Several questions regarding the writing of SoP I have several questions regarding the writing of SoP (for math Ph.D. admission to some US universities), which are written down sequentially. There may be some vague questions. I will be helpful in any comments. Thanks in advance.


One of the US university ask only SoP describing background and interests, no CV at all. Should I write all necessary details like my past achievements, which course I have attended(sort intro to the key topics of these syllabi), my CGPA, or percentage of marks in my SoP?
Should I include any professor's(of the university where I am going to apply) name and his work(some articles and books) that I used in my past study?
Is there any rule of decorating the SoP, I mean use of margin, font size, space between paragraphs. I asked this question because, in some lines, I have to write some mathematical notation(contained in the name of a topic), and in this case, I have to use Latex. So is there any problem If I submit it as a .pdf file made by latex language?
Should I include any sentence like, "I have plan to take some courses on..... in the upcoming semester''? Here upcoming means, if a grad school selects me, then the gap between the joining and current semester.
If some grad school offers an independent study program, should I write a sentence like " the independent study program of your university is also a flexible way of enhancing my knowledge required for research"? I know that I am intended to join as a research student, but still, not all requirements can not be completed just after passing the MS degree, at least in case myself.
After completing the MS program, I have joined some university in the home country as a regular Ph.D. student. So there is a one year gap between passing MS degree and applying for US university. So should I write what I have done in this gap year of that particular university? I have done some credit courses (in this gap year) that are helpful for research in my domain.
I think your overarching question is "What do I include in a statement of purpose for US PhD applications". You can find several great answers to that question if you search this forum. Further there are many, many sample SoPs available online. If you review previous forum answers as well as sample SoPs, you will be able to answer these very specific questions on your own.

And please do have a native English speaker proofread your SoP, your CV, and all other application material before you submit.