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17 hours ago
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A Deep Dive into Applied Math – The Self-Taught Way
This summer, I’ve committed to an intellectually ambitious (and deeply personal) project: independently completing the MIT Applied Math Curriculum. I’ll be auditing classes (in person and online), connecting with professors and mentors, and tackling the OpenCourseWare (OCW) assignments and exams wherever available.
In this post, I’ll outline the motivations behind this journey, share a bit about my academic and research background, and lay out the specific plan I’m following. If you're mainly interested in the course list, feel free to skip down to The Plan.
Why Take on the MIT Applied Math Curriculum in 2025?
Currently, I’m a dual Master’s student at Harvard and Georgia Tech, specializing in Machine Learning and Computational Biology. I also serve as a research assistant across several labs, where I work at the intersection of Applied Math, Theoretical Neuroscience, and Deep Learning. My previous experience includes co-founding an ML startup. This fall, I’m preparing to apply to PhD programs focused on AI and mathematical biology.
My journey here hasn’t been linear. I originally studied Biology and Cognitive Science at UC San Diego, and my early internships leaned toward Product Management. Along the way, I taught myself to code—initially for web and mobile development—and gradually became captivated by the parallels between information processing in computers and biology. That fascination, particularly with neural networks, led me into graduate programs in CS and Biology, where I began conducting ML research and independently learning the mathematical foundations necessary to interpret cutting-edge papers.
As I progressed, something unexpected happened—I fell in love with math itself. Although foundational topics like Linear Algebra, Probability, and Vector Calculus are often sufficient for ML, I’ve noticed that the most innovative thinkers around me draw upon a much broader and deeper mathematical toolkit. They’re able to tap into concepts from PDEs, Dynamical Systems, Numerical Methods, and Optimization Theory, and apply those ideas in novel ways.
After speaking with mentors, including professors and graduate students from Harvard and MIT, the consensus was clear: if I want to push the boundaries of my research and sharpen my mathematical intuition, pursuing a rigorous curriculum like MIT’s Applied Math track is an excellent foundation.
I've been fortunate to gain access to audit select courses, both online and in person, and this self-directed program is my way of organizing, committing to, and sharing that experience. Hopefully, others interested in ML, bioinformatics, or computational theory might find this roadmap helpful too.
The Plan: Courses I’ll Be Studying
MIT’s Applied Math curriculum is thoughtfully designed, blending mathematical theory with real-world applications. I’ve selected a sample path based on the 2024–2025 course listings, emphasizing courses available via MIT OCW, edX, and other open resources, supplemented with similar material at Harvard, Georgia Tech, and nearby institutions.
✅ Core Courses (Foundation Building)
18.600: Probability and Random Variables
🧠 Restricted Electives (Applied Focus)
6.041A/B: Probabilistic Systems Analysis
18.650: Statistics for Applications
🔄 Electives and Supplementary Topics
Optimization Theory (18.335 or equivalent)
Stochastic Processes
Information Theory
Dynamical Systems
Mathematical Biology (as applicable to my research)
What Comes Next?
I don’t plan to rigidly confine this journey to a summer timeline. While I’ll be actively involved in summer research and class auditing, this project will evolve organically throughout the year. My goal isn’t just to tick off course boxes, but to deeply internalize the material—to make the math intuitive, applicable, and generative for future work.
I’ll be posting updates, study notes, problem solutions, and reflections here periodically. Ideally, this process will lead to:
More elegant and powerful approaches to ML modeling
Cross-disciplinary research ideas
New ways to think about problems in neuroscience and biology
And who knows—once I’ve finished Applied Math, maybe I’ll give the Pure Math curriculum a shot next!
Follow Along If you're curious, want to join the ride, or have resources to suggest—drop a comment or connect. I’m excited to see where this self-studying journey leads!
