Math 312: Linear Algebra: Syllabus	Fall 2012

We will cover the following topics, although perhaps not in this order:

• systems of linear equations, existence and uniqueness, Gauss--Jordan elimination
• linear transformations and their geometry
• vector spaces and subspaces, dimension
• determinants and geometry
• eigenvectors and eigenvalues, diagonalization, complex eigenvalues
• dynamical systems, Markov chains
• Google's PageRank algorithm
• orthonormal sets, Gram--Schmidt process, orthogonal projection
• least-squares solutions
• inner product spaces and Fourier series
• singular value decomposition (SVD), with applications to image compression and principal component analysis (PCA)
• additional applications, possibly including facial recognition, wavelets, finance