Algebra: Aus dem Englischen übersetzt von Annette A’Campo (Birkhäuser Advanced Texts Basler Lehrbücher)

by Michael Artin

Diese ungewöhnliche Einführung in lineare Algebra und Algebra ist über viele Jahre aus den Vorlesungsnotizen des Autors gewachsen und zeichnet sich aus durch einen harmonischen Aufbau des behandelten Stoffes. Als eine Besonderheit umfasst dieser nebst den üblichen Inhalten auch die Betonung spezieller Themen wie Symmetrie, lineare Gruppen und quadratische Zahlkörper. Der Text besticht insbesondere durch eine für den Studenten besonders verständliche Präsentation des Stoffes. Zahlreiche Beispiele und Übungsaufgaben erhöhen seinen Wert als studienbegleitende Literatur für die ersten drei bis vier Semester des Studiums der Mathematik und verwandter Gebiete. Dieses sehr lebendig geschriebene Lehrbuch umfasst sowohl lineare Algebra (Matrizen, Vektorräume, lineare Abbildungen und Bilinearformen) als auch Algebra (Gruppen, Ringe, Moduln, Darstellungen von Gruppen und Körpertheorie). Darüberhinaus werden die Themen Symmetrie, lineare Gruppen und quadratische Zahlkörper ausführlicher behandelt. Diese Kapitel illustrieren nicht nur die enge Verbindung zwischen Algebra einerseits und Geometrie bzw. Zahlentheorie andererseits, sie lassen auch besonders viel von der Begeisterung und dem persönlichen Engagement des Autors spüren. Er hat in dieses Buch die Summe der Erfahrungen einfliessen lassen, die er im Laufe vieler Jahre mit Algebravorlesungen gemacht hat. Der Stoff wird sehr verständlich präsentiert und ist mit einer Fülle von Beispielen angereichert, die die abstrakte Begriffsbildungen motivieren und veranschaulichen. Dadurch ist das Buch, das ausserdem zahlreiche Übungsaufgaben enthält, auch zum Selbststudium hervorragend geeignet.

Genres: Mathematics, Algebra, Textbooks, Reference, Science, Nonfiction, Stem

719 pages, Paperback

First published January 1, 1991

Reviews

[Saarthak · Rating 5 out of 5]

I really don't think there is a lot to say about this book other than the fact that it's the most definitive guide to introductory abstract algebra out there. I'm not sure how or why I started working my way through this book but I thoroughly enjoyed every moment of it, from getting stuck on some trivial proofs that I couldn't wrap my head around to having these random 'flashes of insight' while solving an exercise problem. Artin's emphasis on rigorousness while not missing out on intuition is rather remarkable. I'll probably have to re-read this and some other books a couple of times to get a firm grasp on the subject, but needless to say, it was worth the time.

[Ji · Rating 5 out of 5]

This is by default, the best book on algebra.It's delivered so elegantly that anybody can benefit from reading it.

[jillian · Rating 4 out of 5]

notationally i think it’s pretty solid, although it’s definitely an undergrad book. does a good job of familiarizing the reader with the symmetric group! wish there were a section on composition series, solvability, nilpotency, etc. i honestly wouldn’t mind if it replaced chapters on matrix groups with composition series (yeah…it doesn’t even define the commutator subgroup im pretty sure???) certainly leans on linear algebra which, depending on Why you’re learning abstract algebra, can definitely be good. but there’s also a more modern, category theoretic centric approach to learning missing from this book. i think dummit and foote is a better resource for learning algebra beyond a college level understanding

[Arya Tabaie · Rating 5 out of 5]

Written in casual English, nonetheless very thorough and rigorous.
Gives very nice and natural introductions into many "next topics" such as Galois theory and especially Algebraic Number Theory.

[smoh cat · Rating 4 out of 5]

This book is easy to read if I were already introduced to algebra. I had to read Dummit and Foote as a reference. I tend to think of this book as an artistic presentation of algebra rather than a textbook that introduce me systematic to abstract algebra. I wish the author could put down definitions separately from the text so when I need to go back for something it doesn't make me read through remarks just to find a definition.

[DJ]

Taking a modern algebra class with a professor who wrote the book we are using. Seems like a good teacher but I suspect it would be repetitive to read the same arguments at home I'll hear in lecture. This book looked to be an unorthodox approach to modern algebra and came highly recommended. Greatly enjoying it so far.

[Santaraksita · Rating 5 out of 5]

The summum bonum all undergrad algebra texts must strive, and fail, to be.

[Robert · Rating 5 out of 5]

One of the most interesting basic abstract algebra books.

[Yusuke · Rating 4 out of 5]

You should read this together with Dummit & Foote.
Intuition is emphasized though out the book.
I really liked an illustrative discussion on rings.

[Bryce Cai · Rating 2 out of 5]

Textbook used during my AA classes. Its a decent introduction, and is quite concise - the other algebra textbooks I used (Dummit, Knapp, Hungerford, Lang) were generally several times longer. I felt like it lacked examples, and the conciseness seemed to come at the cost of intuitiveness (sections did not adequately prepare for problems). There's also some confusing notation issues. Would recommend using Dummit & Foote or Knapp as a secondary textbook for examples and details/comprehension/further topics.

Also, the index in my edition was completely messed up - I believe it was meant for a different textbook entirely. For example, there's apparently a mention of polynomials on page 480, the same page where its index entry is. There's a supposed mention of "bits" (nonexistent in the book), and not a single index entry for rings, homo/isomorphisms, fields, or even 𝘨𝘳𝘰𝘶𝘱𝘴. As someone who finds indexes immensely useful in math texts this is a pretty big annoyance.

[Shai S. · Rating 4 out of 5]

Artin why did you put an entire undergraduate study of mathematics in one book. At least the quotes are cool and the problems would also be cool if they did not lose me so much sleep. But in a good way?

[Jonah Marcus · Rating 4 out of 5]

Used for an accelerated introduction to group theory. We covered chapters 2, 4, 6, 7, 9, 10. It was the hardest class of my life.

The textbook was quite clear although it can feel a bit meandering at times. The problems are often quite difficult.

[Lolita · Rating 5 out of 5]

An excellent book to know the basics of algebra and progress in it.

[NoName66 · Rating 4 out of 5]

first one year modern algebra class, it is a good book, the only bad thing is no introduction of category theory.

[Satyaki · Rating 5 out of 5]

https://www.youtube.com/playlist?list...

Harvard MATH E-222 Abstract Algebra

[Shalini Shankar · Rating 5 out of 5]

The author has done an excellent job in putting both algebra and linear algebra together...!

[Sarbajit Ghosh · Rating 5 out of 5]

Beautifully written, and threads the density of text needle quite deftly

[Stephen Gwon · Rating 4 out of 5]

Classic reference for algebra

[Siddharth Gupta]

Goof