Modern Algebra

[beero1000]

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...)

 

[fast]

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...)

Years ago, I made a 100 on my algebra final. The professor said she had taught for 20 years and I was the 1st. I thought that was awesome since that's not representative of my general grades, lol. Also, because she had noticed I was doing well in the class, she was worried after I missed the very first question, but after getting the remainder correct, she went back and noticed a second interpretation of the first question and gave me credit. Yay!

I've always been able to figure things out, as they say, just usually not always in accordance with proper procedures. At any rate, put me down as part of the demand, should you decide to share your notes

 

[beero1000]

I still have months to go, but I've started some of my preliminary prep by figuring out the main topics that I need to cover and in what order. The course is listed as an introduction to abstract algebra and a general survey of groups, rings, and fields. The students will have had some exposure to proofs from the linear algebra prerequisites, so the hope is that I won't have to do more than a quick refresher on proof techniques (here's to hoping ). I have 39 fifty minute lectures to work with, minus classes taken for exams (but plus weekly problem sessions).

• Groups

• Intro to groups and subgroups
• Cyclic groups and permutation groups
• Homomorphisms and isomorphisms
• Cosets and actions
• Normal subgroups and quotient groups
• Sylow theorems

• Rings

1. 
   [*=1]Intro to rings
   [*=1]Integral domains
   [*=1]Ideals
   [*=1]Polynomial rings
   [*=1]Unique factorization domains
   [*=1]Euclidean domains

• Fields

• Intro to fields
• Finite fields
• Fields of fractions
• Field extensions and splitting fields
• Automorphisms
• Galois theory

So, in order to fit the time frame, I'll need to cover each topic over at about 2 lectures on average. Tight but doable, I hope. I think I can go in pretty much that order, but I'll have a better idea of how it'll fit together once I start writing my notes.

 

[ApostateAbe]

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...)

Textbook is not so important. Important thing is to talk loudly, clearly, and act like you love this.

 

[fast]

None of that sounds familiar <gulp>

 

[beero1000]

None of that sounds familiar <gulp>

'Algebra' is a big subject.

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...)

Textbook is not so important. Important thing is to talk loudly, clearly, and act like you love this.

Thanks, I guess...

 

[Bomb#20]

None of that sounds familiar <gulp>

It ought to sound familiar -- it's the most romantic sequence of events in all mathematics. Rejected for publication because it was so advanced the referees couldn't follow the reasoning, written up more clearly while he was in jail, because he was a revolutionary straight out of Les Mis, put into final form in a long letter to a friend during one all-nighter, the next day he goes out and gets himself shot to death in a duel over a woman, and his discoveries are only recognized ten years later when they're found, understood and published by some of the greatest mathematicians of the age. Galois was twenty. How can any math teacher bear not to tell this story?

 

[beero1000]

None of that sounds familiar <gulp>

It ought to sound familiar -- it's the most romantic sequence of events in all mathematics. Rejected for publication because it was so advanced the referees couldn't follow the reasoning, written up more clearly while he was in jail, because he was a revolutionary straight out of Les Mis, put into final form in a long letter to a friend during one all-nighter, the next day he goes out and gets himself shot to death in a duel over a woman, and his discoveries are only recognized ten years later when they're found, understood and published by some of the greatest mathematicians of the age. Galois was twenty. How can any math teacher bear not to tell this story?

 

[lpetrich]

 Évariste Galois
ho.history overview - Papers that debunk common myths in the history of mathematics - MathOverflow
He certainly led a very dramatic life, but he didn't write down his math work the night before his fatal duel. He wrote it down over the months before, when he was jailed for his activism. He fought that duel a month after he was released from jail.

 

[J842P]

 Évariste Galois
ho.history overview - Papers that debunk common myths in the history of mathematics - MathOverflow
He certainly led a very dramatic life, but he didn't write down his math work the night before his fatal duel. He wrote it down over the months before, when he was jailed for his activism. He fought that duel a month after he was released from jail.

Certainly it was embellished but it's still a pretty good story.

By the way beero, I would love to try to follow along with your notes.

 

[barbos]

Group theory in 2 lectures? I guess it's technically possible but I fail to see utility in that.
Also I noticed no mentioning of group representation and stuff.
Anyway, it's one of these things I don't like about american system where there are a lot of introductory courses which are useless if you don't follow up with real course and useless if you do because you go through it again but faster.

