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What is a good textbook in abstract algebra for the beginner?

umanwizard 8y ago
It depends what "beginner" means -- what's your level of sophistication? Are you a budding mathematician or just an interested programmer?
- deleted 8y ago
  [deleted]
- autocorrect23 8y ago
  Assume I know 0 math and want to learn mathematics for mathematics sake. What is the most gentle intro to algebra book?
  - Koshkin 8y ago
    Pinter's A Book of Abstract Algebra.
  - smadge 8y ago
    My undergraduate Abstract Algebra course used Gallian’s “Contemporary Abstract Algebra.” Unfortunately if you are truly looking for an introduction assuming no mathematics, you will need to learn high school algebra and a bit about sets and proofs first.
  - umanwizard 8y ago
    If you know 0 math I would start with basic arithmetic (+, -, *, /) before doing anything else.
  - loparal 8y ago
    True Beauty of Math Volumes I and II. These build up math from the ground up starting with sets and assume you have zero knowledge of math. What's cool is that you don't use any theorems, structures, or notation that you haven't proven or introduced previously in one of the books. I've found them to be very valuable in both understanding the topics that they cover and giving an intuitive understanding of math as process (which the all the classes I took in college tended to gloss over). The first volume is roughly about set theory and the second volume is roughly about abstract algebra. https://truebeautyofmath.com/ https://truebeautyofmath.com/ https://www.amazon.com/True-Beauty-Math-Foundations/dp/1512065919 https://www.amazon.com/True-Beauty-Math-Foundations/dp/15120... https://www.amazon.com/True-Beauty-Math-Giving-Life/dp/1544830084 https://www.amazon.com/True-Beauty-Math-Giving-Life/dp/15448...
    - autocorrect23 8y ago
      Bought the first book. Thanks for the recommendation!
pdpi 8y ago
A good recent release is Bartosz Milewski's Category Theory for Programmers. https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p...
danharaj 8y ago
I like Algebra by Mac Lane and Birkhoff, if by beginner you mean undergraduate.
zozbot123 8y ago
Somewhat less of a "textbook", but good at showing applications of category theory - Fong, Spivak: Seven Sketches in Compositionality https://arxiv.org/abs/1803.05316 https://arxiv.org/abs/1803.05316 (Notably, this includes application to a "graphical" treatment of fairly-elementary linear algebra, which a different HN user is mentioning even as I write this, as a part of math where CT cannot possibly be useful and will only ever confuse students!)
Koshkin 8y ago
In the order of increasing complexity and/or volume: Pinter, Fraleigh, Rotman, Dummit & Foote.

It depends what "beginner" means -- what's your level of sophistication? Are you a budding mathematician or just an interested programmer?

deleted 8y ago
[deleted]
autocorrect23 8y ago
Assume I know 0 math and want to learn mathematics for mathematics sake. What is the most gentle intro to algebra book?
- Koshkin 8y ago
  Pinter's A Book of Abstract Algebra.
- smadge 8y ago
  My undergraduate Abstract Algebra course used Gallian’s “Contemporary Abstract Algebra.” Unfortunately if you are truly looking for an introduction assuming no mathematics, you will need to learn high school algebra and a bit about sets and proofs first.
- umanwizard 8y ago
  If you know 0 math I would start with basic arithmetic (+, -, *, /) before doing anything else.
- loparal 8y ago
  True Beauty of Math Volumes I and II. These build up math from the ground up starting with sets and assume you have zero knowledge of math. What's cool is that you don't use any theorems, structures, or notation that you haven't proven or introduced previously in one of the books. I've found them to be very valuable in both understanding the topics that they cover and giving an intuitive understanding of math as process (which the all the classes I took in college tended to gloss over). The first volume is roughly about set theory and the second volume is roughly about abstract algebra. https://truebeautyofmath.com/ https://truebeautyofmath.com/ https://www.amazon.com/True-Beauty-Math-Foundations/dp/1512065919 https://www.amazon.com/True-Beauty-Math-Foundations/dp/15120... https://www.amazon.com/True-Beauty-Math-Giving-Life/dp/1544830084 https://www.amazon.com/True-Beauty-Math-Giving-Life/dp/15448...
  - autocorrect23 8y ago
    Bought the first book. Thanks for the recommendation!

pdpi 8y ago

A good recent release is Bartosz Milewski's Category Theory for Programmers. https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ https://bartoszmilewski.com/2014/10/28/category-theory-for-p...

danharaj 8y ago

I like Algebra by Mac Lane and Birkhoff, if by beginner you mean undergraduate.

zozbot123 8y ago

Somewhat less of a "textbook", but good at showing applications of category theory - Fong, Spivak: Seven Sketches in Compositionality https://arxiv.org/abs/1803.05316 https://arxiv.org/abs/1803.05316 (Notably, this includes application to a "graphical" treatment of fairly-elementary linear algebra, which a different HN user is mentioning even as I write this, as a part of math where CT cannot possibly be useful and will only ever confuse students!)

Koshkin 8y ago

In the order of increasing complexity and/or volume: Pinter, Fraleigh, Rotman, Dummit & Foote.