A good friend of mine recently finished writing his diploma thesis in mathematics. We often discussed various aspects of his work, ranging from the actual writing process to the creation of figures. This prompted me to gather my notes from my own diploma thesis and I think they may offer some valuable advice for students. My intention is to write several articles, each detailing a certain aspect of creating a diploma thesis. For this first article I want to focus on the writing process, which is probably the integral part of any thesis.

While preparing my thesis, I read a plethora of books about the writing process because I was always intrigued about the (seemingly) ease with which so many people produce so many documents. I was quickly cured of my naivety: Upon closer inspection, many texts turned out to be written rather crappily. Thus, I hoped that by learning about all the rules, my writing would become superb. Unfortunately for all of us, most of the books about writing are also crap. However, I found several texts and book that I personally consider worthwhile. Hence, to start with, here's a list of rules that I recommend following:

Write drunk, revise sober: Since I abhor alcoholic beverages, here's my paraphrased version for mathematics: When writing your first draft, do not worry too much about sectioning, connections to the rest of the text, any redundancies, and so on. However, upon having finished a certain unit of work (a chapter, a section, a subsection, a paragraph), read it again and try to find improvements. In fact, I would suggest an iterative approach: As soon as a single part of the thesis seems to be finished, check how it connects to the rest of the thesis. Fix everything you deem to be incorrect. Rinse and repeat.

This rule is probably the most important rule for any kind of writing endeavour. If you are slightly pedantic and perfectionist (just like me), you will worry too much about things like "How does this section fit in here?", "How should the proofs refer to each other?", "I cannot explain this fact without explaining that fact", and so on. The best course of action is to ignore the nagging little voice inside your head (you do have one, too, haven't you?) and just write something down. Even if you consider it utter rubbish, it is still easier to correct than a blank slate of paper.

Create a leitmotif: In Germany, we also call it roter Faden (literally, red thread), describing a thread that weaves and binds together your thesis. This means that all parts of your thesis should have their justification and their connection. Since you are probably not writing your thesis about several different topics at once, each part needs to have its own justification for being there. When I am reading a thesis or a research paper I like to know why I am reading a certain section. If this motivation is unclear or (even worse) non-existent, reading your material becomes needlessly complicated.

Don't be afraid to remove content: Keeping the leitmotif in mind, some sections are best scrapped after writing them. Yes, you read that correctly. Don't be afraid of removing content after you have written it. If it does not fit (any more) into your thesis structure, it will only clutter up your writing. When writing my thesis, for example, I learned that I had to write some disposable content in order to understand a certain topic correctly. Having written down everything, I saw that it would not fit into my thesis. So I scrapped it and much grumbling ensued. But it turned out alright in the end.

Cite correctly: Citing your sources is the bread and butter of any scientific endeavour, but this is not what I am talking about. Rather, I am talking about how to cite your sources: Suppose there is a proof of something magical in a rather large arcane tome, written by Knuth and Feynman (wow!). You are now tempted to writing something akin to "...and for the proof of baz see the magical proof in [FK79]...". Naturally, "[FK79]" refers to a tome with 2435 pages.

From a reader's pointer of view, this is the most vile thing you could have done. While readers are perfectly capable of perusing the index of a book in order to search for the relevant proof, common courtesy dictates being more precise. In addition, citing correctly also helps you find incorrect references. Checking a reference such as "[Mu11], pp. 41–45" for correctness is much less work than browsing "[Mu11]" and check whether the theorem, proof, whatever is included therein.

Learn how to use a dictionary: If English is not your native language, I strongly suggest learning how to use a dictionary. And by dictionary, I mean a printed book and not an online dictionary. Let me expand on this: Mathematically speaking, a dictionary is not a bijective function. Some people, alas, treat it that way. When you are looking for a word, however, you always require a correct context. You need to know how this word is commonly used, whether it is outdated and so on. Be especially vary when searching for homonyms!

This item of advice does not imply that online dictionaries are useless. Just take their results with a grain of doubt and check whether you use your words correctly.

Adapt your punctuation: The rules for using punctuation in English texts are less rigid than the rules for German texts. Use this to your advantage! Try to mimic the way a native speaker would use punctuation. This tells your mind that you are not writing in your native language anymore, thereby making you less error-prone (or so I have convinced myself; this could be complete balderdash, for all I know).

Omit needless words: I am parroting William Strunk's famous advice. Bear this in mind when writing (scientific) texts. No prizes are awarded to those who consciously try to formulate everything as complicated as possible.

Keep your sentences short: This is most relevant for German authors. In German, we are used to construct intricate nested sentences (which are often not understood by our readers; see the previous item). Don't do that when writing English, or your sentences will become ambiguous.

Don't be afraid of using the same word repeatedly: Some of use have been drilled by schoolteachers to avoid repeated usage of the same word. In academic writing, however, this is often unavoidable. And actually, using the same word to signify the same thing helps readers enormously.

Some literature

  • Mathematical writing by Knuth, Larrabee, and Roberts: This very readable essay helped
    me a lot when writing my thesis. Knuth gives helpful tips about writing (and formatting) proofs, but also mentions some general writing rules. The essay is available as a book or as a PDF.

  • The Elements of Style by Strunk and White: This small book helped improve my writing style. Some of the rules from above are paraphrased from there. The book has had its share of criticism (see an entry in the Language Log, for example), but it's a good start for those who (like me) are overawed by their first large writing project.

  • Wie man eine wissenschaftliche Abschlussarbeit schreibt by Eco: Geared towards the humanities and somewhat outdated. Still, this little book contains a wealth of tips and its anecdotal style makes it fun to read.

  • A manual for writers of research papers, theses, and dissertations by Turabian: Recent editions have seen substantial updates, so the book is really accurate. For my personal taste, it also focuses too much on the humanities. On the plus side, though, the book covers a lot of different topics, ranging from correct citation rules for URLs to the preparation of graphs and tables.

  • Common errors in English usage by Brians: Very useful (even for native speakers, I guess). Don't be deterred by the very tabular look of the book. The lists of incorrect expressions are very fun to read and really help.