# PhD thesis - Names of appendices

I'm writing my PhD thesis (math) and struggling to find titles for the appendices. The thesis has three main chapters and for each one there is an appendix that contains some proofs that did not belong in the chapter itself (e.g. proofs of lemmas and technical details). What should I name the appendices? Currently I'm thinking about "Missing proofs for Chapter X" or "Omitted proofs of Chapter X". Any suggestions?

• Do they share a common topic? – Davidmh Jul 5 '15 at 19:44
• Chapters 1 and 2 are related. Chapter 3 is independent. – Johannes Jul 5 '15 at 20:12

In a mathematics paper or thesis, the most common practice is simply to include all proofs in the body of the document, each one immediately following the statement of its corresponding theorem or lemma. So you should seriously consider just doing that.

Placing proofs in an appendix might be appropriate if they are really ancillary to the main thrust of your thesis. For instance, maybe there is a result that is not really relevant to the rest of the thesis, but you've included it simply because it is interesting. Or you state a result that is well known, but you have written your own proof as an exercise. Or you have multiple proofs of the same statement; you might want to place one of them in the body, and move the other(s) to the appendices.

But in any case, I would think there would not be more than a few proofs that would fit these criteria. As such, it would be most natural to place each proof in its own appendix, rather than to group them by body chapter or any other criterion.

You could give the appendices names like "Appendix A. Proof of Theorem 1.2.3". Or better yet, something more descriptive like "Appendix A. Proof of the Snargleberg–Veeblefester Theorem (Theorem 1.2.3)". Of course, you will want to use LaTeX's \ref to produce the theorem number.

It would be a convenience to the reader if in each appendix, you repeat the statement of the relevant theorem before giving the proof.

If you feel the number of lettered appendices A, B, C, D, etc are becoming excessive, you could move down the hierarchy. Most thesis templates are based on the book document class, in which the top-level text element is the chapter. So if you want, you could write

\backmatter
\section{Proof of the Snargleberg--Veeblefester Theorem (Theorem \ref{snargleberg})}

Blah blah blah.

\section{Proof of the Dumbledore Lemma (Lemma \ref{dumbledore})}

Expecto Patronum.


Producing something like:

A.1. Proof of the Snargleberg–Veeblefester Theorem (Theorem 1.2.3)

Blah blah blah.

A.2. Proof of the Dumbledore Lemma (Lemma 2.3.4)

Expecto Patronum.

I disagree with Pete L. Clark's suggestion to just leave the appendices with non-descriptive titles like "Appendix A". Using descriptive appendix titles will help keep the reader from getting lost.

• The chapters themselves contain the main proofs so I feel like "Proofs for Chapter X" is not accurate. Perhaps "Other proofs of/for Chapter X". – Johannes Jul 6 '15 at 0:19
• I see, then maybe "additional proofs" or "supplementary proofs"? – Nate Eldredge Jul 6 '15 at 1:10
• @Johannes: After thinking some more, I have rewritten my answer. – Nate Eldredge Jul 6 '15 at 1:49
• After thinking some more, I agree with you rather than me. – Pete L. Clark Jul 6 '15 at 2:41

I would think twice about including these results in appendices at all. You have one appendix for each chapter and each "contains some proofs that did not belong in the chapter itself (e.g. proofs of lemmas and technical details)". Why doesn't that belong in the chapter itself? That sounds like exactly the sort of material that I would expect to take up space in a math PhD thesis. You may want to organize things so that the most technical bits can be quickly identified and skipped by the uninterested reader, but putting them in appendices doesn't sound quite right to me. Appendices should contain material which is ancillary to the thesis, not the technical core of the thesis.

Anyway, if you decide to go for the multiple appendices: I would call the Appendix "The Appendix" if there is one of them, and if there is more than one "Appendix A", "Appendix B", and so forth.

Added: After more thought, I agree with @Nate Eldredge's disagreement. If there is more than one appendix, you should probably give some help to the reader by saying what is in each one. Now that I seriously contemplate this possibility though [not that seriously; I still am not convinced that this is a good use of appendices at all, but whatever...] I find the question a bit weird: in that the OP can see his thesis, he is in a much better position than we to make the titles. But a simple, descriptive title should be fine.

• Thanks. I have to use a standard template and the appendices are ordered A, B, C,... but each one needs a name as well. – Johannes Jul 6 '15 at 1:09
• In most LaTeX classes, appendices are like sections or chapters, so they have a descriptive title in addition to their number or letter. – Nate Eldredge Jul 6 '15 at 1:12
• @Nate: They can have a name, but they don't need to (in LaTeX, or in mathematics generally). Johannes: I can only repeat my advice above. The fact that you are having trouble thinking of a name other than "Missing/Omitted Proofs From Chapter X" strongly suggests to me that this material belongs in Chapter X. Unless you're saying that your template requires every chapter to have an appendix? – Pete L. Clark Jul 6 '15 at 1:21
• "I'm not, but this material definitely belongs in an appendix. It's tedious derivations that don't require any intuition or ingenuity, but have to be there nevertheless." How many PhD theses have you read? Over 2/3 of the theses I've looked at (let's say, a few hundred) devote a substantial amount of space to showing mastery of routine material. I cannot recall ever having seen material relegated to an appendix because it does not require ingenuity. Have you talked to your advisor about this? What does she advise? – Pete L. Clark Jul 6 '15 at 2:23
• I suppose it's a question of style now, but I wouldn't move a proof to an appendix merely because it's tedious. The real question is: is it important? Would a reader need to check it to be convinced that your main results are correct and correctly proved? If so, leave it in the body of the paper, no matter how tedious it seems. – Nate Eldredge Jul 6 '15 at 5:06