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Modern Algebra

No, I am not one of these. And are you one of these silly folks who would refer to advanced course as "math" ?
Why wouldn't I? I referred to myself as a "math major". What should I have referred to them as?

(Yes, majoring in math was probably silly, I can't deny that, but what choice did I have? I couldn't major in physics -- the math was too hard!)

Happy Pi Day! :beers:
 
No, I am not one of these. And are you one of these silly folks who would refer to advanced course as "math" ?
Why wouldn't I? I referred to myself as a "math major". What should I have referred to them as?
Nice to meet you Major Math, but I was talking about course names, and no course in any university is called as "math"
 
Are you one of those silly folks who think it's not math, it's "maths"?
There is a name for folks like that. They are called 'English speakers'.

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View attachment 6071
Where "simplified" means the useless letters have been stripped out of the words. So have you learned Strine yet or are you still trying to vote Labour? ;)
 
There are 10 kinds of people in the world: those who understand binary and those who don't. :D


Are you one of those silly folks who think it's not math, it's "maths"?
No, I am not one of these. And are you one of these silly folks who would refer to advanced course as "math" ?
And yes, it's "algebras" - elementary algebra, linear algebra, and so on.

I find this discussion fascinating--mostly because I enjoy the subject matter of word usage. Also, I strive to be more than merely fluent in my native language, although I must admit (or at least do admit) that I'm neither an expert in the usage of the words in question nor the actual subject matter.

Although I have not solidified my position, I am leaning against your objection to their usage. That's not meant to suggest that I have formed a solid opinion regarding your usage. I have a few thoughts on the matter, but my confidence in articulating them isn't high enough as of yet to engage argumentatively.

What does it mean to say of something that it is algebra? From your persective, it would seem to follow that elementary algebra is not algebra but instead an algebra. So, are there different kinds of algebra, or are there simply different aspects of algebra that can be put into various subgroups?

I'm not prepared to make a case, but I think the two-worded term "elementary algebra" (a single term in its own right--with a reference independent of a derivative simple summation of meanings) classifies rather than enumerates algebra. I'm not sure there are different kinds of algebra as there are different kinds of vehicles. I would need to be more intune with what algebra is to hold a higher level of confidence, but the term, "algebra" seems to reference something that is very broad and encompassing.
 
Guys. Can we take the grammar discussion elsewhere? I for one came here to learn a little bit about groups, rings, fields... etc. Me no care where 's' goes.
 
Guys. Can we take the grammar discussion elsewhere? I for one came here to learn a little bit about groups, rings, fields... etc. Me no care where 's' goes.
Mathematics is a language of science so grammar is important.
And rings, fields are supposed to be taught/explained in school, groups - not so much.
 
Guys. Can we take the grammar discussion elsewhere? I for one came here to learn a little bit about groups, rings, fields... etc. Me no care where 's' goes.
Mathematics is a language of science so grammar is important.
And rings, fields are supposed to be taught/explained in school, groups - not so much.

Nonsense. Again. Groups are a major topic in algebra and every undergraduate mathematics degree includes courses that cover group theory.

Either get a clue or please stop posting in my thread.
 
Mathematics is a language of science so grammar is important.
And rings, fields are supposed to be taught/explained in school, groups - not so much.

Nonsense. Again. Groups are a major topic in algebra and every undergraduate mathematics degree includes courses that cover group theory.

Either get a clue or please stop posting in my thread.
I said in schools, as in high schools. So nonsense is all yours.

As for undergrads and Group theory then I don't know much about what they learn, but I once saw a math grad student who had troubles with complex numbers, you can only imagine how much troubles with group theory.
 
It is not algebra, it's algebras.
Just to upset the grammar police again.
Shouldn't it be algebrae rather than algebras?

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I'm scheduled to teach a course on abstract algebra next semester, so I've been considering textbooks for potential adoption. I found this text, which is my front-runner at the moment: Abstract Algebra: Theory and Applications by Judson. It's a free and open-source textbook, and from my initial inspection it seems well written and edited. It also has computational material in Sage to complement the theoretical bits.

Other contenders: A First Course in Abstract Algebra by Fraleigh, and Algebra by Artin.

I figured I'd post the link in case anyone was interested and I'd also ask if anyone has a modern algebra text they'd recommend.

Depending on demand, I may also post my lecture notes here. (But, since this is my first time teaching algebra, you'll just have to wait until I write them first...)
I was going to suggest Euclid but of course he is geometry and you want algebra.
 
This is sad.

The forum is so hostile (because it has so many members inclined towards replying in a hostile manner) that even a thread about a math course resulted in conflict.
 
Nonsense. Again. Groups are a major topic in algebra and every undergraduate mathematics degree includes courses that cover group theory.

Either get a clue or please stop posting in my thread.
I said in schools, as in high schools. So nonsense is all yours.

As for undergrads and Group theory then I don't know much about what they learn, but I once saw a math grad student who had troubles with complex numbers, you can only imagine how much troubles with group theory.

Well, high-school mathematics education is pretty much an exploration of a particular ring - the integers, and a particular field - the real numbers, in a build up to calculus. But the theory of rings and fields as abstract objects is never covered in high school outside of the most advanced students in the most advanced schools geared towards math and science education.