 

[barbos]

Also "Modern Algebra" is a term is not meaningful in modern time. "Algebra" is not used by itself without further specification.
You should call it it "Introduction to (some) algebras" or at least "modern algebras"

 

[Rhea]

By the way beero, I would love to try to follow along with your notes.

Me, too. It's would be interesting to revisit the way things are taught after so many years, and see what ways things are represented now... and to be sober for it. I might retain more.

 

[beero1000]

Group theory in 2 lectures? I guess it's technically possible but I fail to see utility in that.
Also I noticed no mentioning of group representation and stuff.
Anyway, it's one of these things I don't like about american system where there are a lot of introductory courses which are useless if you don't follow up with real course and useless if you do because you go through it again but faster.

Good job taking every advantage to denigrate the American education system, but you need to work on your reading comprehension too.

Also "Modern Algebra" is a term is not meaningful in modern time. "Algebra" is not used by itself without further specification.
You should call it it "Introduction to (some) algebras" or at least "modern algebras"

No. Algebra is used by itself all the time, and modern algebra is a common term to denote the algebra developed in the late nineteenth and early twentieth centuries. As for calling it "algebras", the ironic thing is that algebras are one of the few major algebraic structures that I won't be discussing at all...

 

[barbos]

Good job taking every advantage to denigrate the American education system, but you need to work on your reading comprehension too.

My reading comprehension is fine, and you are mistaken if you think group theory in 10 lectures would be any better than in 2.
No denigration, just a criticism.

Also "Modern Algebra" is a term is not meaningful in modern time. "Algebra" is not used by itself without further specification.
You should call it it "Introduction to (some) algebras" or at least "modern algebras"

No. Algebra is used by itself all the time, and modern algebra is a common term to denote the algebra developed in the late nineteenth and early twentieth centuries. As for calling it "algebras", the ironic thing is that algebras are one of the few major algebraic structures that I won't be discussing at all...

It is not algebra, it's algebras.

 

[beero1000]

My reading comprehension is fine, and you are mistaken if you think group theory in 10 lectures would be any better than in 2.
No denigration, just a criticism.

I do think that more than a month of study is better than not even a week, and while I'm sure you know 6 times 2 isn't 10, you aren't really helping the case for your reading comprehension.

Also "Modern Algebra" is a term is not meaningful in modern time. "Algebra" is not used by itself without further specification.
You should call it it "Introduction to (some) algebras" or at least "modern algebras"

No. Algebra is used by itself all the time, and modern algebra is a common term to denote the algebra developed in the late nineteenth and early twentieth centuries. As for calling it "algebras", the ironic thing is that algebras are one of the few major algebraic structures that I won't be discussing at all...

It is not algebra, it's algebras.

You're seriously doubling down on this?

No, it is not algebras.

Algebras are examples of algebraic structures, while Algebra is an entire branch of mathematics.

 

[barbos]

I do think that more than a month of study is better than not even a week, and while I'm sure you know 6 times 2 isn't 10, you aren't really helping the case for your reading comprehension.

So, how much for Group Theory? 2 months?
I stand corrected, that's not enough.

Also "Modern Algebra" is a term is not meaningful in modern time. "Algebra" is not used by itself without further specification.
You should call it it "Introduction to (some) algebras" or at least "modern algebras"

No. Algebra is used by itself all the time, and modern algebra is a common term to denote the algebra developed in the late nineteenth and early twentieth centuries. As for calling it "algebras", the ironic thing is that algebras are one of the few major algebraic structures that I won't be discussing at all...

It is not algebra, it's algebras.

You're seriously doubling down on this?

No, it is not algebras.

Algebras are examples of algebraic structures, while Algebra is an entire branch of mathematics.

yes, read https://en.wikipedia.org/wiki/Algebra

 

[Bomb#20]

you are mistaken if you think group theory in 10 lectures would be any better than in 2.

There are 10 kinds of people in the world: those who understand binary and those who don't.

It is not algebra, it's algebras.

Are you one of those silly folks who think it's not math, it's "maths"?

 

[bilby]

There are 10 kinds of people in the world: those who understand binary and those who don't.

It is not algebra, it's algebras.

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'.

- - - Updated - - -

 

[barbos]

There are 10 kinds of people in the world: those who understand binary and those who don't.

It is not algebra, it's algebras.

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.