Items related to Introduction to Abstract Algebra (Textbooks in Mathematics)
Synopsis
Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles.
A Quick Introduction to Algebra
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. The author also uses equivalence relations to introduce rational numbers and modular arithmetic as well as to present the first isomorphism theorem at the set level.
The Basics of Abstract Algebra for a First-Semester Course
Subsequent chapters cover orthogonal groups, stochastic matrices, Lagrange’s theorem, and groups of units of monoids. The text also deals with homomorphisms, which lead to Cayley’s theorem of reducing abstract groups to concrete groups of permutations. It then explores rings, integral domains, and fields.
Advanced Topics for a Second-Semester Course
The final, mostly self-contained chapters delve deeper into the theory of rings, fields, and groups. They discuss modules (such as vector spaces and abelian groups), group theory, and quasigroups.
"synopsis" may belong to another edition of this title.
About the Author
Iowa State University, Ames, USA
Review
... The author goes the extra mile to build algebraic concepts by confronting the pedagogic and logical sequence groups-first or rings-first dilemma ... a perfect pure math precursor to Grillet and Knapp’s works. ... The book’s well-thought out sequence supports a set of useful statements on how to use its 11 chapters in a course ... The book is also outstanding for self-study. ... I recommend this book as second to none on abstract algebra for its content, style, and expository efficiency.
―Computing Reviews, January 2011
... a careful treatment of the principal topics of abstract algebra ... This is an attractive book which could be read by everybody because the author supposes not so much knowledge from the reader and gives all the necessary information to continue the reading from [one] chapter to the next. The approach used by the author to introduce modules and group actions is new and innovative. The book is well written ... students and even experienced researchers may benefit strongly from this book. ...
―IACR Book Reviews, October 2010
... This compact book covers topics one would expect to find in an abstract algebra text. ... Smith’s approach is carefully implemented, and topics flow logically from one chapter to the next. The writing is careful and rigorous, yet accessible to hardworking students. The problems are collected at the end of each chapter in two sets, with one set made up of shorter exercises. ... This is an ideal text for an abstract algebra course comprised of mathematics students or CS students who have either a strong minor or second major in mathematics. ...
―Computing Reviews, December 2009
One can trace the author’s research interests to the border between algebra and category theory, which gives the textbook its unique flavour.
―EMS Newsletter, March 2009
The book is well written and flows well. Readers looking for an alternative approach to abstract algebra should consider this volume.
―J.R. Burke, Gonzaga University, CHOICE, July 2009, Vol. 46, No. 11
This book is well written, interesting to read, and the proofs and examples are clear and clean.
―David F. Anderson, Mathematical Reviews, 2009e
"About this title" may belong to another edition of this title.
Search results for Introduction to Abstract Algebra (Textbooks in Mathematics)
Stock Image
INTRODUCTION TO ABSTRACT ALGEBRA
Published by
CRC Press, Boca Raton, London, New York, 2009
ISBN 10: 1420063715
ISBN 13: 9781420063714
Used
Hardcover
First Edition
Seller: Second Story Books, ABAA, Rockville, MD, U.S.A.
Seller rating 4 out of 5 stars
Hardcover. First Edition, First Printing. Octavo, viii, x, 327 pages. In Very Good condition. Bound in the publisher's green cloth bearing white lettering to the spine. Boards have minimal wear. Text block has faint finger marks to the edges. Illustrated. First edition, first printing. NOTE: Shelved in Netdesk Column F, ND-F. 1378217. FP New Rockville Stock. Seller Inventory # 1378217
Quantity: 1 available
Stock Image
Introduction to Abstract Algebra
Seller: Books Puddle, New York, NY, U.S.A.
Seller rating 4 out of 5 stars
Condition: New. pp. 344 Index. Seller Inventory # 26623777
Quantity: 1 available
Stock Image
Introduction to Abstract Algebra
Print on DemandSeller: Majestic Books, Hounslow, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. pp. 344 This item is printed on demand. Seller Inventory # 8272766
Quantity: 1 available
Seller Image
Introduction to Abstract Algebra
Seller: Moraine Books, Ruovesi, Finland
Seller rating 5 out of 5 stars
Hardcover. Condition: Near Fine. Text in English. 327 pp. Stain on the front cover. Faint Scratching. No markings. Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps readers fully understand groups, rings, semigroups, and monoids by rigorouslybuilding concepts from first principles The book begins with a quick introduction to algebra, providing a foundation to exhibit irrational numbers and gain an appreciation of cryptography. It then covers all the basics of abstract algebra, including groups, homomorphisms, rings, and fields. The final chapters deal with more advanced topics, such as factorization, modules, group actions and quasigroups. Study projects at the end of each chapter encompass a range of applications, offering additional opportunities for research. Features Looks at abstract algebra as the main tool underlying discrete mathematics and the digital world Uses semigroups and monoids as stepping stones to present the concepts of groups and rings Presents the fundamentals of abstract algebra, before offering deeper coverage of group and ring theory Provides examples of abstract algebra concepts in matrices and calculus Contains numerous 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. Seller Inventory # 3428
Quantity: 1 available
Stock Image
Introduction to Abstract Algebra
Seller: Biblios, Frankfurt am main, HESSE, Germany
Seller rating 5 out of 5 stars
Condition: New. pp. 344. Seller Inventory # 18623787
Quantity: 1 available
Stock Image
Introduction to Abstract Algebra (Textbooks in Mathematics)
Seller: Mispah books, Redhill, SURRE, United Kingdom
Seller rating 4 out of 5 stars
Hardcover. Condition: Like New. Like New. book. Seller Inventory # ERICA75814200637155
Quantity: 1 available