Anyway, I'm not sure what your objection is, really. Grammatically, speaking of abstract algebra in the singular is regularly used to refer to the study of abstract algebraic structures that include groups, rings, fields, modules, etc. It is common for people to just refer to it as "algebra" and the plural form "algebras" refers to the particular algebraic structure (i.e. a module with a bilinear map). So we can speak of associative algebras, but people won't generally speak of algebras referring to different kinds of algebraic structures (e.g. a group and a vector space). Generally, a first course in abstract algebra covers groups, rings, and fields and perhaps a sprinkling of other topics. It's generally a survey level course. This would be at the level of intermediate undergraduate. You are in a University in the United States so I cannot believe that you haven't heard this terminology before, with the singular "algebra" used to refer to "abstract algebra." Are you just using the Russian transliteration and saying you think the English words should follow the same grammatical structure?

Anyway, I've taken the bait and continued on this derail. Can we get back to the topic at hand, please?
 
This is sad.

The forum is so hostile (because it has so many members inclined towards replying in a hostile manner) that even a thread about a math course resulted in conflict.

I'm going to guess that you haven't met many mathematicians; in my experience they are always at each other's throats. Indeed, that seems to be a common thread amongst academics of all stripes.

The more knowledgeable we become, it seems, the less tolerant we are of dissenting opinion - which makes some sense, as it becomes rare to meet anyone who can justifiably disagree with you, and common to meet people who are in the grip of Kruger-Dunning syndrome.
 
This is sad.

The forum is so hostile (because it has so many members inclined towards replying in a hostile manner) that even a thread about a math course resulted in conflict.

I'm going to guess that you haven't met many mathematicians; in my experience they are always at each other's throats. Indeed, that seems to be a common thread amongst academics of all stripes.

The more knowledgeable we become, it seems, the less tolerant we are of dissenting opinion - which makes some sense, as it becomes rare to meet anyone who can justifiably disagree with you, and common to meet people who are in the grip of Kruger-Dunning syndrome.
Ha-ha, so true. I have seen a fair share of folks with undergrad degrees (sometimes without it) to give me lectures in physics.
It is especially widespread in US where people with undergrad degrees are remarkably confident that they know everything there is to know and that the only reason they have not solved quantum gravity is because they are busy with making money and other more important stuff.
 
This is sad.

The forum is so hostile (because it has so many members inclined towards replying in a hostile manner) that even a thread about a math course resulted in conflict.

I'm going to guess that you haven't met many mathematicians; in my experience they are always at each other's throats. Indeed, that seems to be a common thread amongst academics of all stripes.

The more knowledgeable we become, it seems, the less tolerant we are of dissenting opinion - which makes some sense, as it becomes rare to meet anyone who can justifiably disagree with you, and common to meet people who are in the grip of Kruger-Dunning syndrome.
I have met many mathematicians - more than any other profession, probably (either that, or second behind lawyers). Cases of hostility like that exist, but are in my experience very rare. That said, that is mostly face to face talk. Perhaps, forums are much worse (in fact, the very few cases of hostility I do know are also on line).
In any case, the sort of hostility encountered here seems to be the norm in forums in which religion and/or politics are discussed, at least leaving aside blogs that belong to professional philosophers, most of which are in my experience much less hostile (but then, most of them are more strongly moderated too, so maybe that's the reason).

At any rate, many potentially interested discussions are precluded here by that hostility, usually due to people behaving in defense of threats to their ideology (we don't usually call them "religions", but they seem to have a lot of similarities), but sometimes, apparently the hostility happens even without that.
 
I'm going to guess that you haven't met many mathematicians; in my experience they are always at each other's throats. Indeed, that seems to be a common thread amongst academics of all stripes.

The more knowledgeable we become, it seems, the less tolerant we are of dissenting opinion - which makes some sense, as it becomes rare to meet anyone who can justifiably disagree with you, and common to meet people who are in the grip of Kruger-Dunning syndrome.
I have met many mathematicians - more than any other profession, probably (either that, or second behind lawyers). Cases of hostility like that exist, but are in my experience very rare. That said, that is mostly face to face talk. Perhaps, forums are much worse (in fact, the very few cases of hostility I do know are also on line).
In any case, the sort of hostility encountered here seems to be the norm in forums in which religion and/or politics are discussed, at least leaving aside blogs that belong to professional philosophers, most of which are in my experience much less hostile (but then, most of them are more strongly moderated too, so maybe that's the reason).

At any rate, many potentially interested discussions are precluded here by that hostility, usually due to people behaving in defense of threats to their ideology (we don't usually call them "religions", but they seem to have a lot of similarities), but sometimes, apparently the hostility happens even without that.

Has the thread really been that hostile? I'm pretty sure there were no personal attacks, nor was there any particularly harsh language. It was just a continuing disagreement that was becoming a derail.

Sure, I get annoyed at people who, in the face of several polite corrections, continue to repeatedly state the same incorrect things. It gets to me in particular when the topic is a matter of fact, not opinion, and one in which I am formally an expert. It's frustrating but I don't take it personally and eventually it just adds to my ignore list.
 
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