How would I write a proper paper on a mathematical concept?

[Unity+]

I know how to write regular essay-type paper, but I know these type of papers have a different format(I think).

 

Can someone show me how I would format the paper or direct me to references about how to do this?

[studiot]

To a large extent it depends upon the dictats of the publishing house or conference where you intend (hope?) to publish.

 

These may be obtained from the publisher, sometimes online on their website.

 

The first thing to do is to create the Title and draft abstract, which states the objectives and results, but not the detailed method.

It should also contain keywords that will be used by archivists in future subject searches.

 

The importance of this is it is your sales pitch to the publisher. (S)he will then tell you the required format details.

 

The meat of the paper will follow conventional lines:

 

Introduction

Development and presentation of work

Results and discussion/conclusion

References

Recommendations for further work

Appendices.

 

Here is a short example

 

Title : Greens Functions For General Disk-Crack Problems

 

Abstract : The two dimensional elasticity problem of a circular disk with an embedded edge dislocation is considered. Using Mushkelishvili's variable method and reducing the case under consideration to a Hilbert problem, a closed form solution is obtained. The dislocation solution may be used as a Green's Function to tackle general disk-crack cases. As an example, a disk containing a slant crack subjected to point loads is studied, numerical procedures for calculating the stress intensity factors for both internal and edge cracks are presented.

 

I have highlighted some keywords, but the author has squeezed many more into the abstract.

[Unity+]

To a large extent it depends upon the dictats of the publishing house or conference where you intend (hope?) to publish.

 

These may be obtained from the publisher, sometimes online on their website.

 

The first thing to do is to create the Title and draft abstract, which states the objectives and results, but not the detailed method.

It should also contain keywords that will be used by archivists in future subject searches.

 

The importance of this is it is your sales pitch to the publisher. (S)he will then tell you the required format details.

 

The meat of the paper will follow conventional lines:

 

Introduction

Development and presentation of work

Results and discussion/conclusion

References

Recommendations for further work

Appendices.

 

Here is a short example

 

Title : Greens Functions For General Disk-Crack Problems

 

Abstract : The two dimensional elasticity problem of a circular disk with an embedded edge dislocation is considered. Using Mushkelishvili's variable method and reducing the case under consideration to a Hilbert problem, a closed form solution is obtained. The dislocation solution may be used as a Green's Function to tackle general disk-crack cases. As an example, a disk containing a slant crack subjected to point loads is studied, numerical procedures for calculating the stress intensity factors for both internal and edge cracks are presented.

 

I have highlighted some keywords, but the author has squeezed many more into the abstract.

Thank you for the answer. This should help me greatly.

To a large extent it depends upon the dictats of the publishing house or conference where you intend (hope?) to publish.

 

These may be obtained from the publisher, sometimes online on their website.

 

The first thing to do is to create the Title and draft abstract, which states the objectives and results, but not the detailed method.

It should also contain keywords that will be used by archivists in future subject searches.

 

The importance of this is it is your sales pitch to the publisher. (S)he will then tell you the required format details.

 

The meat of the paper will follow conventional lines:

 

Introduction

Development and presentation of work

Results and discussion/conclusion

References

Recommendations for further work

Appendices.

 

Here is a short example

 

Title : Greens Functions For General Disk-Crack Problems

 

Abstract : The two dimensional elasticity problem of a circular disk with an embedded edge dislocation is considered. Using Mushkelishvili's variable method and reducing the case under consideration to a Hilbert problem, a closed form solution is obtained. The dislocation solution may be used as a Green's Function to tackle general disk-crack cases. As an example, a disk containing a slant crack subjected to point loads is studied, numerical procedures for calculating the stress intensity factors for both internal and edge cracks are presented.

 

I have highlighted some keywords, but the author has squeezed many more into the abstract.

Here is another question.

 

You say that there must be a conclusion. There is some form of conclusion that can be made, but the only conclusion that I have with the work I have made is the idea if an infinite amount of numeral systems based on the amount of dimensions that exist. Another conclusion is the hailstone equations that are derived from the work. How would I address this?

[ajb]

I know how to write regular essay-type paper, but I know these type of papers have a different format(I think).

 

Can someone show me how I would format the paper or direct me to references about how to do this?

 

You should read published papers in the same field. That will give you an idea of the style, language and rigour that is accepted in that field.

 

A quick google search will give you suggestions for the journals avaliable.

 

What I also suggest you do is have a look at the ArXiv, now not all of the preprints there are fully published papers, but it will still give you a good flavour of what is expected.

 

You say that there must be a conclusion. There is some form of conclusion that can be made, but the only conclusion that I have with the work I have made is the idea if an infinite amount of numeral systems based on the amount of dimensions that exist. Another conclusion is the hailstone equations that are derived from the work. How would I address this?

You don't actually need to include a section called "conclusion", though many people do. If you have made reference to how your work sits within the larger framework of modern mathematics, then you may not need to explicitly write a conclusion. Many papers more or less just finish on some result.

 

The same can be said for "suggestions for further work". Some people include it, others don't.

 

My personal style is to have a few comments in a final section. I just give a paragraph on what I have done and then make suggestions on what could be done next. I will usually have plenty of remarks in the main text also.

 

One thing you must do, usually in the introduction, is make some comments on simlar works and if possibile how your work fits into the branch of mathematics you are working on. This is not always so easy as the reality is one may be focused on a small very specialised problem.

The first thing to do is to create the Title and draft abstract...

Right, but remember that you may change these quite a lot as the paper develops.

 

Im my experience, making draft papers early in a project helps me to see what really needs more attention and what I don't really yet understand.

 

Of course other people work differently and you have to find out what works for yourself.

Edited August 5, 2013 by ajb

[Unity+]

 

 

You should read published papers in the same field. That will give you an idea of the style, language and rigour that is accepted in that field.

 

A quick google search will give you suggestions for the journals avaliable.

 

What I also suggest you do is have a look at the ArXiv, now not all of the preprints there are fully published papers, but it will still give you a good flavour of what is expected.

 

 

You don't actually need to include a section called "conclusion", though many people do. If you have made reference to how your work sits within the larger framework of modern mathematics, then you may not need to explicitly write a conclusion. Many papers more or less just finish on some result.

 

The same can be said for "suggestions for further work". Some people include it, others don't.

 

My personal style is to have a few comments in a final section. I just give a paragraph on what I have done and then make suggestions on what could be done next. I will usually have plenty of remarks in the main text also.

 

One thing you must do, usually in the introduction, is make some comments on simlar works and if possibile how your work fits into the branch of mathematics you are working on. This is not always so easy as the reality is one may be focused on a small very specialised problem.

 

Right, but remember that you may change these quite a lot as the paper develops.

 

Im my experience, making draft papers early in a project helps me to see what really needs more attention and what I don't really yet understand.

 

Of course other people work differently and you have to find out what works for yourself.

Thank you for the answers.

[studiot]

 

You say that there must be a conclusion.

 

I should have added that not every section appears in every paper, and some papers may have additional ones I didn't mention.

 

The list is a guide, not prescriptive. Also as mentioned some publishers do prescribe a particular format.

[Unity+]

 

I should have added that not every section appears in every paper, and some papers may have additional ones I didn't mention.

 

The list is a guide, not prescriptive. Also as mentioned some publishers do prescribe a particular format.

It would make sense since many papers are merely a part of one set of papers that describe a specific subject.