Travis McVoy
Projects
Below is some of my work from my undergraduate degree (excluding the Wind Tunnel, which was during 2020).
If you haven't read the book, you'll have no idea why a papaya is here. If you have, you'll know exactly why. Happy learning.
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Experiments coming soon!
Many thanks to my advisor, Prof. O'Connell, for his humor and guidance.
Statistical Learning Theory
For my senior thesis, I am working through the illustrious Understanding Machine Learning From Theory to Algorithms text. The text is widely used as a graduate textbook and clearly serves as a standard in the field when it comes to notation. The first chapter alone has already made it much, much easier to read conference papers. By the end of the thesis, I will have covered the foundations section (chapters 2 through 7) and selected chapters in the algorithms and advanced theory section. As I read, I will be implementing Monte Carlo simulations of key results/ideas. I find that actually implementing code—even just toy examples—really reinforces the ideas and highlights any misunderstandings I may have.
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The project will conclude with an examination of current work in the field of learning theory. For instance, some progress has recently been made in multiclass learnability via what's called a "list learning" paradigm. I want to try to implement list learning.
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DISCLAIMER: My notes and code will be updated as they progress. Do not assume that what is currently uploaded is the current state of my project.
Probability
Skidmore does not regularly offer probability, but I don't see that as a legitimate reason to not learn about probability. There are plenty of open source resources, but I chose MIT's 18.440 (OCW).
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Note: I can make citations work using Overleaf, but my editor of choice is TexMaker. I haven't figured out citations in TexMaker yet, so my notes may have some oddities. Eventually I'll update them, but for now, the main texts I refer to when learning something new are:
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A First Course in Probability by Sheldon Ross
An Introduction to Mathematical Statistics by Larsen and Marx
Mathematical Statistics and Data Analysis by John Rice
Introduction to Probability by Bertsekas and Tsitsiklis
Statistical Inference by Casella and Berger (Rarely use this one as it's a bit advanced)
Occasionally I create simulations that correspond to probabilistic systems
in the problem sets. I find it enjoyable to play around with the number of iterations, the expected winnings of a system etc.
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It should be noted that the simulations I make are done entirely on my own, and are not affiliated with MIT in any way. Therefore, they may contain errors; feel free to email me if you spot an error ;)
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If you'd like to see my code, you may do so via the code button above. If you'd like to actually run my code, email me and I'll send you a file.
Update: One might notice I didn't finish the MIT course. Half way through the spring 2024 semester it was announced that Skidmore would offer a probability course next year. I'm definitely going to take that course so I put this project on pause to free up time for courses I was currently enrolled in. All the same, I'm very happy with how my study of probability went. I had a lot of fun and learned a lot.
Uncertainty Quantification of Diffusion Coefficient Estimation
Summer of 2024 I did research at Carnegie Mellon University.
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Abstract:
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This research intersects materials science and statistics through the lens of random walks. The goal of this project is to examine a less expensive method for obtaining the diffusion coefficient and its associated uncertainty. The results indicate an optimal regression method that minimizes assumption errors in the process of uncertainty quantification.
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Deliverable(s):
1) Presentation at JMM 2025
2) Proof in progress...
Huge thanks to my advisors, Jerry Wang and Rachel Kurchin, for their kindness and wisdom. Much appreciation goes to Jennifer Zhang, whom I worked with closely on this project.
Micromouse
The Micromouse competition is a robotics competition in which teams produce a robot that autonomously solves a maze, and then uses the knowledge it gained to solve the maze even faster.
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For my final project in IL305: Robotics, we were to design our own micromouse. In the video footage you'll see the robot correct itself (avoid hitting a wall) several times before over correcting.
I'd like to acknowledge my group members, Charles and Kaelen, for their excellent work. I'd like to thank Prof. Halstead for offering an amazing course.
Image Encryption and RSA
During my sophomore year, I had the opportunity to do some research in the math department. The original hope was to use some sort of graph theoretic encryption scheme, but my advisor and I abandoned the idea mid-way through. The literature we read left us worried about security, so we switched to RSA. I then implemented algorithms that encrypted and decrypted a matrix of generated integers, where the integers represent encoded RGB values.
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When I finished the project in 2023, I wasn't very pleased with the results because I thought the algorithm was slow. In January 2024 I realized that I misinterpreted the results. We found that an image with 1000^2 pixels typically takes around 4 minutes to decrypt using small primes (50 digits)—which seems awfully slow as 50 digits isn't very secure. Note, though, that we also found that an image with 100^2 pixels takes roughly 2.5 seconds (approximately 1/100th the time) to encrypt. Observe that 1000^2 = 100^3 (suggesting a linear relationship). It may very well be the case that the speed issue comes from Python.
My thanks goes out to my advisor, Kirsten Hogenson, for her guidance and support both in this project and otherwise.
Wind Tunnel
In 2020, my friend quarantined and moved in with me.
Together, we built a wind tunnel that was roughly 25 feet long with a 6x6 foot inlet leading into a 1x2x3 foot testing chamber.
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To read our story and see the building process, please visit the wind tunnel page linked to the button below:
Image source:
My gratitude goes to Prof. Lemus-Vidales for enabling students to pursue exciting projects.
Algebraic Combinatorics
In my Abstract Algebra course, we were given the option to do a test and a brief project or skip the test and do a harder project on material we hadn't seen in the course. The harder projects looked exciting, so that was my choice.
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I completed an expositional piece on the relationship between group actions and homomorphisms. The project concludes with a brief example of applications of group actions to combinatorics via Burnside's Lemma.
Infinitely Coupled Pendula and Lagrangian Dynamics
Image Source: HardewareX Kaheman et al.
During my sophomore year I was approved to do an independent study of upper-level mechanics. For my final project, I derived the Lagrangian and the Euler-Lagrange equations for a pendulum with arbitrarily many coupled masses. I lost the final draft for this project—I still have no idea how—so this work is...well, a bit messy. All the same, this project has a special place in my heart as it's one of my first projects in undergrad, and Mechanics was the last physics course I took (sad). Someday I would love to come back to physics. I owe a lot of who I am today to Jeremy (advisor on this project) and Mr. Malek, my high school physics teacher.
If you could somehow partition gratitude and put it into a set, the set that represents my appreciation for Jeremy Wachter would have the same cardinality as the set of masses on the pendulum we studied together. Jeremy, I miss ya.