Also included are introductions to combinatorics, graph theory, functions, relations, automata and formal languages. Topics include existence, uniqueness and other properties of solutions, linear equations, power series and Laplace transform methods, systems of linear equations, and qualitative analysis. N Topics include systems of linear equations, matrix algebra, determinants, real and complex vector spaces, linear transformations, eigenvalues and eigenvectors, and diagonalization. Attention is given to proofs. Mathematical Statistics and Probability.
Emphasis is on careful proof.
Topics include groups, subgroups, permutation groups, cyclic groups, normal subgroups, quotient groups, homomorphisms, isomorphisms, rings, integral domains, polynomial rings, ideals, quotient rings, fields, and extension fields. Additional topics may include finite fields, Galois theory, and advanced topics from linear algebra. Readings in Mathematics. This course allows students to do advanced work not provided for in the regular courses. Its content will be fixed after consultation with the student and in accord with his or her particular interests.