Multivariate calculus from first principles
Single-variable calculus lived on a line. Machine learning does not. A neural network's weights, an embedding, a gradient: each is a point in high-dimensional space, Rⁿ. The good news is that the geometry you know from the flat plane R² carries over almost word-for-word. A vector is still an arrow from the origin; length, angle, and "shadow onto another vector" all still make sense. We just stop being able to draw it.
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▶ Vectors & Geometry of Rⁿ