First semester of an integrated, two-semester theoretical course in abstract and linear algebra, studied on an axiomatic basis. The major algebraic structures studied are groups, rings, fields, modules, vector spaces, and inner product spaces. Topics include homomorphisms and quotient structures, the theory of polynomials, canonical forms for linear transformations and the principal axis theorem. This course is required of all students majoring in mathematics.
Math 308 is the abstract algebra portion of the two semester sequence. The major topics are groups, rings, and fields. We will cover most of the sections in chapters I-VI of the textbook, and possibly more if time allows.