Honors Introduction to Algebra

4.0 credits · Undergraduate

Honors version of a course in abstract algebra, which treats the subject from an abstract and axiomatic viewpoint, including universal mapping properties. Topics include groups, groups acting on sets, Sylow theorems; rings, Euclidean domains, factorization, structure theorem of finitely generated modules over a principal ideal domain; fields, root adjunction, finite fields, introduction to Galois theory. The course emphasizes understanding the theory with proofs in both homework and exams. MATH 4330-MATH 4340 is recommended for undergraduates who plan to attend graduate school in mathematics. For a less theoretical course that covers subject matter similar to MATH 4340, see MATH 3340.