The student whose excitement for mathematics was stirred by undergraduate courses in discrete mathematics, modern algebra, matrix analysis, combinatorics, or graph theory may want to concentrate in this area at the graduate level, yet concurrently pursue knowledge in some related area of the mathematical sciences. The algebra/ combinatorics program is designed to integrate concepts from algebra, combinatorics, and graph theory with one or more of the areas of analysis, computational mathematics, operations research, or statistics. The master's degree concentration is structured around the following courses: matrix analysis, abstract algebra, combinatorial analysis, graph theory, and applicable algebra. All of these courses emphasize the algebraic, combinatorial, and graph-theoretic structures used to model problems arising in engineering, the life sciences, economics, statistics, operations research, and computer science.
Matrix analysis treats a variety of topics in matrix theory which support a modern applied curriculum. Abstract algebra surveys groups, rings, fields, and lattices. Combinatorial analysis emphasizes applied topics from enumeration, graph theory, optimization, and block designs. Graph theory is the study of paths and networks, connectivity, trees, coverings, and coloring problems. The applicable algebra course seeks to apply concepts from the above courses to problems in areas such as computer design and reliable communication of digital information.
Beyond these courses, master's degree students concentrating in algebra or combinatorics are encouraged to develop a major strength in one of the applied fields within the Mathematical Sciences Department. PhD students will generally follow the diversified MS program prior to advanced study, but ultimately specialize in one of the following areas: combinatorics, graph theory, convexity, matrix algebra, coding and designs, field theory, ring theory, or algebraic semigroup theory.