This course studies objects called algebraic structures. The first algebraic structure studied is a group, the most general setting for solving linear equations with one operation, such as the integers with addition. Students study a wide range of different examples, exploring the similarities and differences of these examples. In the second half, students study rings, the general setting for solving equations with two operations, such as the integers with addition and multiplication. This course develops the relationships among structures, substructures, factor structures, and structurepreserving maps.
Further topics develop connections to number theory.
Students may recognize ideas related to those developed in Math 3720, and should see generalizations of concepts first introduced in high school algebra. Students make heavy use of the ideas and techniques of logic and proof, as taught in Math 2683 and used in other mathematics courses, and these are reviewed briefly in this course. This course is scheduled to meet four hours per week. The extra hour provides a place and time for the instructor to give extra assistance to students. It is not required that students attend these assistance sessions, and no new material is introduced there, but it is strongly recommended that students take advantage of them.