My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 25th, 2010, 08:28 AM   #1
Newbie
 
Joined: Feb 2010

Posts: 6
Thanks: 0

Solving real roots polynomial equation

I have shown some more methods which is much quicker than previous ones for solving real roots polynomial equations. These examples are from’ Solving Real Roots Polynomial Equations’(New And Simple Methods Of Solving Real Roots Polynomial Equations Part-2). Try it to see whether it works well. Click here.
http://www.rkmath.yolasite.com
RKJCHENNAI is offline  
 
February 25th, 2010, 09:41 AM   #2
Senior Member
 
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

Re: Solving real roots polynomial equation

I've looked briefly through the first paper. I haven't looked close enough to say much about the methods or the novelty of the results, but a few things:

I see no reference to other mathematicians here. Have you built on on (or even examined) work that's been done in the last century on roots of polynomial equations? How does your method depart from these methods and why? This is always a useful thing to see when someone claims their result is new-- it provides motivation and shows that this isn't just some guy who has "discovered" some nonsense, or something that's already well-known. It's shocking (and suspicious) to see a "new" result in the solution to polynomial equations which does not rely on any methods from higher algebra. Can you provide any insight on how you've proven something new with elementary methods? Also, how do you know your results are new?

You really need to work on the formatting: it's difficult to follow what's going on. In particular:
* departing form standard notation makes it difficult for mathematicians to read. (e.g. is much clearer notation than . Also, your equations are difficult to distinguish from text; you should really be making use of a different font or style (e.g. math is always in italics, text is never in italics.)
* If you insist on using word (instead of typesetting it in LaTeX), use a different font than calibri. Preferably one which is standard in mathematical papers (Latin Modern, Garamond, etc.) It looks nicer, and is much easier to take seriously (I'm not joking here.)
* It is traditional to provide proofs immediately after first introducing a theorem; perhaps a quick remark, or an example beforehand is illuminating, but I shouldn't have to go to the end of the paper to read a proof of a statement on page one.
* Your results are completely unmotivated; prose helps make math papers clearer. Especially, I don't get any sense of why I should care about what you have to say.

I may have time to take a look at this in more detail this weekend.
cknapp is offline  
February 27th, 2010, 07:45 AM   #3
Newbie
 
Joined: Feb 2010

Posts: 6
Thanks: 0

Re: Solving real roots polynomial equation

Quote:
"cknapp"
Quote:
I see no reference to other mathematicians here.
Code:
All are my own ideas. I didn’t take anything from anywhere. This is only a draft. I like to add many things including a few references?, general proofs, some more examples, explanations and good formatting( all in good English), Only if my works are appreciated
Quote:
Have you built on on (or even examined) work that's been done in the last century on roots of polynomial equations?
Code:
I saw them, only after writing these  papers. Because I didn’t study any degree.
Quote:
How does your method depart from these methods and why?
Code:
All are simple formulas.
Easy and suitable to school students.

Quote:
This is always a useful thing to see when someone claims their result is new-- it provides motivation and shows that this isn't just some guy who has "discovered" some nonsense, or something that's already well-known. It's shocking (and suspicious) to see a "new" result in the solution to polynomial equations which does not rely on any methods from higher algebra.
Code:
Please note that these formulas are only for real roots polynomial equations.
After seeing many math websites in net, I satisfied myself that no one discovered it before. I have shown that my method works well.Perhaps I may be wrong. You  (mathematicians and scholars) will decide.
Quote:
Can you provide any insight on how you've proven something new with elementary methods?
Code:
All are based on simple facts , already known by all.
I think differently. 
See the proofs, especially theorem 6. It does not need any proof. Theorem 1 is another form of theorem 6. My works all are mainly based  on theorem 1. I will try to give you a detailed notes.
Quote:
Also, how do you know your results are new?
Code:
After seeing many math websites in net, I satisfied myself that no one discovered it before. Perhaps I may be wrong. You  (mathematicians and scholars) will decide.
Quote:
it's difficult to follow what's going on
Code:
I have poor English knowledge. I can’t explain accurately in English as I think. That is why I wrote main points only. I didn’t explain any thing.
Quote:
You really need to work on the formatting: In particular:
* departing form standard notation makes it difficult for mathematicians to read. (e.g. is much clearer notation than . Also, your equations are difficult to distinguish from text; you should really be making use of a different font or style (e.g. math is always in italics, text is never in italics.)
* If you insist on using word (instead of typesetting it in LaTeX), use a different font than calibri. Preferably one which is standard in mathematical papers (Latin Modern, Garamond, etc.) It looks nicer, and is much easier to take seriously (I'm not joking here.)
* It is traditional to provide proofs immediately after first introducing a theorem; perhaps a quick remark, or an example beforehand is illuminating, but I shouldn't have to go to the end of the paper to read a proof of a statement on page one.
Code:
You are correct. Your suggestion all are accepted. Thank you.
Quote:
* Your results are completely unmotivated; prose helps make math papers clearer. Especially, I don't get any sense of why I should care about what you have to say.
Code:
It is only a request.
Quote:
I may have time to take a look at this in more detail this weekend
.

