Course Search
Courses may be offered in one of the following modalities:
- Traditional in-person courses (0–29 percent of coursework is delivered online, the majority being offered in person.)
- Hybrid/blended courses (30–79 percent of coursework is delivered online.)
- Online courses (100 percent of coursework is delivered online, either synchronously on a designated day and time or asynchronously as a deadline-driven course.)
- Hyflex (Students will be assigned to attend in-person or live streamed sessions as a reduced-size cohort on a rotating basis; live sessions are also recorded, offering students the option to participate synchronously or view asynchronously as needed.)
If you are enrolled in courses delivered in traditional or hybrid modalities, you will be expected to attend face-to-face instruction as scheduled.
MTH 457: Abstract Algebra
3 credits
Study algebraic structures, including groups, rings, and fields. Investigate important examples, such as permutation groups, normal subgroups, product and quotient groups, commutative rings, integral domains, ideals, quotient rings, and polynomial rings. Explore relationships between structures using homomorphisms and isomorphisms. Understand, prove, and apply theorems from algebra.
Learning Goals
Students will demonstrate effective oral and written communication of mathematical concepts. Students will demonstrate a comprehensive knowledge of abstract algebra concepts needed by mathematics majors for integration into the (education) workforce and/or graduate study. Students will demonstrate the ability to use the principles of logic and induction in mathematical proofs. Students will demonstrate the ability to determine whether given mathematical structures form groups, rings, or fields using an axiomatic approach. Students will demonstrate the ability to classify mappings as homomorphisms or isomorphisms. Students will be able to use the laws of deductive logic to read and write mathematical proofs.
*The learning goals displayed here are those for one section of this
course as offered in a recent semester, and are provided for the purpose of
information only. The exact learning goals for each course section in a
specific semester will be stated on the syllabus distributed at the start
of the semester, and may differ in wording and emphasis from those shown
here.