A arbitrarily chosen subset of small algebra:
Solving linear, quadratic, cubic, and quartic equations
Intersection of two conics
Small matrices (up to 4x4) and systems of linear equations
Complex coefficients and careful attention to roundoff error.
More:
Small linear and quadratic programming
Cubic and quartic splines and spline surfaces
Root finding by bisection
Newton's method and Newton-Raphson
1D minimization by golden section search
Even more:
Simpson's rule and Runge-Kutta
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