Math 312: Linear Algebra: Syllabus |
Fall 2012 |
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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