From Calculus to Number Theory

Emily Shambaugh '24

Student Snapshot: Emily Shambaugh ’24 

Emily Shambaugh ’24 didn’t come to Dickinson with intentions of majoring in math, but a calculus course turned her sights in that direction. Last summer she participated in a Research Experience for Undergraduates, funded by the National Science Foundation, focused on number theory. After graduation, she plans to earn a Ph.D.


Mechanicsburg, Pennsylvania.



Clubs and organizations:  

Pi Mu Epsilon honor society and Mathematics Majors Committee.


John Dickinson Scholarship.

Best thing about my major:

I actually did not intend to be a math major when I first came to Dickinson! But then I took Multivariable Calculus my first semester of freshman year. I love how supportive the math faculty are. They are all really approachable if you have any questions or need major-related advice.

On choosing Dickinson:

I decided to attend Dickinson because of its small close-knit community and the statistics on how many students go into a job or graduate school after graduation.

Favorite class:

My favorite class that I have taken so far is Math 472: Complex Analysis. This is one of the last classes you take as a mathematics major, and it’s interesting to see how the concepts work together to do some really cool math.

Favorite professor:

It’s hard to choose only one, but it’s probably Assistant Professor of Mathematics Holley Friedlander. She is very approachable and willing to work with her students and discuss research opportunities with them. Professor Friedlander has also helped me find and apply for programs outside of Dickinson, such as Research Experiences for Undergraduates (REUs) and conferences, which I am very thankful for.

Post-Dickinson plans:

Enroll in a Ph.D. program, ideally in number theory. I have really grown to enjoy the subject through the classwork and research that I have done over the past year, and I would love to be able to study it further.

If I could have dinner with anyone, living or dead, it would be …

… Ramanujan, because I would love to see how he came up with a lot of his ideas, especially since he died young and didn’t get to publish the majority of his work.

Proudest accomplishment so far:

Getting accepted to and participating in a Research Experience for Undergraduates funded by the National Science Foundation.

About my REU:

This past summer I took part in a Research Experience for Undergraduates (REU) on integer partition identities. I took on this project because of my interest in a branch of mathematics called number theory, and the problem that was proposed was very interesting to me. We focused on providing an alternate proof on a previously proven partition identity, which allowed for the partition to be used in other branches of mathematics. I learned a lot about working with a team and communicating ideas with a team through this project.

I am also currently doing research to pursue departmental honors in mathematics, under Professor Holley Friedlander, on polynomial partitions and factorization patterns.  

Most important thing I’ve learned so far:

Messing up things is a part of life. What matters most is how you handle it and grow from your mistakes. I’ve also learned that it’s best to go through life with an open mind. I actually didn’t apply to Dickinson as a mathematics major, but I fell in love with the subject and the department and couldn’t be happier with my decision to major in mathematics.

Read more Student Snapshots.



Published March 7, 2024