Numbers, Sets and Functions Presentation Notes Planning and Delivering your Presentation This document should be read together with the ‘Planning and Writing your Mini-project’ document. The Presentation Task Your task is to choose a topic from the Calculus I or Introduction to Proba- bility modules 1 from the list in Appendix A and give a 5 minute presentation explaining it to your tutorial group. You should choose the same topic for your mini-project and presentation and I would expect the details of the content to be similar. Arrangements You will deliver your presentation in your usual Week 6 tutorial (on 31 Oc- tober 2019 or 1 November 2019) using the board in the tutorial room 2 . The audience will be your fellow students and your tutor. Your tutor will arrange the order in which students speak. Please stay in the tuto- rial after giving your presentation to support your fellow students and learn from their presentations. Your tutor will provide written feedback after the presentation. Presentations will be timed precisely and you will be stopped if you over- run significantly. There will be a short time for questions and discussion after each presentation. 1 If you are on a degree programme which includes only one of Calculus I and Introduc- tion to Probability then you will need to choose from that list only. 2 I have deliberately asked you to prepare a board talk not a talk based on computer slides. This is to encourage you to focus on the mathematical content and how you will communicate it rather than on producing fancy slides. Delivering a good presentation with no equipment other than a board forces you to confront the material in a particular way which is very valuable. 1
Frequently Asked Questions Q: Does this presentation count towards my final mark for the module? No. This presentation is formative only. However, you will make a similar presentation in Week 12 which will contribute 10% towards your mark for the module. If you give your Week 6 presentation on a topic from Calculus I then your Week 12 presentation should be on a topic from Introduction to Probability and vice versa 3 Q: Do I need to cover exactly the same material as my mini-project? No. Your presentation should be on the same topic but you shouldn’t try to cover everything from the mini-project in the presentation. Q: What happens if someone else in my tutorial group picks the same topic? If this happens then ignore it and give the same presentation you would have done otherwise. In particular, do not try to change your presen- tation on the spot to make it look different or try to give a follow-up talk starting where their presentation stopped. Q: Can I use prepared slides rather than a whiteboard? No. Giving a talk from prepared slides is a valuable skill but it is not what is being tested here. Q: Can I use a prepared handout? If your presentation requires a complex figure that would be hard to draw in real time then you may bring a single page handout (bring enough copies to pass aroud so that everyone in the audience can see a copy). I would expect very few presentations to need this but the option is there if appropriate. Q: Can I bring notes or a script to read from? You can bring notes but my strong recommendation is not to. If you do bring notes you should treat them as a safety net (ie leave them on the table to look at if your mind goes blank) rather than reading from them. 3 unless you only take one of these modules in your degree programme 2
Further Guidance Choosing a Topic Your first job is to pick your topic. There is a list of titles to choose from at the end of this document and you must pick one of these. Choose one which you find interesting and which you think you will have something to say about. The titles are chosen to be moderately broad. You will need to be a bit selective in choosing exactly what material to cover within the topic. Gathering your material Having done that a good next step is to write down as many things as you can about your topic looking at all the places it crops up (explicitly or implicitly) in the module. You could do this in diagrammatic form with ‘blobs’ for concepts, examples, results etc. and lines indicating how they are linked 4 . You will probably find that your topic crops up in several different places. For example, suppose that your topic was ‘Bijections 5 ’. You will notice that after the definition and examples we see a connection with inverse functions, then a bit later bijections crop up again in connection to counting and again in the definition and examples of countably infinite sets. If you look further afield you might also find bijections (mentioned explicitly or indirectly) in your Calculus I notes. Having gathered all this material you will probably find there is too much for a mini-project and certainly too much for a presentation. Look at what you have and refine it. Which parts do you think are most important? Which parts interest you the most? Which parts would you be most enthusiastic about explaining? You should now have a topic and some aspects of that topic to focus on in your mini-project. For the presentation you will need to focus in even more, perhaps picking out just a single definition, technique or theorem and one example or ap- plication. You need to make sure your presentation can be followed in real time (unlike written material where the reader can stop to think or jump 4 This way of representing information is sometimes called a mind-map. 5 I have deliberately picked a topic from Numbers, Sets and Functions as an illustration. Remember that your topic must be from one of your other modules and must be chosen from the list. 3
backwards and forwards through the text). When preparing, don’t try to fit too much material in. Think hard about what you are going to write down (the most important points and anything that you will need to refer back to) and what you can get away with just saying. Imagine you are delivering a section of the lecture for that part of the module. How will you communicate the most important aspects of your chosen concept as clearly and accurately as you can. For this exercise, don’t assume that your audience has seen the concept before although you may assume they have seen any relevant background. Here is a possible route to preparing the presentation. • Identify what aspect you want to focus on for your presentation. For example you may want to: explain a definition, state and prove a theorem, or demonstrate a technique. Don’t be tempted to do too much; you only have 5 minutes. This is not long so you need to be focussed on what it is you want to communicate and structure the presentation with this aim in mind; there will be no time for digressions. • Decide exactly what material to present. This will include making up your own examples and making connections between different parts of the module. Think about how you can add value to the way the material was presented in lectures. • Think about how to arrange the material. A good presentation will have a clear structure which will help the audience to follow what is going on. • Decide on how you will use the board. What needs to be written down (anything particularly important and anything you need to refer to several times in the presentation) and what you can just say without writing. • Finally, write down a good approximation to what you will write on the board on paper. You can then add (perhaps in a different colour) some notes in the margin about what you will say. Preparing this will get the talk into your head so you don’t need to bring this paper with you. While speaking you shouldn’t feel you are following a script but should allow yourself to vary things spontaneously. 4
• Practise your presentation to make sure that the timing is right and to find out where you need to choose your words most carefully. Giving a good presentation depends on delivery as well as content. You need to stay calm, speak confidently and engage with the audience. Here are a few comments: • You may be concerned about feeling nervous in your presentation. Al- most everyone finds speaking to a group a bit intimidating so this is nothing unusual. Remember that the audience is on your side. • Make sure you engage with your audience. This means making eye contact and reacting to the audience (noticing that someone is looking confused for example). Think of your talk as a performance and try to capture the attention of the audience by the way you talk. • Good board use needs thought and practice. Don’t write too small (or too big). Make sure that anything you need to refer to throughout the talk is in a sensible place on the board and doesn’t get erased. • Don’t read from a script. My recommendation is not to have written notes with you at all as they create a barrier between you and your audience. Also going without notes forces you to prepare well. If you really must use notes then treat them as a safety net only and don’t expect to refer to them during the presentation. Think about who your role models for clear and engaging explantions and delivery are. It’s not a good idea to try to copy someone else’s style but by thinking about what it is they do well you will absorb some of their approach naturally. 5
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