Dear Members of the Admissions Committee,
I am delighted to provide my endorsement for [Student Name]‘s application to your program. I had the privilege of mentoring her during a mathematical research mentorship in [Year], where she demonstrated exceptional independence and intellectual rigor. She taught herself the theory of recursion, entirely unfamiliar to her at the time, in order to solve a challenging problem in computational Ramsey theory.
Initially, I was hesitant to assign her the task of modifying code I had written for a recently published research paper, particularly because the algorithms in question rely heavily on structural recursion. Yet only two weeks later, she presented Python code that computed an elegant solution to our problem. When I asked her how she had worked around the missing features in my original program, she explained that she had extended it herself and then integrated those extensions into her own implementation. Achieving this required a depth of understanding that typically takes an undergraduate student at least a full term to develop, yet she acquired it in a matter of weeks.
Over the following months, we studied several research papers, developed part of a Python library for Ramsey-theoretical functions, and explored their applications. The project involved reading material spanning algebraic graph theory, combinatorics, and applied network theory. Each week, [Student Name] asked precise, technically informed questions, often about material from sources beyond our planned bibliography. This further illustrated her curiosity, discipline, and determination to master every theoretical detail relevant to the project.
She later presented our work at a national undergraduate mathematics conference, becoming one of the youngest participants in that event. Her career goals align closely with her commitment to understanding how abstract mathematics can illuminate real-world systems. She is particularly interested in evolutionary game theory and is currently developing a simulation project that, like our work together, integrates mathematical theory with computer programming. She also described how our project inspired her to build a graph-theoretic sudoku solver, another instance of her ability to apply abstract concepts to concrete problems. These qualities are characteristic only of the strongest undergraduate students I have taught.
I am confident that your program would be an ideal environment for the continued development of [Student Name]’s outstanding work ethic, her aptitude for independent research, and her capacity to synthesize ideas across different areas of mathematics.
Should you require any additional information, please feel free to contact me.