Mathematics: Groups and Rings

An introduction to the basic concepts of abstract algebra emphasizing examples, including modular arithmetic, symmetric groups, cyclic groups, polynomial rings, homomorphisms, and isomorphisms. May not be taken concurrently with or after MATH 3551. Prerequisite: MATH 2055 (preferred) or CS 1640.

Prereqs enforced by the system: MATH 2055 or CS 1640; Open to degree and PACE students

The core of the course concerns the study of groups. Groups are a fundamental algebraic structure in mathematics. While there are many directions from which you can approach groups without scaring them, one perspective is that they provide a language for quantifying symmetry just as numbers provide a language for quantifying amounts. After defining groups and providing examples of important families of them, we'll investigate their internal structure and what we can learn about relating different groups to each other via isomorphisms and isomorphisms. At the end of the course we will provide a brief introduction to rings and fields.

Lecture and discussion. Students should expect to spend 6-8 hours outside of class reading the textbook, reviewing notes, and working on homework problems.

Grades are based on weekly assignments, midterm exam, final exam and discussion participation.