id: 06491690
dt: b
an: 2015f.00761
au: Smith, Jonathan D.H.
ti: Introduction to abstract algebra. 2nd ed.
so: Textbooks in Mathematics. Boca Raton, FL: CRC Press (ISBN
978-1-4987-3161-4/hbk; 978-1-4987-3162-1/ebook). xii, 331~p. (2016).
py: 2016
pu: Boca Raton, FL: CRC Press
la: EN
cc: H45
ut: textbook; algebra; groups; group actions; permutations; modules; fields;
quasigroups
ci: Zbl 1157.00001
li: doi:10.1201/b19403-13
ab: Publisher’s description: The book presents abstract algebra as the main
tool underlying discrete mathematics and the digital world. It avoids
the usual groups first/rings first dilemma by introducing semigroups
and monoids, the multiplicative structures of rings, along with groups.
This new edition of a widely adopted textbook covers applications from
biology, science, and engineering. It offers numerous updates based on
feedback from first edition adopters, as well as improved and
simplified proofs of a number of important theorems. Many new exercises
have been added, while new study projects examine skewfields,
quaternions, and octonions. The first three chapters of the book show
how functional composition, cycle notation for permutations, and matrix
notation for linear functions provide techniques for practical
computation. These three chapters provide a quick introduction to
algebra, sufficient to exhibit irrational numbers or to gain a taste of
cryptography. Chapters four through seven cover abstract groups and
monoids, orthogonal groups, stochastic matrices, Lagrange’s theorem,
groups of units of monoids, homomorphisms, rings, and integral domains.
The first seven chapters provide basic coverage of abstract algebra,
suitable for a one-semester or two-quarter course. Each chapter
includes exercises of varying levels of difficulty, chapter notes that
point out variations in notation and approach, and study projects that
cover an array of applications and developments of the theory. The
final chapters deal with slightly more advanced topics, suitable for a
second-semester or third-quarter course. These chapters delve deeper
into the theory of rings, fields, and groups. They discuss modules,
including vector spaces and abelian groups, group theory, and
quasigroups. This textbook is suitable for use in an undergraduate
course on abstract algebra for mathematics, computer science, and
education majors, along with students from other STEM fields. See the
review of the first edition in [Zbl 1157.00001].
rv: