Abstract Algebra
Structures and Applications
1st Edition
Published on 17. July 2015
Book
Hardback
720 pages
978-1-4822-4890-6 (ISBN)
Description
A Discovery-Based Approach to Learning about Algebraic Structures
Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence.
The book presents the core topics of structures in a consistent order:
Definition of structure
Motivation
Examples
General properties
Important objects
Description
Subobjects
Morphisms
Subclasses
Quotient objects
Action structures
Applications
The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics.
"Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Groebner bases."
Choice Reviewed: Recommended
Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence.
The book presents the core topics of structures in a consistent order:
Definition of structure
Motivation
Examples
General properties
Important objects
Description
Subobjects
Morphisms
Subclasses
Quotient objects
Action structures
Applications
The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics.
"Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Groebner bases."
Choice Reviewed: Recommended
Reviews / Votes
"... lucid, detailed, and versatile main text comes with a wealth of illustrating examples and very instructive exercises in each single section of the book, and each chapter ends with a section containing project ideas (and hints) to challenge the student to write her or his own investigative or expository papers on related topics. ... an excellent introduction to the principles of abstract algebra for upper undergraduate and graduate students, and a valuable source for instructors likewise. No doubt, this text is a highly welcome addition to the already existing plethora of primers on abstract algebra in the mathematical literature."-Zentralblatt MATH 1323
"This is a text for a serious upper-level undergraduate course in abstract algebra. It adopts a 'groups first' approach to the subject, and, although it starts from scratch, winds up covering more than enough material to fill out two semesters. The topic coverage is very extensive for an undergraduate text ... The author does an excellent job of balancing theory with applications. ... The inclusion of all the topics described above and the large number of exercises, examples and projects make for an undeniably interesting text ... a well-written book with interesting features ... "
-MAA Reviews, November 2015 "... lucid, detailed, and versatile main text comes with a wealth of illustrating examples and very instructive exercises in each single section of the book, and each chapter ends with a section containing project ideas (and hints) to challenge the student to write her or his own investigative or expository papers on related topics. ... an excellent introduction to the principles of abstract algebra for upper undergraduate and graduate students, and a valuable source for instructors likewise. No doubt, this text is a highly welcome addition to the already existing plethora of primers on abstract algebra in the mathematical literature."
-Zentralblatt MATH 1323
"This is a text for a serious upper-level undergraduate course in abstract algebra. It adopts a 'groups first' approach to the subject, and, although it starts from scratch, winds up covering more than enough material to fill out two semesters. The topic coverage is very extensive for an undergraduate text ... The author does an excellent job of balancing theory with applications. ... The inclusion of all the topics described above and the large number of exercises, examples and projects make for an undeniably interesting text ... a well-written book with interesting features ... "
-MAA Reviews, November 2015
"Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Groebner bases."
Choice Reviewed: Recommended
More details
Series
Language
English
Place of publication
Oakville
Canada
Target group
College/higher education
Illustrations
152 s/w Abbildungen, 6 s/w Tabellen
6 Tables, black and white; 152 Illustrations, black and white
Dimensions
Height: 280 mm
Width: 210 mm
Weight
1905 gr
ISBN-13
978-1-4822-4890-6 (9781482248906)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Book
07/2022
2nd Edition
Chapman & Hall/CRC
€173.20
Shipment within 10-20 days
Person
Stephen Lovett is an associate professor of mathematics at Wheaton College. He is a member of the Mathematical Association of America, American Mathematical Society, and Association of Christians in the Mathematical Sciences. He earned a PhD from Northeastern University. His research interests include commutative algebra, algebraic geometry, differential geometry, cryptography, and discrete dynamical systems.
Content
SET THEORY. NUMBER THEORY. GROUPS. QUOTIENT GROUPS. RINGS. DIVISIBILITY IN COMMUTATIVE RINGS. FIELD EXTENSIONS. GROUP ACTIONS. CLASSIFICATION OF GROUPS. MODULES AND ALGEBRAS. GALOIS THEORY. MULTIVARIABLE POLYNOMIAL RINGS. CATEGORIES. APPENDICES. LIST OF NOTATIONS. BIBLIOGRAPHY. INDEX.