by Alexander Grosz

General guidelines

Preparation:

• Don't give a lecture. Give a talk! The audience will not take notes, so make sure that even people without perfect memory are able to follow your talk and try to keep references to previous slides to a necessary minimum.
• Be as approachable as possible and as technical as necessary. Some types of representations are a better fit for a talk than others. E.g. think about explaining the abstract ideas of an algorithm compared to listing pseudo-code.
• Give your talk a nice outline. You don't climb a mountain by always looking at your feet, but you glance at the summit to give every step proper purpose. The audience should know where you want to go and have some idea of how to get there at any point.
• Illustrate important points before getting too technical about them! Think about how you understood things by developing an example first; you guide the audience through that process quickly.
• Tell a story, not just a chapter of a book. The story is exciting (or the audience should at least believe that you think so). Don't forget that the audience is _your_ audience. Engage with them and don't just look at your slides.
• Use the available methods to your advantage. Figures in an article or a book are typically static (if they even exist). On (your own) slides, you can interact with them, build them up sequentially, change them, etc. to get your points across.

For the talk:

• Breathe! Take a deep breath right before you start your talk. You're nervous and that's okay. That's why you need to breathe.
• Stopping a bit early is okay, exceeding the time is not. As long as you cover your topic in reasonable depth with sufficient mathematical details, you will be fine.
• Adjust your pacing and slides. The slides shouldn't be too full and overwhelming. Also, make sure you don't just skip through "easier" slides too quickly. If it's only up there for 5 seconds, is it really worth it?
• Let the audience not just see/hear, but also digest the content, especially for the foundations of your talk. Let the most important content sink in or even reinforce it in some way. You don't want to lose all of them after the first 5 minutes because you're too fast. Know your audience and try to make it as easy as possible for them to understand the basic concepts of your topic.

Checklist

• Check your content!
  Depending on your topic selection, you will not be able to cover everything from the suggested literature. We do not necessarily expect you to present everything! Try to read and understand as much as possible from the literature and then think about what would make for a good selection of content to introduce the other seminar participants to the topic. This can be your own preference, e.g. the parts you liked best, understood best or think are most representative. You can (and most likely should) also present examples that you came up with yourself to understand the content better.
• Check your slides!
  Nobody (I know of) has ever done a good presentation by just copy-and-pasting definitions, theorems and proofs from a book to a slide. It is crucial that you think about how to present your content selection as well as you can in the limited time you're given. Take a step back while creating the slides every once in a while and think about whether you would be happy to be in your own talk's audience! Make sure that you make the talk as accessible as possible to your peers while keeping sufficient mathematical depth for some details to give a good impression of the methods in your topic. Most likely, you did not understand everything when reading it for the first time. Your audience has much less time to do so during your talk, so you need to guide them by presenting the content clearly and using intuition (e.g. through examples and non-examples) to accelerate this process.
• Check your time!
  You are expected to stay within a reasonable time limit. In order to make sure you achieve this, please also give your talk to your friends or record yourself with a webcam as preparation. This will not only allow you to check your time management, but you will also get ideas on how to improve your talk! Watch your pace and whether you need to jump between different slides because you need to refer back to previous information while you're at it - this is usually a sign of missing information on the slide that you currently want to talk about.