Abstract Algebra
Structures and Applications
Seiten
2015
Apple Academic Press Inc. (Verlag)
978-1-4822-4890-6 (ISBN)
Apple Academic Press Inc. (Verlag)
978-1-4822-4890-6 (ISBN)
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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 Gröbner 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 Gröbner bases."
Choice Reviewed: Recommended
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.
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.
| Reihe/Serie | Textbooks in Mathematics |
|---|---|
| Zusatzinfo | 6 Tables, black and white; 152 Illustrations, black and white |
| Verlagsort | Oakville |
| Sprache | englisch |
| Maße | 210 x 280 mm |
| Gewicht | 1905 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-4822-4890-5 / 1482248905 |
| ISBN-13 | 978-1-4822-4890-6 / 9781482248906 |
| Zustand | Neuware |
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