Look at the CAPM for the financial content, and mean-variance optimisation for the maths. It's basically minimising a quadratic function, but in many dimensions

Look at the CAPM for the financial content, and mean-variance optimisation for the maths. It's basically minimising a quadratic function, but in many dimensions, with two constraints - the efficient frontier. You use Lagrange multipliers and arrive at a neat linear system. Lots of fun parabolas and hyperbolas :-)