. Being a tutor at the PTC also meant being a counselor and an advice giver. It was this aspect of tutoring that sparked my interest in consulting.

Planning to do work in modified massive gravity. Construction of models of gravity, which rely on the propagation and transmission of gravitons with mass to reproduce the effects of vacuum energy.