1.Maximization, minimization, and motivation. 2.Vectors and matrices. 3.Diagonilization and canonical forms for symmetric matrices. 4.Reduction of general symmetric matrices to digital form. 5.Constrained maxima. 6.Functions of matrices. 7.Variational description of characteristics roots. 8.Inequalities. 9.Dynamic programming. 10.Matrices and differential equations. 11.Explicit solutions and canical forms. 12.Symmetric functions, kronecker products and circulants. 13.Stability theory. 14.Markoff matrices and probability theory. 15.Stochastic matrices. 16.Positive matrices, perron’s theorem and mathematical economics.