מתודות חישוביות, למידת מכונה וביקורת: שלושה סדנאות תאורטיות

תקציר מקורי באנגליתarXiv:2610.07220v1 Announce Type: new Abstract: We present three practical tutorials on numerical computation and machine learning for mathematical research, developed for the DANGER: Data, Numbers, and Geometry workshop held at the Banff International Research Station in April 2026. The first develops a numerical approach to exterior calculus from pointwise evaluations of differential forms, using a flux formulation of the exterior derivative. Examples in Euclidean space and on the sphere illustrate geometric identities, topological features, and the effects of approximation and finite precision. The second examines how mathematical structure guides neural network design through examples involving elliptic curves, quivers, and a boundary value problem. It explores how architectural choice