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Please note that my guide abandoned me and I am studying and preparing my masters thesis myself. There is no help from any faculty in my department as they can not bother, as they are not guide. Being enrolled in a 3rd world institute, this is not surprising.

I read 5 research papers (4 are on odd zeta values and 1 on Goldbach Conjecture) in number theory and I will explain the steps involved and prove statements which authors didn't prove. So, my thesis is expository and I have not proved any original results. I have written a rough draft of explanations of the papers.

But I don't know what should I write in the preface or beginning of my thesis, explaining what I have done as I have no idea of these sort of technical language. Also, I searched on internet about expository thesis but most theses were on proving some results or generalizing some conjecture. I could not find a work related to mine. So, I am asking here. I have also to be very cautious so that I am not accused of plagrism.

First 4 papers are about 4 different methods used in studying irrationality of odd zeta values and the 5th paper is a bit different.

Can someone please tell what to write in the preface.

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You write:

  1. What are the problems you are studying.
  2. Why are they important.
  3. What are your own contributions. (Maybe: "We present detailed proofs of the results...". Or maybe: "We summarize the results about A...".)
  4. Is there anything new in your contributions? Mention that, too. Maybe you are writing in a different language, combining results that have not been explicitly combined before, providing a more detailed proof of some statement than you could find, etc.
  5. What has been done before? A brief literature review is appropriate.

You should combine those parts in a way that feels natural. They are not section headings.

Plagiarism

To avoid plagiarism, do not copy text from elsewhere. Write in your words. This is especially true of free text, such as the introduction and literature review.

Furthermore, cite your sources. For example: "This proof follows the proof by [4], but we include additional details."

It might not be useful to rewrite theorems and definitions in your own words. If they are common knowledge (can be found in several textbooks), you can use the common ones. If the definition is less established, or if there are several variants and you have chosen to use a particular one, then a citation is appropriate, and explicitly mentioning any verbatim copying.

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