Galois Theory 4th Edition by Ian Nicholas Stewart (PDF)

Description

Since 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today’s algebra students. New to the Fourth EditionThe replacement of the topological proof of the fundamental theorem of algebra with a simple and plausible result from point-set topology and estimates that will be familiar to anyone who has taken a first course in analysisRevised chapter on ruler-and-compass constructions that results in a more elegant theory and simpler proofsA section on constructions using an angle-trisector since it is an intriguing and direct application of the methods developedA new chapter that takes a retrospective look at what Galois actually did compared to what many assume he didUpdated referencesThis bestseller continues to deliver a rigorous yet engaging treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Next to the somewhat more advanced and dated presentation in van der Waerden’s “Algebra”, this is the clearest, the most complete, and the most reader friendly account of Galois theory. Dr. Stewart shows utmost respect for the reader by avoiding gratuitous abstraction and the jargon of Bourbaki and his acolytes. Of particular value are the lengthy remarks explaining the intuition behind various concepts and placing them in the context of their historical development.Galois theory is regarded as one of the crown achievements of 19th century mathematics, and it led to important developments in mathematics such as group theory and the theory of fields. Paradoxically, it’s original objective, the problem of solving algebraic equations by means of radicals, is of no practical relevance today (and never really was…): any such equation can be solved efficiently and accurately by means of numerical algorithms, regardless of whether its Galois group is solvable or not.

⭐This book is an in depth advanced study of Galois Theory, with additional biographical insight.It will be an additional aid for a course I’ll be teaching.

⭐This text contains considerably more material than I would include in a single undergradute course.

⭐A complex theory explained clearly in a beginner’s level. Even an engineer like myself, with little background in mathematical formalism, can follow the text.

⭐There are some good things about this book, and some worse ones.The good:The book describes Galois theory and for the most part proves the relevant theorems, etc. The examples included are also a plus.The bad:The exercises in this book are just awful. I’ve done many of them, and for the most part they’re only loosely related to the chapter content. It would be nice if the exercises explored the fascinating content of the chapters in greater depth rather than sending the reader down a variety of unrelated rabbit holes.It’s also really disappointing to see words like “clearly” thrown about in several of the proofs in this book. I can fill in the gaps of the proofs with a little effort, but it makes the reading experience a lot more confusing.This is the only Galois theory book I’ve personally read, but based on what I’ve heard in different circles, Cox’s book might be a better alternative.

⭐I treated myself to the hardback edition, which as you see, is significantly more expensive than the paperback. Disappointingly, the book is bound just like a cheap paperback but in a piss-thin cardboard cover with no dust-jacket. The book will fall apart easily with use, and the low score represents this complaint.The content does seem to be excellent – but get the paperback!

⭐I studied Galois theory from the previous edition of this book at university 6 years ago, and bought this book recently after feeling nostalgic for the good old days.This is a solid book in the subject.

⭐Eliminati i madornali errori nelle formule della terza edizione, ora il testo è sostanzialmente corretto. Ma ci sono parecchi aspetti da migliorare, come i troppo pochi esempi di applicazione della teoria, e l’assenza delle soluzioni degli esercizi proposti, almeno di quelli marcati con l’asterisco perché tutt’altro che banali.El libro está muy bien y explica de forma sencilla temas complicados.Lo que es una lástima es que un libro que no es precisamente barato tenga una impresión tan mala. La letra es demasiado pequeña, lo que hace minúsculos los subíndices en algunas fórmulas y las imágenes parecen desenfocadas.Una lástima que cada vez se cuiden menos estos aspectos de impresión y, mucho más, en un libro de este precio.Es un libro que añade una vision de la teoria de Galois. Está muy bien en la descripción de la teoria

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