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Tensor Calculus and Differential Geometry - Calculus on Curved Spaces

Doing calculus on curved surfaces and spaces: the metric, curvature, geodesics, and the geometry behind relativity and modern machine learning

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What you'll unlock:

  • 1. Beyond Flat Space: Curves, Surfaces, and the Idea of a Manifold
  • 2. The Metric Tensor: Measuring Distance on Curved Spaces
  • 3. Vectors, Covectors, and Tensors: Objects That Transform Correctly
  • 4. Curvature: How Space Bends
  • 5. Geodesics: The Straightest Possible Paths
  • 6. The Covariant Derivative and Parallel Transport
  • 7. Differential Geometry in Machine Learning: Information Geometry and the Natural Gradient
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