Modern Algebra ((4))

Catalog description

A study of the classical algebraic structures in mathematics. Number theory topics include: divisibility theory, induction and well ordering, Euclidean Algorithm, linear Diophantine equations, continued fractions, Euclid's Lemma and unique prime factorization of positive integers, modular arithmetic, and theorems of Euler and Fermat. Abstract Algebra topics include: groups (Zn, Un, Cyclic and Dihedral Groups, Frieze Groups, isometries of the plane, homomorphisms, subgroups, and quotient groups), rings (Z, Zm, Q[x], and matrices), domains (integral and Euclidean), fields (Q, R, C, and Zp), ordered fields, subfields of C, and solutions of polynomials over R and C.