An Introduction to Abstract Algebra: Sets, Groups, Rings, and Fields - Steven H Weintraub

Descriere An Introduction to Abstract Algebra: Sets, Groups, Rings, and Fields - Steven H Weintraub

\n \nThis book is a textbook for a semester-long or year-long introductory course in abstract algebra at the upper undergraduate or beginning graduate level.\n \n \n\n \nIt 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.\n \n \n\n \nIn 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.\n \n \n\n \nAs 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.\n \n \n\n \nEach 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.\n

Detalii

Brand

World Scientific Publishing Company

Categorie

ENSTK

EAN / GTIN

9789811247552

Magazine

1

Disponibilitate

in stock