Which Famous Mathematician's Books Should I Study for Self-Study on Algebra?

[annoymage]

peace,

well, actually, i just finished my first year on University, and suddenly interested to do some "formal" self study for the first time, as i have thought this before but never have the initiative to start

i'm a math major, and still unclear of what kind of math i am. But, by referring to this
http://en.wikipedia.org/wiki/Areas_of_mathematics

i thought i like the "algebra" area. And I thought doing research on great mathematicians books would be better for me. Is it? Or maybe studying something like "magic square" would be better.
But, i made a decision on studying on mathematicans books.

And i would like to know, whose book should i study in Algebra areas. I don't know any famous mathematicians. Can Gauss would be a wise decision?? At first, i wanted to try Euclid, but he's more to geometry and topology thing right?

thanks

p/s, sorry if i have a bad english, hoho

 

[jbunniii]

I personally would not recommend starting with someone like Gauss for your first exposure to algebra. You should start with something modern enough to be recognizable as algebra today - groups, rings, fields, etc.

You could go back as far as Van der Waerden's "Algebra" (originally published in the 1930s) but I wouldn't recommend starting with anything earlier than that. If I had to pick one book to start with it would be Herstein's "Topics in Algebra."

 

[annoymage]

hmm, i don't mean to rude,
but i want to ask,
what made you think that I should start with modern and then i can study Gauss.
Can you explain it to me

i'm really sorry, but i guess my ways of writing is just like provoking someone. But my english so bad that i can't think other words to make it nicer. ngahaha, soo sorry

 

[Office_Shredder]

The way mathematics is written today is very different from how it was written before the 1900's. Different definitions, standards for an acceptable proof etc. Reading something written by Gauss as a way of learning mathematics would be like reading a dictionary written in 1600 to learn the English language

 

[annoymage]

i see, hmm, anyway, what book should you choose, if you are in my situation?

 

[jbunniii]

hmm, i don't mean to rude,
but i want to ask,
what made you think that I should start with modern and then i can study Gauss.
Can you explain it to me

i'm really sorry, but i guess my ways of writing is just like provoking someone. But my english so bad that i can't think other words to make it nicer. ngahaha, soo sorry

Your English is fine, and you don't seem rude at all. It is a good question.

The reason is because algebra has been abstracted and refined a lot since Gauss, and it is often easier to understand from the modern viewpoint (in a sense one can see the forest more easily, instead of just the trees). Also, a great deal of what is now considered fundamental to the subject was not known until after Gauss. For example, the Sylow theorems are the bedrock upon which (finite) group theory rests, but these date from the late 1800s.

 

[annoymage]

My knowledge is still preliminary in group and ring theory
ok, now i follow yours which is Herstein. Until i hear other option and opinion which maybe better. But in the mean time i have to polish my knowledge on some basic knowledge.

And i hope that's the best decision to made

 

[Acut]

I agree with jbunnii.
Reading the classical works is a bad idea for a beginner.
I've once read Euclid's elements for math competitions, and I've found it more beautiful than useful.
It's a nice reading after you have a certain degree of mastery in the subject, though.

 

[mathwonk]

i think you might like gauss' disquisitiones arithmeticae.

 

[annoymage]

wow, thanks, you know, I've read 1/4 of herstein topic in algebra, i think it really change my life you know ;P, thanks to jbunniii for the recommendation. hmm it seems, gauss' disquisitiones arithmeticae are more on number theory right? but it doesn't hurt to read... anyway thanks ;P

 

[mathwonk]

number theory was one of the sources of abstract algebraic ideas. e.g. gauss gives an argument for modular integers that can be seen to anticipate the concept of cosets in group theory, and the usual proof of the theorem that the order of a subgroup divides that of the group.