Math research papers: making your contribution
When people think of math, they don't think of research papers on math, they think of simple equations written down on paper, not essays. Young mathematicians writing their first paper may be stressful, but mathematical communication is the best way for your written and spoken math to be viewed perfectly. Your goal is to convince your audience to see and understand your work, as well as convince them that what you're saying about your deductions is true. Think of your essay as a map through your road to your end result is through the pages of your paper. You are the only person who knows the route so it's your duty to maintain a through way to explain everything without confusing your audience. As you write your paper, there are key things to focus in on.
Organization, Structure, And Voice
Before anything, structure your paper. It's the most important step because if you cannot communicate what you're trying to get through to your audience, you will have a failed essay. Start from an already simple form. Once you structure your paper and plan out what you're going to say, begin the basic outline of what you're proving so that you can follow it step by step.
Keep Things Easy To Read
Write down your proofs and results as clear as you possibly can. It is possible to be too detailed in your work. Too many symbols in one step is something to generally avoid. You should never, ever confuse your audience. You need to make sure you can communicate what you want, as well as be able to provide communication to your proper audience in a way that they'll understand. If you start to get too into every single thing, your paper is going to be more of an exercise to read than it was to write. All details just cannot be shown because there isn't space for every single one of your proofs on your essay.
If you're writing your first Mathematical research paper, always make sure to ask questions. If you have any possible questions, it's always a great idea to talk to your adviser or professor to determine what they specifically want if you're at all confused. Though it may not be like high school, teachers are still there to help you learn and many students, even mathematicians can forget that they're there. Of course, they won't hold your hand through everything, but it's good to get a little boost of confidence and knowledge of what you're supposed to be doing.