Code:
Thanks.
Code:
By the by, Part-1 is posted in net a year back. So far no one told ‘ it is not new ’ , ‘ theory is wrong ‘,’ it is useless and difficult ‘.
  I received four replies. 
  First reply was almost like your reply.
 Second one – ‘ it is not a breakthrough ’.
 third – ‘ I think its an amazing discovery. a powerful and unique method. awesome work on the whole.’
Fourth one – ‘ is it a joke ? ‘ 
                        So,  You  (mathematicians and scholars) will give the verdict that ‘ it is a breakthrough or not’, ‘it is a new method or not’, ‘it is simple or not’, ‘it is useful or not’ and ‘appreciate it or not’.  
Thank you.
RKJCHENNAI is offline  
February 27th, 2010, 04:39 PM   #4
Senior Member
 
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

Re: Solving real roots polynomial equation

Quote:
Originally Posted by RKJCHENNAI
All are my own ideas. I didn’t take anything from anywhere. This is only a draft. I like to add many things including a few references?, general proofs, some more examples, explanations and good formatting( all in good English), Only if my works are appreciated
Unfortunately, it's unlikely that an amateur working alone will discover something new that mathematicians find of any interest. Of course, it is possible. More likely than not, though, your results (even if new) will be of little interest to the mathematical community.

Quote:
I think differently.
A bold statement in mathematics.

Quote:
See the proofs, especially theorem 6. It does not need any proof.
A dangerous statement in mathematics.

Quote:
I have poor English knowledge. I can’t explain accurately in English as I think. That is why I wrote main points only. I didn’t explain any thing.
Fair enough.


Quote:
[quote:26nofcko]* Your results are completely unmotivated; prose helps make math papers clearer. Especially, I don't get any sense of why I should care about what you have to say.
It is only a request.[/quote:26nofcko]
I had mostly meant that there is little explanation. You explained why above.


The statement of theorem 1 needs to be refined: if k=0, then it is vacuous-- all polynomials with a 0-valued constant have 0 as a root.
Also, if n=1, then the two statements ( and ) are contradictory.

Your proof does not give anything unless n=3. You need to show that it holds for all polynomials that you are interested in.

n=3 has been "solved"-- we can very easily find all roots of a degree 3 polynomial. For n>4 polynomials are not necessarily solvable, so methods for approximating roots are certainly useful; unfortunately, a lot of work has gone into these, and I fail to see anything terribly original in your ideas.

I hope that's not too blunt...
cknapp is offline  
March 1st, 2010, 10:58 PM   #5
Newbie
 
Joined: Feb 2010

Posts: 6
Thanks: 0

Re: Solving real roots polynomial equation

Quote:
Unfortunately, it's unlikely that an amateur working alone will discover something new that mathematicians find of any interest. Of course, it is possible. More likely than not, though, your results (even if new) will be of little interest to the mathematical community.
okay.

Quote:
See the proofs, especially theorem 6. It does not need any proof.
I didn’t mean it. Actual(indirect) meaning is that the proof is very, very simple. Any one can prove it. Because it is obvious.

Quote:
I had mostly meant that there is little explanation. You explained why above..
Misunderstanding.
Sorry.

Quote:
The statement of theorem 1 needs to be refined: if k=0, then it is vacuous-- all polynomials with a 0-valued constant have 0 as a root.
X is not equal to 0 (to be included)

Quote:
Also, if n=1, then the two statements ( and ) are contradictory.
n > 1 (it is already told)

Quote:
Your proof does not give anything unless n=3. You need to show that it holds for all polynomials that you are interested in.
Yes. I have general proofs.

Quote:
n=3 has been "solved"-- we can very easily find all roots of a degree 3 polynomial. For n>4 polynomials are not necessarily solvable, so methods for approximating roots are certainly useful; unfortunately, a lot of work has gone into these, and I fail to see anything terribly original in your ideas.

I hope that's not too blunt...
I am disappointed.
RKJCHENNAI is offline  
March 5th, 2010, 04:12 PM   #6
Senior Member
 
Joined: Apr 2008

Posts: 435
Thanks: 0

Re: Solving real roots polynomial equation

Disappointing you or not, I agree with cknapp. Having skimmed through your papers, the first thing that strikes me is the new format. It is far more difficult to read through notations atypical of established papers than those I am accustomed to reading. It was an interesting challenge to read through your work.

Perhaps the general proofs for cases when n is not equal to 3 would add validity to your claims, but these claims do not seem to substantiate a new development in math. I'm sorry.
jason.spade is offline  
Reply

  My Math Forum > College Math Forum > Abstract Algebra

Tags
equation, polynomial, real, roots, solving



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
real roots of polynomial panky Algebra 1 December 10th, 2013 07:15 AM
find real roots of the polynomial rayman Abstract Algebra 0 April 20th, 2012 05:34 AM
polynomial equations - real roots advancedfunctions Calculus 2 March 11th, 2010 12:36 PM
Finding roots of Polynomial with real coefficients domaPL Real Analysis 1 January 12th, 2008 10:28 AM
Finding roots of Polynomial with real coefficients domaPL Number Theory 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.