Thread: Course material

Hi!
Next autumn, I'm going to take a course in Abstract Algebra. Therefore, I would like to buy a book on this mathematical discipline, and I have found a couple of suitable books. However, I don't know which is the best, and I would like you to express your view on this matter.

"Abstract Algebra" by David S. Dummit, and Richard M. Foote

"Abstract Algebra" by John A. Beachy and William D. Blair

"Abstract Algebra" by Pierre Antoine Grillet

"First Course in Abstract Algebra" by John B. Fraleigh

"Basic Abstract Algebra" by P. B. Bhattacharya

"Abstract Algebra: An Introduction" by Thomas W. Hungerford

If you're able to contact the professor and obtain the book he's using for the course early, I would do that.

I'll try to, but unfortunately I don't think that I'll be able to.

Originally Posted by thyristor

Hi!
Next autumn, I'm going to take a course in Abstract Algebra. Therefore, I would like to buy a book on this mathematical discipline, and I have found a couple of suitable books. However, I don't know which is the best, and I would like you to express your view on this matter.

"Abstract Algebra" by David S. Dummit, and Richard M. Foote

"Abstract Algebra" by John A. Beachy and William D. Blair

"Abstract Algebra" by Pierre Antoine Grillet

"First Course in Abstract Algebra" by John B. Fraleigh

"Basic Abstract Algebra" by P. B. Bhattacharya

"Abstract Algebra: An Introduction" by Thomas W. Hungerford

I would go with Hungerford, or if you can find it, Algebra by Michael Artin.

The classic graduate texts in algebra are the books by Jacobson, Van der Waeerden and Lang, but they may be a bit more than what you are looking for.

I personally think Hungerford's book is awful to learn from. My recommendation is Dummit and Foote.

Originally Posted by salsaonline

I personally think Hungerford's book is awful to learn from. My recommendation is Dummit and Foote.

salsaonline is closer to algebra than am I. I would pay attention to his recommendation.

Of course, when I speak of Hungerford, I'm referring to his graduate textbook.

My problem with the book is that it didn't strike me as being very good about getting the main point of a proof across. Instead, the proofs get overwhelmed by unnecessary details. For example he'll say things like "By (3.1.2), such and such is true." So you look up what (3.1.2) is, and it will turn out to be something dumb like the definition of a group. That kind of unnecessary wordiness can really impede on the learning process.

I should point out that Artin is also considered to be a classic. I think that both Dummit and Foote and Artin are technically undergraduate textbooks. But they're good enough that even a graduate student would find them useful.

I like Dummit and Foote mostly because it has very good exercises. In some sense, the exercises are the most important part, since with math you learn by solving problems more than by reading through the chapters.

Originally Posted by salsaonline

Of course, when I speak of Hungerford, I'm referring to his graduate textbook.

My problem with the book is that it didn't strike me as being very good about getting the main point of a proof across. Instead, the proofs get overwhelmed by unnecessary details. For example he'll say things like "By (3.1.2), such and such is true." So you look up what (3.1.2) is, and it will turn out to be something dumb like the definition of a group. That kind of unnecessary wordiness can really impede on the learning process.

I should point out that Artin is also considered to be a classic. I think that both Dummit and Foote and Artin are technically undergraduate textbooks. But they're good enough that even a graduate student would find them useful.

I like Dummit and Foote mostly because it has very good exercises. In some sense, the exercises are the most important part, since with math you learn by solving problems more than by reading through the chapters.

I learned my algebra either without a text or from Lang's book. Lang's book is good to learn from because there are enougth mistakes that you have make sure that you go through all the proofs carefully. I actually have two printings, and I recall that there is one theorem in which there is a mistake in the proof. In the second printing the erros has been corrected, and it is wrong for an entirely different reason -- I don't recall the theorem off the top of my head.

On reason that the errors helped, is that in the class there were no lectures by the professor. We did all the lecturing, and you had to be on your toes to make sure that the proofs that you presented were correct, even if Lang's were not.

Story on an algebra class.

This particular class was a year or so ahead of me, but I knew the prof reasonably well -- used to play basketball with him in the evening.

He was a nice guy but had a stern demeanor and a hawkish appearance. He did a small bit of lecturing in his classes.

There were a couple of Chinese students, recently arrived in the country, and not familiar with U.S. customs and student demeanor. So one of the domestic students took them asside and explained : If Prof X, says something that you do not fully understand, the proper means of getting clarification is to leap out of your chair and say in loud voice "Bullshit".

So, during the lecture, the inevitable happened and Jack, the prof, whirled around, but noticed the American graduate student literally rolling on the floor, unable to breath. He figured it out instantly.

Same two Chinese students.

One spoke excellent English and was readily understood. The other was completely incomprehensible.

The same graduate student asked the clear one why it was that he spoke such good English while the other could not be understood. After all, they had both been in the U.S. for the same lenght of time, and had known each other and been educated together in China.

The response: "Oh, he doesn't make sense in Chinese either."

Originally Posted by DrRocket

Same two Chinese students.

One spoke excellent English and was readily understood. The other was completely incomprehensible.

The same graduate student asked the clear one why it was that he spoke such good English while the other could not be understood. After all, they had both been in the U.S. for the same lenght of time, and had known each other and been educated together in China.

The response: "Oh, he doesn't make sense in Chinese either."

Poor guy. I hope he was better in mathematics

Thanks a lot for your answers, both of you. I think that I'll go with Dummit and Foote, for one reason, it's cheaper than "Algebra" by Artin (at least where I looked) and for another, I like exercises

I've ordered the book now, so I hope that it will be good