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Is there a good textbook that covers these? I am primarily interested in a computer science perspective to these algebraic structures.

by wsxcde 7y ago

earthicus 7y ago
Many of them feature prominently in Stepanov's books, Elements of Programming and From Mathematics to Generic Programming. 'Elements' is a technical monograph, while the other is a more lightweight read, halfway between semi-pop-science and a textbook. There's also an old textbook by Birkhoff & Bartee called 'Modern Applied Algebra' that i like. It's not super duper computer science-y but might be worth browsing through the table of contents at least. Edit: I snapped some photos of the table of contents since you can't see it on the amazon page: https://imgur.com/a/RFIf4CD https://imgur.com/a/RFIf4CD
gtycomb 7y ago
'Topics In Algebra' by I.N.Herstein. Back in college years this was my first book. Despite many other books (which might look easier) I always came back here because of the care it takes to walk through well crafted progression of concepts. (Not a 'computer science' book but you will need something like this for the Algebra part)
nandemo 7y ago
My favourite abstract algebra textbook is Fraleigh's A First Course in Abstract Algebra. Unlike the article here, which just dumps you a bunch of definitions, the book introduces each structure with proper motivation. It's not a CS approach though. https://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/0201763907 https://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/... (the 1-star reviews apply to the Kindle version, not the contents. Just get the paperback and you'll be fine) If you want a CS approach I suggest learning basic Haskell then tackling the fantastic Typeclassopedia. The downside is you'll be missing on structures/theorems that are super useful in math but not that useful in programming. https://wiki.haskell.org/Typeclassopedia https://wiki.haskell.org/Typeclassopedia
- commandlinefan 7y ago
  Wow, if the kindle edition looks anything like the preview, I understand the 1-star reviews - it's not just bad, it's a travesty. The pages aren't even in order, and some of the diagrams are missing.
jvvw 7y ago
Just as a warning most maths algebra beginner textbooks will focus on groups, rings and fields and not talk about most of the other structures mentioned (including Fragleigh and Herstein recommended by others - they are incredibly different styles, and although I have extremely fond memories of Herstein, there are better books than those two especially if you aren't actually doing a maths degree, but my knowledge of textbooks is 20 years out of date). On the other hand once you have a good grasp of a few structures, learning about and understanding others becomes much easier. I guess it all depends on why you want to learn about them and what you want to do with them
hackernews7899 7y ago
Check out “Seven Sketches in Compositionality“ by Spivak and Fong. You can find a free copy provided by the authors online. It is an introductory book to applied category theory.
- wsxcde 7y ago
  This was a great recommendation, thanks!

Is there a good textbook that covers these? I am primarily interested in a computer science perspective to these algebraic structures.

by wsxcde 7y ago

Is there a good textbook that covers these? I am primarily interested in a computer science perspective to these algebraic structures.

earthicus 7y ago

Many of them feature prominently in Stepanov's books, Elements of Programming and From Mathematics to Generic Programming. 'Elements' is a technical monograph, while the other is a more lightweight read, halfway between semi-pop-science and a textbook. There's also an old textbook by Birkhoff & Bartee called 'Modern Applied Algebra' that i like. It's not super duper computer science-y but might be worth browsing through the table of contents at least. Edit: I snapped some photos of the table of contents since you can't see it on the amazon page: https://imgur.com/a/RFIf4CD https://imgur.com/a/RFIf4CD

gtycomb 7y ago

'Topics In Algebra' by I.N.Herstein. Back in college years this was my first book. Despite many other books (which might look easier) I always came back here because of the care it takes to walk through well crafted progression of concepts. (Not a 'computer science' book but you will need something like this for the Algebra part)

nandemo 7y ago

My favourite abstract algebra textbook is Fraleigh's A First Course in Abstract Algebra. Unlike the article here, which just dumps you a bunch of definitions, the book introduces each structure with proper motivation. It's not a CS approach though. https://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/0201763907 https://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/... (the 1-star reviews apply to the Kindle version, not the contents. Just get the paperback and you'll be fine) If you want a CS approach I suggest learning basic Haskell then tackling the fantastic Typeclassopedia. The downside is you'll be missing on structures/theorems that are super useful in math but not that useful in programming. https://wiki.haskell.org/Typeclassopedia https://wiki.haskell.org/Typeclassopedia

commandlinefan 7y ago
Wow, if the kindle edition looks anything like the preview, I understand the 1-star reviews - it's not just bad, it's a travesty. The pages aren't even in order, and some of the diagrams are missing.

jvvw 7y ago

Just as a warning most maths algebra beginner textbooks will focus on groups, rings and fields and not talk about most of the other structures mentioned (including Fragleigh and Herstein recommended by others - they are incredibly different styles, and although I have extremely fond memories of Herstein, there are better books than those two especially if you aren't actually doing a maths degree, but my knowledge of textbooks is 20 years out of date). On the other hand once you have a good grasp of a few structures, learning about and understanding others becomes much easier. I guess it all depends on why you want to learn about them and what you want to do with them

hackernews7899 7y ago

Check out “Seven Sketches in Compositionality“ by Spivak and Fong. You can find a free copy provided by the authors online. It is an introductory book to applied category theory.

wsxcde 7y ago
This was a great recommendation, thanks!