Algebra Is Aluffi's Algebra: Chapter 0 the Ultimate Guide for Undergrads?

[micromass]

• Author: Poalo Aluffi
• Title: Algebra: Chapter 0
• Amazon link https://www.amazon.com/dp/0821847813/?tag=pfamazon01-20
• Level: Undergrad

 

[fourier jr]

I want to see this book. I haven't read a bad thing about it yet.

 

[espen180]

This book presents all the familiar topics in algebra, but emphasizes categorical language. Therefore, it is probably best suited as a second or third book on algebra. A student getting their first exposure to algebra from this book will probably be unable to appreciate the elegance of the categorical formalism, and may be unimpressed by the level of abstraction it offers.

 

[Sankaku]

This is one of my favourite textbooks ever. I bought it last year on sale directly from the AMS at a pretty good price. The typesetting is gorgeous and it is printed on high-quality paper, which seems to be getting rare these days.

It is amazingly written, full of insight and humour, and takes a clean approach to incorporating the categorical view from the beginning. My favourite quote so far:

Proving the snake lemma is something that should not be done in public, and it is notoriously useless to write down the verification for others to read: the details are all essentially obvious, but they quickly lead to a notational quagmire. Such proofs are collectively known as the sport of diagram chase, best executed by pointing several fingers at different parts of a diagram on a blackboard while enunciating the elements one is manipulating and stating their fate.

MAA review:
http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=70277

Aluffi's page (with errata):
http://www.math.fsu.edu/~aluffi/

 

[Kreizhn]

I always stress to my colleagues that they take a serious look at this book: it is incredibly insightful, well structured, and just an all around fantastic read. While I often have to (sometimes physically) wrestle Dummit & Foote or Lang from the iron-clasp grip of their fingers, once they pick up a copy of Aluffi they never put it back down.

As more-or-less mentioned above, the entire book is written with homological algebra in the back of the mind, and so the book even begins with a (fairly informal) treatment of category theory. It is true that this may not be the greatest book for a student first trying to break through the fog of abstract mathematics through self-study, but I believe it could easily be adapted into an undergraduate textbook. Aluffi's insight is brilliant and his sense of humor is in full display through the text.

A word of caution though: The book is very new and as of the last time I checked, still in its first edition. Consequently, the book is still riddled with typos. The reader would be well advised to keep the book's errata (located on Aluffi's website) well at hand. I have personally contributed several dozen previously unfound typos to Aluffi, and I've only thoroughly read the first 3/4 of the book.