Undergraduate Algebra
Lang, Serge.
creator
author.
SpringerLink (Online service)
text
xxu
2005
Third Edition.
monographic
eng
access
XII, 389 p. online resource.
Undergraduate Algebra is a text for the standard undergraduate algebra course. It concentrates on the basic structures and results of algebra, discussing groups, rings, modules, fields, polynomials, finite fields, Galois Theory, and other topics. The author has also included a chapter on groups of matrices which is unique in a book at this level. Throughout the book, the author strikes a balance between abstraction and concrete results, which enhance each other. Illustrative examples accompany the general theory. Numerous exercises range from the computational to the theoretical, complementing results from the main text. For the third edition, the author has included new material on product structure for matrices (e.g. the Iwasawa and polar decompositions), as well as a description of the conjugation representation of the diagonal group. He has also added material on polynomials, culminating in Noah Snyderâ€™s proof of the Mason-Stothers polynomial abc theorem. About the First Edition: The exposition is down-to-earth and at the same time very smooth. The book can be covered easily in a one-year course and can be also used in a one-term course...the flavor of modern mathematics is sprinkled here and there. - Hideyuki Matsumura, Zentralblatt.
The Integers -- Groups -- Rings -- Polynomials -- Vector Spaces and Modules -- Some Linear Groups -- Field Theory -- Finite Fields -- The Real and Complex Numbers -- Sets.
by Serge Lang.
Mathematics
Algebra
Field theory (Physics)
Mathematics
Algebra
Field Theory and Polynomials
QA150-272
512
Springer eBooks
Undergraduate Texts in Mathematics
9780387274751
http://dx.doi.org/10.1007/0-387-27475-8
http://dx.doi.org/10.1007/0-387-27475-8
100301
20180115171353.0
978-0-387-27475-1