id: 06351554
dt: b
an: 2015b.00742
au: Anderson, Marlow; Feil, Todd
ti: A first course in abstract algebra. Rings, groups, and fields. 3rd ed.
so: Boca Raton, FL: CRC Press (ISBN 978-1-4822-4552-3/hbk). xvi, 536~p. (2015).
py: 2015
pu: Boca Raton, FL: CRC Press
la: EN
cc: H45
ut: abstract algebra; rings; groups; fields; textbook
ci: Zbl 1093.00002
li:
ab: Publisher’s description: Like its popular predecessors, this book
develops ring theory first by drawing on students’ familiarity with
integers and polynomials. This unique approach motivates students in
the study of abstract algebra and helps them understand the power of
abstraction. The authors introduce groups later on using examples of
symmetries of figures in the plane and space as well as permutations.
New to the third edition: ‒ makes it easier to teach unique
factorization as an optional topic; ‒ reorganizes the core material
on rings, integral domains, and fields; ‒ includes a more detailed
treatment of permutations; ‒ introduces more topics in group theory,
including new chapters on Sylow theorems; ‒ provides many new
exercises on Galois theory. The text includes straightforward
exercises within each chapter for students to quickly verify facts,
warm-up exercises following the chapter that test fundamental
comprehension, and regular exercises concluding the chapter that
consist of computational and supply-the-proof problems. Historical
remarks discuss the history of algebra to underscore certain
pedagogical points. Each section also provides a synopsis that presents
important definitions and theorems, allowing students to verify the
major topics from the section. See the review of the second edition in
[Zbl 1093.00002].
rv: