An Introduction to Abstract Algebra

類似書籍推薦給您

This book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level. It treats set theory, group theory, ring and ideal theory, and field theory (including Galois theory), and culminates with a treatment of Dedekind rings, including rings of algebraic integers. In addition to treating standard topics, it contains material not often dealt with in books at this level. It provides a fresh perspective on the subjects it covers, with, in particular, distinctive treatments of factorization theory in integral domains and of Galois theory. As an introduction, it presupposes no prior knowledge of abstract algebra, but provides a well-motivated, clear, and rigorous treatment of the subject, illustrated by many examples. Written with an eye toward number theory, it contains numerous applications to number theory (including proofs of Fermat's theorem on sums of two squares and of the Law of Quadratic Reciprocity) and serves as an excellent basis for further study in algebra in general and number theory in particular. Each of its chapters concludes with a variety of exercises ranging from the straightforward to the challenging in order to reinforce students' knowledge of the subject. Some of these are particular examples that illustrate the theory while others are general results that develop the theory further.

BASIC ABSTRACT ALGEBRA: EXERCISES AND SOLUTIONS

類似書籍推薦給您

This book is mainly intended for first-year University students who undertake a basic abstract algebra course, as well as instructors. It contains the basic notions of abstract algebra through solved exercises as well as a "True or False" section in each chapter. Each chapter also contains an essential background section, which makes the book easier to use. Sample Chapter(s) Introduction CHAPTER 3: Binary Relations Request Inspection Copy Contents: Introduction Sets and Logic Mappings Binary Relations Groups Rings and Fields Polynomials and Rational Fractions Bibliography Index Readership: First and second year mathematics and computer science students interested in abstract algebra. Also good for instructors.