MATH 378 - Number Systems

Units: 3

Numbers: natural, rational, real, and complex. Algebraic laws: commutative, associative, and distributive. Brief introduction to groups, rings, and fields. Divisibility and unique factorization for integers and polynomials. Integers modulo n as finite rings and fields. The rational numbers as a non-complete countable ordered field. The real numbers as a complete uncountable ordered field. Sequences and limits including Cauchy sequences, lim inf and lim sup. Complex numbers including De Moivre’s theorem and related trigonometric identities. Factoring polynomials over the various number systems. The Fundamental Theorem of Algebra.

Prerequisite(s): for undergraduates and enrollment requirement(s) for graduate students: MATH 350 or MATH 370 with a grade of C (2.0) or better.