Tyler Gonzales will head off to graduate school in applied mathematics at Yale University this fall with a significant, sustained, independent research project already completed—his senior honors thesis. As a Blugold Fellow, Tyler has been involved in student-faculty collaborative research since his first year on campus. His honors thesis represents the culmination of all of that experience: this project “wrapped up my undergrad, putting everything I learned into practice,” he tells us.
Tyler—a mathematics major and physics minor—began working on his thesis last year with his faculty mentor, Dr. Sam Scholze, Assistant Professor of Mathematics. His thesis, Stability Bounds for Reconstruction from Sampling Erasures, examines mathematical techniques in signal processing. He sums it up this way: “When you receive a noisy signal and wish to better understand what you’ve been sent, there are certain ways to reconstruct the lost data so that you can better analyze the original signal. There are many real world applications, such as encryption, for example.” The first stages of the project involved “a lot of math, grinding through equations.” Now, in the final stages of research, Tyler spends time using MatLab to model the techniques he’s using to reconstruct the signals, to see how efficient they are.
Tyler decided to undertake a thesis in order to learn deeply about an area he hadn’t investigated before. His thesis work also differs from his other research experience in two main ways. First, he tells us that he’s getting significantly more experience with research writing in his field—while thesis length varies dramatically from field to field, Tyler’s math thesis will ultimately be a 50- to 60-page document. As he’s undertaken this writing project, he’s developed a writing process that will serve him in graduate school and beyond. He’s learned to think of his thesis paper as telling a story, he tells us. And he’s also figured out that he works best when he breaks up writing into manageable chunks, rather than trying to tackle the whole project at once. More often than not, he has enjoyed the writing process—"sometimes it’s frustrating,” he says, “but often, it’s a lot of fun.”
Second, Tyler’s thesis work is more independent than previous research experiences. He still has weekly meetings with his advisor, but Tyler is shaping the project’s direction, reading research articles to see how his project fits into the field, and doing all of the writing. When he meets with his advisor, they often focus on editing Tyler’s writing. Eventually, Tyler and his advisor plan to publish an article based on his thesis research.
For students interested in pursuing an honors thesis, Tyler advises that it’s crucial to cultivate a good support network, and to find an encouraging research mentor who is willing to work with you. Since the thesis is a big project, it’s important to ask for help when you need it. He also admits that he did not know everything about the topic he was writing on when he started the project. You do not have to be an expert on something to write a thesis on it, because the whole point is to learn through research and writing. Tyler acknowledges that “[the honors thesis] sounds hard, but it is a fun and educational experience.”
Tyler developed research skills and identified future areas for research as a McNair Scholar and Blugold Fellow. He also won the prestigious Goldwater Scholarship, which supports students pursuing a career in STEM research. Tyler has been an involved and engaged student in other ways as well, such as by serving as a teaching assistant for Dr. aBa Mbirika. Tyler also valued the honors courses that offered meaningful discussions, opened up enriching projects, and encouraged him to become a well-rounded thinker. He says that much of his personal growth “wouldn’t have been possible” without the Honors Program.
After his time at Yale, Tyler hopes to become a professor or work in the national security industry. As a current senior, there are things he will miss after graduation: hanging out with his friends, late night studying, and the beautiful campus. Tyler has cultivated a lot of mentorships, friendships, and other connections here, and he knows it will be hard to leave the people who helped shape him. We in the Honors Program are excited to follow Tyler’s journey as he embarks on the next stage of his career.
To learn more about writing an honors thesis, join Tyler, the Honors Director, and other thesis writers at an info session on April 12 at 4 pm at this Zoom link.