Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Can anyone give me site with Fermat's last theorem proof by A. Whiles?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Hmm .. that might take awiles ...

Start here on Wikipedia. External Links may help.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I'm opening it...

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**siva.eas****Member**- Registered: 2005-09-17
- Posts: 166

I think this link would help http://www.mbay.net/~cgd/flt/flt08.htm

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Thank you Siva, but it's not the full proof.

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**siva.eas****Member**- Registered: 2005-09-17
- Posts: 166

From http://cgd.best.vwh.net/home/flt/flt01.htm it seem that this site has the proof http://www.math.princeton.edu/~annals/i … 141_3.html but it seems that you can only get access to the article through certain universities.

Offline

**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,562

Maybe this will help some. It's way over my head.

http://cgd.best.vwh.net/home/flt/flt08.htm

or same linky

**igloo** **myrtilles** **fourmis**

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Not my area either ... I think you would need a special interest in the subject to understand it. But interesting to read about, nonetheless

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Thank you very much.

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I have a great idea:

Do you want to *understand* it?

I'm offering to discute the proof from the begining to the end. We'll post what we don't understand.

Are you in?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

1. What is an *eliptic curve*?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I'm starting exploring internet...

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

2. What is *cartesian plane*?

*Last edited by krassi_holmz (2005-12-31 23:18:33)*

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

2 (answer). As i understood it is just Euclidean plane. Is that right?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

3. What is *Riemann surface*?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

3.(answer): I think I understood what is this.

But how to explain it?

A Riemann surface is a surface-like configuration that covers the complex plane with "sheets.". When we have a functin over the complex plaine C, which is not "single valued":

∃ z1,z2 ∈ **C**: (z1)=(z2)=y.

What will we get for the inverse function of (z)?

Here's "logical" answer:

-¹(z) =={1-¹(z) OR 2-¹(z)}.

In the general case -¹(z) may be union of k "single valued" functions.

The riemann surface of -¹(z) is the union of the graphs of these functions.

We can use Euclidean plane, too.

*Last edited by krassi_holmz (2006-01-01 00:23:37)*

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Here's a simple example:

we use the function f(x)=x^2.(picture 1)

f-¹(y) = {sqrt(y) (picture 2) OR -sqrt(y) (picture 3)}

Then the Riemann surface of the function f-¹(y) is the union of the plots(picture 4)

*Last edited by krassi_holmz (2006-01-01 10:19:25)*

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

I think the following site is the best:

I'm following the proof that siva(thank you) gave me.

There you can download the full solution. Or you can do this by clicking:

here for zipped .pdf file

here for PostScript

and here for .dvi

(I've tested only the .pdf format)

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,534

Your graphs are a great introduction to Riemann Surfaces, krassi!

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

4. Weierstrass * p* function?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

5. What is *pole*?

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

6. Singularity

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

Please help me if you know some of these.

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

7. Domain:

A set of values for which f is defined.

For example the function f=n!, defined over Natural numbers (**N**) has domain **N**. It also can be said "function f *over* **N** "

IPBLE: Increasing Performance By Lowering Expectations.

Offline

**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

8. A function is *analitic* if is differentiable???

IPBLE: Increasing Performance By Lowering Expectations.

Offline