John M. Howie

eBook, PDF

Fields and Galois Theory (eBook, PDF)

Beschreibung

This book provides a gentle introduction to this popular subject. Assuming a background of a first course in abstract algebra, the book covers rings, ideals, quotients and homomorphisms, introduces polynomials, field extensions and splitting fields, gives a description of finite fields, and includes a brief account of the use of such fields in coding theory. It provides a readable, "student-friendly" introduction that takes a more "natural" approach to its subject (compared to the more formal introductions by Stewart and Garling), and that features clear explanations and plenty of worked examples and exercises - with full solutions - to encourage independent study.

Technische Details

• Geräte: PC
• ohne Kopierschutz
• Größe: 1.54MB

Barrierefreiheit

• Text-to-Speech

Autor

John M. Howie, University of St Andrews, UK

Produktdetails

• Verlag: Springer London
• Seitenzahl: 226
• Erscheinungstermin: 5. September 2007
• Englisch
• ISBN-13: 9781846281815
• Artikelnr.: 44133427

Rezensionen

From the reviews:

"This is a short but very good introductory book on abstract algebra, with emphasis on Galois Theory. Very little background in mathematics is required, so that the potential audience for this book range from undergraduate and graduate students, researchers, computer professionals, and the math enthusiasts." (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, July, 2013)

"The author wrote this book to provide the reader with a treatment of classical Galois theory. ... The book is well written. It contains many examples and over 100 exercises with solutions in the back of the book. Sprinkled throughout the book are interesting commentaries and historical comments. The book is

suitable as a textbook for upper level undergraduate or beginning graduate students." (John N. Mordeson, Zentralblatt MATH, Vol. 1103 (5), 2007)

"To write such a book on a widely known but genuinely non-trivial topic is a challenge. ... J. M. Howie did exactly what it takes. And he did it with such vigour and skill that the outcome is indeed absorbing and astounding. ... Every paragraph has been scheduled with utmost care and the proofs are crystal clear. ... the reader will never feel forlorn amidst brilliant theorems, which makes the book such a good read." (J. Lang, Internationale Mathematische Nachrichten, Issue 206, 2007)

"Howie's book ... provides a rigorous and thorough introduction to Galois theory. ... this book would be an excellent choice for anyone with at least some backgound in abstract algebra who seeks an introduction to the study of Galois theory. Summing Up: Highly recommended. Upper-division undergraduates; graduate students." (D. S. Larson, CHOICE, Vol. 43 (10), June, 2006)

"The latest addition to Springer's Undergraduate Mathematics Series is John Howie's Fields and Galois Theory. ... Howie is a fine writer, and the book is very self-contained. ... Iknow that many of my students would appreciate Howie's approach much more as it is not as overwhelming. This book also has a large number of good exercises, all of which have solutions in the back of the book. All in all, Howie has done a fine job writing a book on field theory ... ." (Darren Glass, MathDL, February, 2006)

"The book can serve as a useful introduction to the theory of fields and their extensions. The relevant background material on groups and rings is covered. The text is interspersed with many worked examples, as well as more than 100 exercises, for which solutions are provided at the end." (Chandan Singh Dalawat, Mathematical Reviews, Issue 2006 g)