Systems of linear equations and matrices, abstract vector spaces and linear transformations, orthogonality, eigenvalues, eigenvectors, and diagonalization. Some attention is given to the development of abstract reasoning and a variety of applications of linear algebra in natural and social science. Linear differential equations, Integral transforms, integrating in series and system of linear differential equations with applications. A systematic study of groups, rings and fields complete with substructures, homorphisms, endomorphism, isomorphisms and automorphism and field extensions. A rigorous treatment of limits and continuity with an introduction to a topology for the reals, completeness of the reals, differentiability and integrability and sequences, series and the theory of convergence.
Topics vary, depending on the interest of students and staff.
Open only to senior mathematics majors. Under the supervision of a full-time member of the mathematics faculty, the student will prepare a seminar to be presented orally and in writing. A student may complete any mathematics requirement by independent study and periodic evaluations by a full-time member of the Mathematics faculty.