MATH 407 - Intro to Modern Algebra & Number Theory

(3.00)

The basic abstract algebraic structures (rings, integral domains, division rings, fields and Boolean algebra) will be introduced, and the fundamental concepts of number theory will be examined from an algebraic perspective. This will be done by examining the construction of the natural numbers from the Peano postulates, the construction of the integers from the natural numbers, the rationals as the field of quotients of the integers, the reals as the ordered field completion of the rationals and the complex numbers as the algebraic completion of the reals. The basic concepts of number theory lead to modular arithmetic; ideals in rings; and to examples of integral domains, division rings and fields as quotient rings. The concept of primes yields the algebraic concepts of unique factorization domains, Euclidean rings, and prime and maximal ideals of rings. Examples of symmetries in number theory and geometry lead to the concept of groups whose fundamental properties and applications will be explored.

Course ID: 55241
Consent: No Special Consent Required
Components: Lecture
Prerequisite/Corequisite: You must have completed MATH 301 with a grade of C or better.