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I'm a Masters' student in maths and it's close to my thesis oral defense. As such, I'm preparing my slides to present them. However, I'm feeling that my presentation has too many slides (albeit my equations are quite long as well), but at the same time I'm afraid of handwaving things too much if I omit some prrofs and such. To add more doubts, I watched a friend's defense and it was quite smooth, but later he told me there was 96 slides.

How do I decide if my thesis is getting too long? Is there some time metric (like time per slide) that can help? Is it OK if I omit the proofs of my theorems (and only mention the ideas of demonstrations while I'm talking)?

I saw some other questions and articles around, but I wanted some advice more related to mathematics, where rigorous proofs are expected and equations can get quite long.

Edit: It seems I have 45-60 minutes to present all the content, however I see fit (no presentation templates and such)

  • Which country? The norms vary widely, even within the same discipline. – Tommi Mar 6 '19 at 6:02
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How long should your presentation be? Find out your institution’s instructions + guidelines! We absolutely can’t answer this part for you; every institution will have its own timetable and expectations, and you must find out what those are and follow them. How to find these? You can try asking your advisor, asking the general co-ordinator for your department’s thesis presentations, and looking for instructions in the department’s website or handbook.

And for the subsequent question, how many slides? This is just a part of a much bigger question: how to write and give a good presentation? As you get experience of presenting, you’ll develop a personal style, and the rate of slides will be part of that, but just as a guideline to start with: a typical rate is one slide every 1–2 minutes. Personally I prefer aiming for the slower end of that, one slide per 2 minutes (e.g. 12–15 slides for a half-hour presentation, allowing time for questions at the end); it forces you to keep the slides down to just the key points, not overloading the audience with more than they can read, and gives you time to expand on the slides with what you say in person. Having too many slides, and too much on them, is a much more common problem than having too few slides. But, again, finding a rate of slides that suits you is part of the bigger issue of finding a presentation style that suits you; and that’s a very big and fun problem to work on, but not one with a simple answer.

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The norms for defences vary a lot between universities and sometimes even between different subfields within the same department (e.g., applied and pure math). Therefore only your supervisor or somebody else who is familiar with the customs of your department will be able to answer:

  • How much time you have.
  • Whether detailed proofs will be expected or not.
  • What you can expect your audience to know.

Given that you already attended a defence at your department, your guess is already better than what you can possibly get from the Internet.

As for the length of your talk, there is only one reliable way to find out: Test it, ideally with a human audience. If we knew your style and such, we might give you a minute-per-slide estimate, but a test talk is much more accurate and something you should do anyway. If any possible, get feedback from somebody from your group on your slides and also what you say.

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Your advisor is the best source of an answer for this. I suspect you have something like an hour (maybe less) to present, followed by questions. You don't likely need to present details of any lemmas, but should outline proofs of main theorems. At least give a hint as to the direction someone would follow if they wanted to try to reproduce your work.

If you say too little, you will get more questions, so be prepared to fill in detail if you don't include it in the talk. But the ones who will judge your work are already experienced in your general area, so may not need as much detail as other people might if it is a public talk.

But the insights into your work are much more important than the detail, which can get quite pedantic.

But you can also do a trial run a few days before the talk, presenting your work to a toy duck or to a friend or two. In the latter case, you will get some feedback on it.

  • Thanks for the answer! Also, may I shorten propositions and theorems in the presentation, or should I show them as I wrote in the written thesis? – AspiringMathematician Mar 5 '19 at 19:23
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    You make a considerable amount of assumptions that do not translate to every (math) department in the world. For example, I know at least one where defences were limited to half an hour and every decent mathematician should be able to follow them. – Wrzlprmft Mar 5 '19 at 19:45
  • @Wrzlprmft, yes, the "hour" came more from thinking about doctoral defense presentations. The advisor will know the actual rules. I agree about "every decent..." at the MS level, but not thereafter. But if it is "insight driven" rather than detail driven, more people will be able to grasp the main thread. – Buffy Mar 5 '19 at 19:48
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    @Buffy: At least at my alma mater, the rules for PhD were more or less the same: The talk should last one hour sharp and be addressed at a general audience of scientists from the field. Anyway, debating about this is mostly futile since for every reasonable combination of rules, you will find one department that uses them. – Wrzlprmft Mar 5 '19 at 19:53
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    @Buffy: Sure, but I would not even offer speculations on this. – Wrzlprmft Mar 5 '19 at 20:04
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I would aim for 30-45 minutes for oral presentation. 20 slides max. Let the committee pick at it if they want--perhaps they don't want! If they pick, just explicate, using the chalkboard.

  • If I try to fit everything into 20 slides, I'll only present the definitions and main results, and maybe one example. Every proof will only be mentioned, and no preliminary work (important but well-established results) will be shown. Isn't it handwaving too much? – AspiringMathematician Mar 5 '19 at 19:32
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    If you are worried about cutting too much, put that material in an appendix just in case. – Federico Poloni Mar 5 '19 at 20:21
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    @AspiringMathematician: How much detail you can include isn’t limited by the number of slides; it’s limited by the time you have. If you only have 30 minutes to present, then writing fifty slides packed with details won’t show more proofs — it’ll just make it harder for the audience to follow the key points. Equally, experienced mathematicians in the audience will understand that there isn’t time to give detailed proofs of everything. If you use your twenty slides well, to clearly present the main definitions and results, that can make an excellent talk. – PLL Mar 5 '19 at 20:54
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    In Finland you have 15 minutes, in Denmark an hour. "Aiming for" a generic number makes no sense without further information. – Tommi Mar 6 '19 at 6:07

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