New York University 4 credits Mathematics
This course is a continuation of the study of algebraic structures started in Abstract Algebra 1. The notion of rings and fields are thoroughly studied, as well as polynomials over rings such as the ring of integers. This course develops ideas to prepare the students to study Galois theory, one of the most important theories in algebra. The topics include Euclidean domains, principal ideal domains, unique factorization domains, imaginary and real quadratic number fields, extension fields and roots of polynomials, constructions with straight edge and compass, and elements of Galois theory. Prerequisites: MATH-UH 2012 or MATH-UA 122 or MATH-UA 132 or MA-UY 1424 or MATH-SHU 131, or MATH-SHU 201.
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