1. The mathematics of finding functions that
extremize/optimize a given functional (variational derivative)

2. The mathematics of extremizing a functional subject to given constraints (isoperimetric problem)

3. The mathematics of extremizing a given functional at a boundary (end point problem)

4. The mathematics of finding the shortest (or longest) path (geodesic problem)

5. The mathematics of setting up the equations of mechanics from a single scalar (Hamilton's principle)

6. The mathematics of phase fronts and their interference (Hamilton-Jacobi theory)

7. The mathematics of tensors (multi-linear algebra)

8. The mathematics of parallel transport (covariant differentiation)

9. The mathematical classification of of parallel transport (torsion and curvature)

10.The mathematics of a strained elastic medium (metric-induced geometry)

2. The mathematics of extremizing a functional subject to given constraints (isoperimetric problem)

3. The mathematics of extremizing a given functional at a boundary (end point problem)

4. The mathematics of finding the shortest (or longest) path (geodesic problem)

5. The mathematics of setting up the equations of mechanics from a single scalar (Hamilton's principle)

6. The mathematics of phase fronts and their interference (Hamilton-Jacobi theory)

7. The mathematics of tensors (multi-linear algebra)

8. The mathematics of parallel transport (covariant differentiation)

9. The mathematical classification of of parallel transport (torsion and curvature)

10.The mathematics of a strained elastic medium (metric-induced geometry)