# Fermat's Last Theorem

• Jul 21st 2007, 10:32 AM
melumj
Fermat's Last Theorem
I'm tryin to finish my bs in mathematics. I am looking to talk with someone who has done any kind of work with this Theorem. I dont have to work with it, I just need to understand some overall ideas pertaining to a few specific aspects of the Theorem. If anyone can help, please let me know.

Josh
• Jul 21st 2007, 10:37 AM
Jhevon
Quote:

Originally Posted by melumj
I'm tryin to finish my bs in mathematics. I am looking to talk with someone who has done any kind of work with this Theorem. I dont have to work with it, I just need to understand some overall ideas pertaining to a few specific aspects of the Theorem. If anyone can help, please let me know.

Josh

ThePerfectHacker knows a lot about this topic (Fermat is one of his favorite mathematicians), but he will not be online until later in the evening (around 6 hours from now) or maybe even tomorrow.

Can you state the specific aspects that you are interested in. I MAY be able to help you, if not, it will give anyone else willing to help specific things to address
• Jul 21st 2007, 10:49 AM
melumj
What I Need
Its actually 2 classes tied together. One deals with Elliptic and Modular Functions related to the proof. My teacher provided his personal materials and materials from Ribenboim, Wiles, Cox, and Wiles. I simply need to prepare a notebook regarding my thoughts on these areas of the problem.
1. Geometric considerations
2. A specific geometric model using the variables x, y, and z derived the equation x^p + y^p = z^p
3. The Frey Curve
4. 2x2 matrix group
5.Modular sub-group from the 2x2 group
6. Taniyama-Shimura conjecture
7. Galois representations
8. Hecke Algebras
9. The genus of a curve

I just need to simply talk about these aspects and how they tie into fermats last theorem. Thats one notebook. The other is similar.

I would love to find someone that could help point these aspects out or provide information on what to look for exactly.

Thanks,
Josh
• Jul 21st 2007, 10:53 AM
Jhevon
Quote:

Originally Posted by melumj
Its actually 2 classes tied together. One deals with Elliptic and Modular Functions related to the proof. My teacher provided his personal materials and materials from Ribenboim, Wiles, Cox, and Wiles. I simply need to prepare a notebook regarding my thoughts on these areas of the problem.
1. Geometric considerations
2. A specific geometric model using the variables x, y, and z derived the equation x^p + y^p = z^p
3. The Frey Curve
4. 2x2 matrix group
5.Modular sub-group from the 2x2 group
6. Taniyama-Shimura conjecture
7. Galois representations
8. Hecke Algebras
9. The genus of a curve

I just need to simply talk about these aspects and how they tie into fermats last theorem. Thats one notebook. The other is similar.

I would love to find someone that could help point these aspects out or provide information on what to look for exactly.

Thanks,
Josh

yeah, so I can't help much with these. You're better off waiting for someone else to answer. Until then, I don't think checking out wikipedia would be a bad idea
• Jul 21st 2007, 11:00 AM
melumj
Thanks
Well i've spent days looking on the internet and have the book Fermat's Last Theorem for amateurs. Its just a lot to handle, dont think my teacher realized this, because he's way to smart for his own good, haha. I'm just having trouble understanding a topic and figuring out how it applies to FLT.

Thanks anyways

Josh
• Jul 21st 2007, 11:01 AM
galactus
I would suggest getting the book "Fermat's Enigma" by Simon Singh. It's the story of this incredible theorem down through the centuries. It will answer your questions.
It's a good book.
• Jul 21st 2007, 11:04 AM
Jhevon
Quote:

Originally Posted by melumj
Well i've spent days looking on the internet and have the book Fermat's Last Theorem for amateurs. Its just a lot to handle, dont think my teacher realized this, because he's way to smart for his own good, haha. I'm just having trouble understanding a topic and figuring out how it applies to FLT.

Thanks anyways

Josh

How long do you have to turn in the assignment? There is a book called "Fermat's Enigma" by Simon Singh. It reads like a novel. It is not very technical on the higher levels of math, but i think it does a good job of illustrating the conceptual connections between all the various topics used to prove Fermat's Last Theorem and the theorem itself, and it is otherwise a fun read. It was recommended to me by TPH

EDIT: Haha, galactus beat me to it. So you read the book galactus? I finished it about a week ago, loved it!
• Jul 21st 2007, 11:14 AM
melumj
Time frame
I technically have until Aug. 26 to finish these notebooks, but wanted to have it done sooner due to issues with my teacher and the school. I'm also working 2 jobs and dont have a significant amount of spare time. I'll look into it though.
• Jul 21st 2007, 11:15 AM
galactus
Yes, I read it about 10 years ago. I still have it. I looked up some of the topics posted and they're in there. Hecke, Frey, etc.

It should be ideal for the aforementioned project. I am surprised the professor didn't recommend it.

Order it from Amazon or eBay. It should arrive quickly and you'll have plenty of time. Good luck
• Jul 21st 2007, 05:50 PM
ThePerfectHacker
It is extremely difficult for an undergraduate student to be able to understand these concepts.

You need to know:
1)Field and Group Theory
2)Algebraic Number Theory
3)Modular Forms
4)Elliptic Curves
5)Galois Representations and Cohomology
6)Projective Geometry
7)Complex Analysis would help.

There is too much, and they are all too advanced especially number 3 and 5. This is why there are very few people in the world that know this.
• Jul 21st 2007, 06:06 PM
Jhevon
Quote:

Originally Posted by ThePerfectHacker
It is extremely difficult for an undergraduate student to be able to understand these concepts.

You need to know:
1)Field and Group Theory
2)Algebraic Number Theory
3)Modular Forms
4)Elliptic Curves
5)Galois Representations and Cohomology
6)Projective Geometry
7)Complex Analysis would help.

There is too much, and they are all too advanced especially number 3 and 5. This is why there are very few people in the world that know this.

I agree. i don't think melumj has to go too deep into this stuff though. i think he just has to illustrate the overall conceptual connections between the different areas of math and comment on them
• Jul 21st 2007, 06:11 PM
ThePerfectHacker
Quote:

Originally Posted by Jhevon
I agree. i don't think melumj has to go too deep into this stuff though. i think he just has to illustrate the overall conceptual connections between the different areas of math and comment on them

There is no elementary why to explain these concepts. That is the problem.
• Jul 21st 2007, 06:22 PM
melumj
Thanks
You guys are right. I dont have to go very far into depth. Thats why its frustrating though, it is very complex stuff. Learning just one area pertaining to the theorem could take years in itself, let alone all topics. Anyways, thanks for the chat. Makes me realize he cant expect a ton from me. Takes some pressure off if you know what I mean.

Josh
• Jul 21st 2007, 06:23 PM
Jhevon
Quote:

Originally Posted by melumj
You guys are right. I dont have to go very far into depth. Thats why its frustrating though, it is very complex stuff. Learning just one area pertaining to the theorem could take years in itself, let alone all topics. Anyways, thanks for the chat. Makes me realize he cant expect a ton from me. Takes some pressure off if you know what I mean.

Josh

Yeah. but i really think that book that galactus and i recommended will be a big help. get it and read it as soon as possible