Introduction to Abstract Algebra

Jonathan D. H. Smith

ISBN 10: 1420063715 / ISBN 13: 9781420063714

Verlag: CRC Press, 46, 2009

Beschreibung

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.

Bestandsnummer des Verkäufers 3428

Bibliografische Details

• Titel: Introduction to Abstract Algebra
• Verlag: CRC Press, 46
• Erscheinungsjahr: 2009
• Sprache: Englisch
• ISBN-10: 1420063715
• ISBN-13: 9781420063714
• Einband: Hardcover
• Zustand: Near Fine
• Verkäuferkataloge:
  • Mathematics

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

Iowa State University, Ames, USA