Course Description: | This course introduces the theory of groups and develops the theory of linear algebra. Topics covered include modular arithmetic, RSA cryptography, abstract groups, homomorphisms, normal subgroups, quotient groups, group actions, symmetry groups, permutation groups, matrix groups, theory of general vector spaces, inner products, linear transformations, spectral theorem for normal matrices, and Jordan normal form. Students do calculations in modular arithmetic and apply these to RSA cryptography; find eigenvalues, eigenvectors, minimal polynomials, and normal forms for linear transformations; analyze groups of permutations, symmetries, and matrices; and prove simple results in group theory and linear algebra. |