Elements of Abstract Algebra

Nonfiction, Science & Nature, Mathematics, Algebra
Cover of the book Elements of Abstract Algebra by Allan Clark, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Allan Clark ISBN: 9780486140353
Publisher: Dover Publications Publication: July 6, 2012
Imprint: Dover Publications Language: English
Author: Allan Clark
ISBN: 9780486140353
Publisher: Dover Publications
Publication: July 6, 2012
Imprint: Dover Publications
Language: English

This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.
Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory) reviews linear algebra and introduces fields as a prelude to Galois theory. In addition there is a full discussion of the constructibility of regular polygons. Chapter IV (Galois Theory) gives a thorough treatment of this classical topic, including a detailed presentation of the solvability of equations in radicals that actually includes solutions of equations of degree 3 and 4 ― a feature omitted from all texts of the last 40 years. Chapter V (Ring Theory) contains basic information about rings and unique factorization to set the stage for classical ideal theory. Chapter VI (Classical Ideal Theory) ends with an elementary proof of the Fundamental Theorem of Algebraic Number Theory for the special case of Galois extensions of the rational field, a result which brings together all the major themes of the book.
The writing is clear and careful throughout, and includes many historical notes. Mathematical proof is emphasized. The text comprises 198 articles ranging in length from a paragraph to a page or two, pitched at a level that encourages careful reading. Most articles are accompanied by exercises, varying in level from the simple to the difficult.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.
Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory) reviews linear algebra and introduces fields as a prelude to Galois theory. In addition there is a full discussion of the constructibility of regular polygons. Chapter IV (Galois Theory) gives a thorough treatment of this classical topic, including a detailed presentation of the solvability of equations in radicals that actually includes solutions of equations of degree 3 and 4 ― a feature omitted from all texts of the last 40 years. Chapter V (Ring Theory) contains basic information about rings and unique factorization to set the stage for classical ideal theory. Chapter VI (Classical Ideal Theory) ends with an elementary proof of the Fundamental Theorem of Algebraic Number Theory for the special case of Galois extensions of the rational field, a result which brings together all the major themes of the book.
The writing is clear and careful throughout, and includes many historical notes. Mathematical proof is emphasized. The text comprises 198 articles ranging in length from a paragraph to a page or two, pitched at a level that encourages careful reading. Most articles are accompanied by exercises, varying in level from the simple to the difficult.

More books from Dover Publications

Cover of the book The New Life/La Vita Nuova by Allan Clark
Cover of the book The Art Nouveau Style Book of Alphonse Mucha by Allan Clark
Cover of the book Art Deco Interiors by Allan Clark
Cover of the book Theory of Electromagnetic Wave Propagation by Allan Clark
Cover of the book Nonlinear Transformations of Random Processes by Allan Clark
Cover of the book Introduction to Real Analysis by Allan Clark
Cover of the book Pictorial Archive of Lace Designs by Allan Clark
Cover of the book Iberia and España by Allan Clark
Cover of the book 150 Masterpieces of Drawing by Allan Clark
Cover of the book The Nature and Power of Mathematics by Allan Clark
Cover of the book Problems and Worked Solutions in Vector Analysis by Allan Clark
Cover of the book Real Analysis by Allan Clark
Cover of the book Bevels and Jewels Stained Glass Pattern Book by Allan Clark
Cover of the book The Narrative of Arthur Gordon Pym of Nantucket by Allan Clark
Cover of the book The Boarded-Up House by Allan Clark
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy