Topics in Mathematics: Primes of the form x^2+ny^2


In this course, we will start from topics in elementary number theory such as Fermat's little theorem and quadratic reciprocity law to reach the realm of algebraic number theory and class field theory. We will be mainly discussing number theoretic topics around quadratic imaginary fields and their extensions, introducing notions such as ring of integers, fractional ideals, prime behavior, and class number. We will use computational tools such as the software Magma to explicitly compute these invariants we introduce in the course. Students enrolled in this course are expected to have some exposure to abstract algebra (familiarity to terms such as groups, rings, and fields). A prerequisite of Math 430 Modern Algebra is recommended,
Course Attributes: FA NSM; AS NSM

Section 01

Topics in Mathematics: Primes of the form x^2+ny^2
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