CS, Monash University
I study computer science, mathematics, and linguistics, and write about questions worth returning to. AI is my current research focus, alongside interests in algorithms, systems, formal methods, and the connections between language and computation. I build tools around my reading and experiments to make ideas easier to test and understand.
A public notebook on computation, mathematics, and language: ideas worked through, research questions, and things built along the way.
The fundamental theorem of algebra asks whether a root exists, yet its proof hunts for a lowest point. Following that proof: how root-finding and optimization rewrite into each other, how the landscape changes when they do, and why the complex plane has no false pits.
Derive the correction by fifteen, allocate tolerance budgets, and expose estimator failures with a smooth counterexample.
Assemble trapezoidal, midpoint and Simpson rules; prove global errors, mesh identities, and smoothness limits.
Choose nodes by orthogonality; prove root properties, maximal precision, positive weights, and the Hermite error formula.
Derive open and closed quadrature weights and prove their precision and signed errors with Peano kernels.
Stable entry points into the note system: concepts and technical areas, grouped straight from the notes.
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