Background and Goals: One of the main goals of the course (along with every course in the algebra sequence) is to expose students to rigorous, proof-oriented mathematics. Students are required to have taken MATH 217, which should provide a first exposure to this style of mathematics. A distinguishing feature of this course is that the abstract concepts are not studied in isolation. Instead, each topic is studied with the ultimate goal being a real-world application.

Content: groups, rings, and fields, including modular arithmetic, polynomial rings, linear algebra over finite fields, and permutation groups. Applications from areas such as error-correcting codes, cryptography, computational algebra, and the Pólya method of enumeration.

Alternatives: MATH 412 (Introduction to Modern Algebra) is a more abstract and proof-oriented course with less emphasis on applications and is better preparation for most pure mathematics courses. MATH 567 is a more advanced course on coding theory.

Subsequent Courses: MATH 312 is one of the alternative prerequisites for MATH 416 (Theory of Algorithms), and several advanced EECS courses make substantial use of the material of MATH 312. Another good follow-up course is MATH 475 (Elementary Number Theory).