How to start writing a paper on Number Theory or Group Theory

[ghanar]

Hello :)
That's my 2nd year in Math, and I want to start writing an article on NT or Group Theory. I know most of the basic GT and some NT. I still don't know residues/congruences completely, I face problems about understanding the theorems. There are a lot of theorems in these chapters and they look like coming from sky- or let me say 'space'. How can I learn these topics completely ? I really want to start to write a paper, it may be too short or not innovative , and I'm not patient. I'm stuck and I need something to bring me back to Math world. Thanks :)

 

[mfb]

You don't write papers (=publications) to learn something, you write papers if you have new results. To learn something, you can read papers (or books, depending on the level).
Or do you mean something else?

 

[ZapperZ]

Hello :)
That's my 2nd year in Math, and I want to start writing an article on NT or Group Theory. I know most of the basic GT and some NT. I still don't know residues/congruences completely, I face problems about understanding the theorems. There are a lot of theorems in these chapters and they look like coming from sky- or let me say 'space'. How can I learn these topics completely ? I really want to start to write a paper, it may be too short or not innovative , and I'm not patient. I'm stuck and I need something to bring me back to Math world. Thanks :)

As mfb has stated, this is a bit vague. What do you mean by "writing an article/paper?" What is the purpose? Are you doing it for your own self-education, or are you intending to submit this to some publication/journal?

In the academic world, the phrase "writing a paper" typically means to submit something to a scholarly journal. To do that, one must know the nature of the journal (i.e. what exactly does it publish?) and also the nature/status of the particular field of study. I don't think you have this knowledge yet.

Zz.

 

[homeomorphic]

You don't write papers (=publications) to learn something, you write papers if you have new results.

That's actually not quite true. I expect if I talked to math professors about my math disillusionment, due to pressure to publish when I don't know anything about math (I'm being hyperbolic; I have a PhD in it), what they would tell me is that I need to stop just learning math and do math (publishable math, that is) to learn it.

Of course, that's for someone who's sort of almost there, but not quite there, in terms of knowing what's going on in research. However, even at a lower level, it might not be a bad idea to write some stuff up for your own purposes. They just shouldn't expect to be publishing it (except there might be some sort of lower-level places that would take an expository article). Terrence Tao specifically recommends doing this in his blog, I guess for both the writing practice, learning by putting it in your own words, and so that you'll have a reference for the material later on, if you need it. In my view, if you eventually go to grad school and write a thesis, those things can be killers sometimes, so any little way you can prepare for it will help. I think I would have been a few weeks ahead, at least, if I was already comfortable with LaTeX, as well as drawing diagrams and putting them in and all that. Might not seem huge, but it could have made a difference to get me off to a quicker start--my adviser would have been a little less impatient with me, and I would have been a little less impatient with myself. I gave some talks for classes in undergrad and the prof suggested I learn LaTeX and type to practice, and I didn't listen because I figured I'd just learn it as needed, but it would have helped.

Also, there's nothing stopping anyone from finding results that are new to them, but probably not new to everyone. In fact, that's probably a good idea to play around with stuff on your own initiative, rather than get 100% from textbooks, although you do want to learn the standard stuff in textbooks, as well.

 

[ZapperZ]

We should stop jumping the gun and wait for the OP to come back and explain what was meant by "writing a paper".

Zz.

 

[ghanar]

Hi :)
By "writing a paper" , I meant to find something new in NT or Abstract Algebra. To share the results I'm going to find.

 

[Borek]

To share the results I'm going to find.

Start looking for the results then.

 

[jtbell]

That's my 2nd year in Math

2nd year undergraduate, or 2nd year graduate school?

 

[ghanar]

undergrad.

 

[ZapperZ]

Hi :)
By "writing a paper" , I meant to find something new in NT or Abstract Algebra. To share the results I'm going to find.

undergrad.

So, at your level of education, how would you know that you've found something "new"?

Zz.

 

[ghanar]

That's right too. I'm not capable to understand that if I find something new.

However, I'm just impatient. You can say, "you need to grow up first, need to get masters degree etc." but I really want to study on especially NT. And I know someone who made a research on a new topic on NT, and he wrote the things he found. The topic was XXX? primes.

So what should I have to do? I'm in a really bad condition...

 

[micromass]

That's right too. I'm not capable to understand that if I find something new.

However, I'm just impatient. You can say, "you need to grow up first, need to get masters degree etc." but I really want to study on especially NT. And I know someone who made a research on a new topic on NT, and he wrote the things he found. The topic was XXX? primes.

So what should I have to do? I'm in a really bad condition...

Go to your professors and ask them if you can do research with them. If they agree, then they will present something that is doable.