eMail: wolfgang.globke @ univie.ac.at
Linear equations, matrix algebra, linear optimization, eigenvalues.
Sets, relations, modular arithmetic, logic, cryptography, recursion, graphs and trees.
Matrices and polynomials, canonical forms of matrices, scalar products and hermitian products, isometry groups, self-adjoint endomorphisms, spectral theorem.
Groups, rings, fields, abstract vector spaces and linear maps, coordinate representation by column vectors and matrices, systems of linear equations, determinants, eigenvalues and eigenvectors.
Linear Lie Groups, Lie algebra and exponential maps, Lie's and Engel's theorems, complex semisimple Lie algebras, compact Lie groups.
Elementary linear algebra and multi-variable calculus: Vectors and matrices, linear equations, cross product, partial derivatives, extremal values, Lagrange multipliers, systems of ordinary differential equations.
Single variable calculus: Sequences and series, limits, continuity, derivatives, Taylor expansion, ordinary differential equations.
Lie groups and Lie algebras as left-invariant vector fields, Lie subgroups, homogeneous manifolds, symmetric spaces, semisimple Lie groups, locally symmetric spaces.
Linear algebraic groups, arithmetic groups, hyperbolic plane, proper actions, fundamental and Siegel domains, Harish-Chandra's theorem.