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When a book is titled "Algebra", it's always a bit ambiguous whether that means "high school algebra" or "abstract algebra". I clicked on this link thinking it

When a book is titled "Algebra", it's always a bit ambiguous whether that means "high school algebra" or "abstract algebra". I clicked on this link thinking it was about group/field/ring/etc theory and wondering what an 'intermediate' treatment of those topics would look like.

gxs 5y ago
I have Artin’s Algebra on my bookshelf, most people who see it always tell me they took it in high school. I’m always impressed.
- alexdowad 5y ago
  Funny stuff. I remember reading a comment by Professor Terry Tao, where he mentioned that one of his weaker areas of mathematics is "algebra". I guess he should have paid more attention in 9th grade math classes!
- nicklaf 5y ago
  You know for a few confused seconds I didn't see the joke about the title and took your statement literally, assuming you were talking about some precocious student, who perhaps had been lucky enough to be tutored or concurrently enrolled while still in high school. Funny story, though: this is the upper division algebra text we used at UC Davis, and one amusing anecdote that our professor relayed was that this book was in fact written for MIT freshmen. Supposedly, this is why the book introduces linear algebra from scratch rather than assuming it as a prerequisite....
  - gxs 5y ago
    Yep, this is the text the professor used in my abstract algebra class at UC Berkeley. I know they use a bunch of other ones. I definitely wouldn’t have been ready to take this as a freshman - my high school math education was definitely lacking.
azalemeth 5y ago
I thought this too -- in fact the contents of this site are about the level of what good 16-year-olds learn in my country. I'd love to read an accessible 'intermediate' introduction to abstract algebra. Something I've inferred -- and would love to be corrected on -- is that in the US there's a relatively well-defined course implied by the words "calculus" or "algebra". I can guess what they are, but I'm not certain, and it seems to change!
- canjobear 5y ago
  You’re right. This book contains what US high schoolers learn in “Algebra 2.”
- admiral33 5y ago
  Before College all math courses in the US 'build up' to Calculus 1 & 2 [1,2] presumably to prepare motivated students for engineering. Calculus 2 is the highest you can go in a public High School before a student will start thinking about starting their college career early or doing an independent study. This one track path is not without its side effects. As you can see by skimming this textbook the information on linear systems is lacking - something that might be more interesting to those who want to study CS. [1]: https://www.khanacademy.org/math/calculus-1 https://www.khanacademy.org/math/calculus-1 [2]: https://www.khanacademy.org/math/calculus-2 https://www.khanacademy.org/math/calculus-2
lkozma 5y ago
That's true, but "high school algebra" in some countries also includes some group/ring theory basics (or it used to).
ginko 5y ago
I thought it'd introduce a concept of 'intermediates' and define an algebra on those.
pwdisswordfish8 5y ago
If it were abstract algebra, the title would be ‘Basic Algebra’. https://golem.ph.utexas.edu/category/2013/12/the_long_grind_of_writing_a_bo.html#c045428 https://golem.ph.utexas.edu/category/2013/12/the_long_grind_...

gxs 5y ago

I have Artin’s Algebra on my bookshelf, most people who see it always tell me they took it in high school. I’m always impressed.

alexdowad 5y ago
Funny stuff. I remember reading a comment by Professor Terry Tao, where he mentioned that one of his weaker areas of mathematics is "algebra". I guess he should have paid more attention in 9th grade math classes!
nicklaf 5y ago
You know for a few confused seconds I didn't see the joke about the title and took your statement literally, assuming you were talking about some precocious student, who perhaps had been lucky enough to be tutored or concurrently enrolled while still in high school. Funny story, though: this is the upper division algebra text we used at UC Davis, and one amusing anecdote that our professor relayed was that this book was in fact written for MIT freshmen. Supposedly, this is why the book introduces linear algebra from scratch rather than assuming it as a prerequisite....
- gxs 5y ago
  Yep, this is the text the professor used in my abstract algebra class at UC Berkeley. I know they use a bunch of other ones. I definitely wouldn’t have been ready to take this as a freshman - my high school math education was definitely lacking.

azalemeth 5y ago

I thought this too -- in fact the contents of this site are about the level of what good 16-year-olds learn in my country. I'd love to read an accessible 'intermediate' introduction to abstract algebra. Something I've inferred -- and would love to be corrected on -- is that in the US there's a relatively well-defined course implied by the words "calculus" or "algebra". I can guess what they are, but I'm not certain, and it seems to change!

canjobear 5y ago
You’re right. This book contains what US high schoolers learn in “Algebra 2.”
admiral33 5y ago
Before College all math courses in the US 'build up' to Calculus 1 & 2 [1,2] presumably to prepare motivated students for engineering. Calculus 2 is the highest you can go in a public High School before a student will start thinking about starting their college career early or doing an independent study. This one track path is not without its side effects. As you can see by skimming this textbook the information on linear systems is lacking - something that might be more interesting to those who want to study CS. [1]: https://www.khanacademy.org/math/calculus-1 https://www.khanacademy.org/math/calculus-1 [2]: https://www.khanacademy.org/math/calculus-2 https://www.khanacademy.org/math/calculus-2

lkozma 5y ago

That's true, but "high school algebra" in some countries also includes some group/ring theory basics (or it used to).

ginko 5y ago

I thought it'd introduce a concept of 'intermediates' and define an algebra on those.

pwdisswordfish8 5y ago

If it were abstract algebra, the title would be ‘Basic Algebra’. https://golem.ph.utexas.edu/category/2013/12/the_long_grind_of_writing_a_bo.html#c045428 https://golem.ph.utexas.edu/category/2013/12/the_long_grind_...