# Guidelines on Writing a Math Thesis

#### caffeinemachine

##### Well-known member
MHB Math Scholar
Hello MHB,

I am in the process of writing my thesis.

I need some guidance on the same.

I need results from basic real analysis. I will be happy to provide their proofs in my thesis but I am not sure whether or not it is appropriate. In other words, I am not sure what do people expect to see in a thesis? Self-Containment with capital S and capital C or 'a proof can be found in \ref{book/paper}' or something in the middle of the two?

#### mathbalarka

##### Well-known member
MHB Math Helper
Basic results can be omitted and refferred for staying-on-topic purpose, but general results cannot be missed. For example, I give three cases here :

1. When you are writing about some results related to connected spaces in topology, you must not omit Jordan's theorem.

2. If the result is too trivial or elementary, no reference is necessary. If you are writing a deep article or thesis or paper about structure of Gaussian integers (integers adjoined with $i$), then omit the fact that they form a group.

3. If the result is basic, but neither elementary nor trivial, refer a good place in which a good proof is given. If, for example, you are writing about density of primes of the form $x^4 + y^2$, give reference to a book in which either Dedekind's beautiful proof lies. (In fact, if your article is a bit topology-partial, give you might even want to give Zagier's proof into it)

PS : Follow at your own risk. I neither have been a thesis-writer nor an expert on mathematical presentation. I too, along with some co-authors, am going to write a paper (on a number theoretic topic) for the first time, so no guarantee neither warranty.

#### Ackbach

##### Indicium Physicus
Staff member
Hello MHB,

I am in the process of writing my thesis.

I need some guidance on the same.

I need results from basic real analysis. I will be happy to provide their proofs in my thesis but I am not sure whether or not it is appropriate. In other words, I am not sure what do people expect to see in a thesis? Self-Containment with capital S and capital C or 'a proof can be found in \ref{book/paper}' or something in the middle of the two?

I should think it would depend both on the level of your thesis as well as your intended audience. A Ph.D. dissertation should definitely only reference proofs in, say, textbooks or papers, while providing a solid and followable amount of detail for the original material. One exception might be if a proof occurs only in one paper, and it's nearly unreadable. Good scholarship would dictate that you would rewrite it more clearly so your audience can follow.

MHB Math Scholar