Swarthmore recently announced the new applied mathematics major, a special math concentration utilizing conventional math for use in more specialized fields in many disciplines, including biology, engineering, and physics. On February 8, mathematics professors Nsoki Mavinga and Joshua Goldwyn held an info session for the new emphasis for majors and minors in the Science Center.
“Pure mathematics, statistics, and applied mathematics provide the three primary specializations within the mathematical sciences,” said Professor Victor Barranca. “Considering the higher level facets of applied mathematics are distinct from both pure mathematics and statistics, the department considered it important to represent this specialization in its curriculum. Past course offerings in applied mathematics have been met with great enthusiasm, and a diverse body of students has expressed a strong desire to delve deeper into the discipline.”
While applied math focuses on the use of the subject in conventional professions, the regular math major is based more on theory — with more emphasis on proofs and explanations.
“Applied math fits well in a liberal arts setting because it is interdisciplinary in nature, and provides opportunities for students to explore connections between their coursework in mathematics, engineering, natural sciences, and other fields,” said Professor Goldwyn. “The applied math option provides an additional route through the math major that may appeal to some students with an interest in this area of mathematics.”
Students who are interested in the applied math major must have a mathematics-concentrated schedule, fulfilling the requirements for a regular math major while including other classes such as Differential Equations and Fundamentals of Applied Mathematics. Introduction to Computer Science and Probability in Statistics are also required for the major.
“[I encourage] everyone with an interest in mathematics and how it can be applied in ‘real world’ situations [to apply]. Applied math can be especially rewarding for students who enjoy working across disciplines,” said Goldwyn. “Typical problems in applied math can lead to development of innovative mathematical approaches and uses of advanced computational methods, and these problems can be drawn from physics, chemistry, biology, engineering, data science, and many other fields.”
Julia Dalrymple ’21, however, is not quite ready to jump into the new course of study.
“The reason I’m not just automatically switching over to the major is because it’s too new,” said Dalrymple, who is majoring in math with an emphasis on statistics. “From what I’ve seen, all of the classes are pretty new. I’ve never even heard of some of them.”
According to Dalrymple, students should do their research before committing to the necessary classes.
“One of the classes, I think it’s called ‘Stochastic and Numerical Methods,’ you can’t take at Haverford or Bryn Mawr because there is no equivalent to it and no precedent. If the people taking the classes say they are good, then I would recommend it,” Dalrymple said. “If I had gone into school already hearing about it, I probably would have gone into the major.”
Barranca describes that class in particular as a core class in providing a novel perspective on previous coursework.
“Stochastic and Numerical Methods (MATH 66) addresses a fundamental issue typical in modern applications of mathematics: since real-world problems are generally so challenging that they lack exact quantitative answers, there is a significant need for mathematical modeling and developing approximate solutions,” said Barranca. “Numerical analysis and stochastic processes together provide a strong and broad framework for studying such multifaceted phenomena.”
The major may be of more particular interest to those who wish to use math in applicable professions. According to Goldwyn, applied math majors will have more opportunities to study fields of mathematics based in differential equations, models, and numerical methods.
“I always liked the applied part of math over the theoretical,” said Dalrymple. “Coming here, I knew that meant working with statistics, which is used in everything. I’m also a biology minor, and we use stats all the time.”
According to Professor Barranca, what distinguishes the statistics concentration from the applied math concentration is the perspectives and techniques used to approach issues.
“Since the real-world applications that motivate mathematical endeavors are inherently complicated, applied mathematics often involves constructing models to capture the essence of phenomena and uses them to make predictions or understand underlying mechanisms,” said Barranca. “In applications that directly involve data, applied mathematics and statistics demonstrate particular synergy, granting a complementary set of tools commonly used together in important emerging interdisciplinary fields, ranging from atmospheric science to machine learning to computational biology.”
Even though the statistics and applied math majors have more readily conceived applications past college, some people may opt for the more traditional math major to appreciate the ideas and theory behind the ideas.
“I am personally interested in understanding the theory behind mathematical concepts and engaging with rigorous and precise mathematical proof. As such, my interests align more with the conventional math major than the applied math major,” said Tarang Saluja ’22. “I would encourage students to major in applied mathematics if they want to learn about how they can use mathematics to work on solving problems in the real world.”
The implementation of the concentration is still a step forward in offering Swarthmore students the chance to experiment with what they might enjoy.
“The applied math major is great for students who want to find connections between mathematics and other disciplines as opposed to finding connections mostly within mathematics. It is great that Swarthmore is offering a mathematics track for students who enjoy applications more than theory and want to experiment with both sides,” said Saluja.
Regardless of the students’ choices, the Swarthmore math department will advise and support all students under its wing.
“The math department is committed to being a supportive and inclusive department, and we seek to provide many ways for students to further their mathematical education,” said Goldwyn.