In an increasingly data-driven world, quantitative reasoning skills are crucial for academics and professionals. The Mathematical Sciences for Quantitative Reasoning (MSQR) course is designed as a stepping stone for students considering STEM-based Master’s programs and for those seeking to polish their quantitative reasoning skills.
We sat down with David Romoff, a full-time faculty member with the Enterprise Risk Management Master of Science (M.S.) degree program and the lead instructor for the MSQR course, to learn more about the course curriculum, its goal and the skills the students will walk away with from the course.
Tell us about your background. How long have you been teaching with the School of Professional Studies?
I studied philosophy and psychology as an undergraduate and then math and finance in business school. I wanted to be in a quantitative role so I joined Bear Stearns for a few years. After the company collapsed, I returned to graduate school and joined the Actuarial Science master’s program at Columbia University. My newly earned degree brought my quantitative skills up to a new level. After graduation, I was hired at AIG to work on global enterprise risk management modeling. After five years at AIG, I went to On Deck Capital, where I was responsible for the machine learning algorithms that modeled expected losses.
In 2017, I began teaching at Columbia in the Enterprise Risk Management program as a Lecturer for the Financial Risk Management course. As I was designing the course, I realized it would be particularly hard for some students due to the depth of the mathematics foundation required to truly understand and implement the course concepts. I ended up building a quantitative risk management introduction course, as well. While building the two courses, I also contributed a risk modeling class and proposed a fourth class—Financial Risk Management Practices.
What was the inspiration for the MSQR course? What is the main goal of the course?
The main goal of the course is to give students the foundation that they need in order to thrive in all kinds of quantitative master’s programs. And that ability is not just about mathematical calculations themselves, but really understanding the ideas and being able to communicate them, as well. Along with the ability to communicate ideas comes the ability to receive them. For many people, if the first outright expression in terms of symbols and formulas doesn't resonate, there’s a second chance to communicate a story. And so you really have two chances to learn all these ideas, and quantitative communication is that second chance. The course is not just about math—it’s also about understanding data and information, solving real world problems and effectively communicating quantitative ideas.
The main goal of the course is to give students the foundation that they need in order to thrive in all kinds of quantitative master’s programs. And that ability is not just about mathematical calculations themselves, but really understanding the ideas and being able to communicate them, as well."
What are some of the key skills that the course helps the students develop?
The first is the knowledge to create relevant statistics by constructing your own distribution and understanding the philosophy of hypothesis testing in order to work with the distributions that you have constructed—in other words, one of the skills we work on is to become an amateur statistician. The second is using linear algebra to understand and model systems. This is just a subfield of mathematics that emerges to describe the behavior and variability of systems of variables. Other skills include learning differential calculus for the sake of having intuition on how optimization works. And once you have intuition on how optimization works, you understand how regression and modeling work, and regression and modeling are the fundamental tools by which we understand the world and forecast.
The class will offer students the opportunity to get better at Excel and there will be a small amount of programming in VBA. They have the option to submit their work in the programming language of their choice, if they already are strong with a language.
What is the structure of the course? Do students gain practical experience in applying the theoretical concepts to real-life situations?
The course is on Tuesdays and Thursdays with three and a half hours of instruction each class session. During that long time period, we will rotate between explanation and application. Basically, after 10 to 15 minutes of presentation, the students will then get their turn for 10 to 15 minutes to build what has been presented or answer related questions. There's a lot of content, it’s been organized so that Tuesdays I’ll be delivering a breadth of ideas, and Thursdays I’ll go into greater depth, allowing students time to process the learning and do any follow-up work over the weekend.
What advice do you have for students who are considering the course or who are enrolled in the course?
My advice is to warm up on the topics that they find most interesting and valuable for what they want to study so that they're ready to receive more and see how to apply the ideas. So if they’re interested in applied analytics, they might want to brush up on their linear algebra and take that to the next level; if they’re looking to succeed in the widest range of master’s programs, a focus on statistics might best reinforce the basics and rebuild their foundation.
What are your hopes for the students that take the class?
I think a great outcome would be if students develop a deeper understanding of how mathematical concepts and quantitative reasoning can be leveraged to solve real world problems, as well as learn to communicate these ideas effectively. This will set the stage for making future quantitative classes interesting and approachable through both mathematical and applied insight. The key to learning things that appear boring is to find a way to make them interesting—that’s the key. So part of this class will be quite a few entertaining applications, and hopefully that feeling of stimulation and interest will carry over into whatever they go on to study.
Learn more about the Mathematical Science for Quantitative Reasoning course here.