Irving Integers, Polynomials, and Rings

A Course in Algebra
Erscheinungsjahr 2006
ISBN: 978-0-387-21831-1
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 288 Seiten, eBook

Reihe: Undergraduate Texts in Mathematics

This book began life as a set of notes that I developed for a course at the University of Washington entitled Introduction to Modern Algebra for Tea- ers. Originally conceived as a text for future secondary-school mathematics teachers, it has developed into a book that could serve well as a text in an - dergraduatecourseinabstractalgebraoracoursedesignedasanintroduction to higher mathematics. This book di?ers from many undergraduate algebra texts in fundamental ways; the reasons lie in the book’s origin and the goals I set for the course. The course is a two-quarter sequence required of students intending to f- ?ll the requirements of the teacher preparation option for our B.A. degree in mathematics, or of the teacher preparation minor. It is required as well of those intending to matriculate in our university’s Master’s in Teaching p- gram for secondary mathematics teachers. This is the principal course they take involving abstraction and proof, and they come to it with perhaps as little background as a year of calculus and a quarter of linear algebra. The mathematical ability of the students varies widely, as does their level of ma- ematical interest.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Irving, Ronald S.

Inhaltsverzeichnis

Introduction: The McNugget Problem.- Introduction: The McNugget Problem.- Integers.- Induction and the Division Theorem.- The Euclidean Algorithm.- Congruences.- Prime Numbers.- Rings.- Euler’ Theorem.- Binomial Coefficients.- Polynomials.- Polynomials and Roots.- Polynomials with Real Coefficients.- Polynomials with Rational Coefficients.- Polynomial Rings.- Quadratic Polynomials.- Polynomial Congruence Rings.- All Together Now.- Euclidean Rings.- The Ring of Gaussian Integers.- Finite Fields.