Next week I will be delivering a 30-minute talk for a graduate seminar class, which is a class where graduate students deliver, uhm, seminars. *o*. After reading countless Google’s hits on “How to deliver a mathematical talk filetype:pdf”, I’m still clueless as to what I should include in my talk. In fact, it took me hours to prepare the abstract even if the material is largely complete. The last several talks I that delivered about two years ago lasted for abouts 7-15 minutes minutes were like “death by Beamer slides”. Nobody asked questions, and everyone just stared, admittedly clueless, about the boxes with dots and x’s (called rook boards) and lines and dots with arrows and Greek thingies on them (called directed graphs). As the slides progressed the x’s changed positions and colors and the arrows flipped directions — it appeared that I was merely giving my audience a nonsensical visual treat, which may well be better rendered by an episode from Family Guy. In fact, I believe I think have delivered four conference talks in the past – but I was beginning researcher back then and as such I had the license to ensure that the talk is incomprehensible by (a) actually proving results, and force the audience to follow the proof (b) using a fancy orange or pink Beamer template (c) packing as many diagrams and text on a single slide (d) using terminology with an unmotivated definition, and last (but the one I’m most guilty of), (e) making the talk appear more impressive than it actually is. Now that my first graduate degree is well within reach, I believe that my license to commit (a)-(e) has been replaced with the responsibility to be well-motivated, concise, comprehensible and interesting (if not entertaining). Transgression letter (e), in particular, is easy to commit — just pepper your slides with exotic notations when a more standard one is available. On contrary, giving a clear presentation requires planning and practice.
Now, I am writing this blog post with the hope that I’ll stumble upon a magical ingredient to make an interesting talk. The most helpful advise I got so far was Brian Reich’s “Academic Presentations“. However, Reich never touches on what to actually include in the presentation. One of his advise that baffles me the most is “Present ideas, not details,” which is a bit too idealistic — I don’t suppose everything can be communicated as an idea by neglecting the details. For example, if I wanted to talk about a convolution formula that generalizes a classical one, should I say, “We were able to derive a convolution formula that looks like the classical one, except that we added a few more parameters and use square brackets instead of parentheses. It’s like a Christmas tree with shiny balls in it.” Or should I say, “This is what the convolution for our sequences looks like: <insert a jumble of symbols>.” I think it’s best to trim off ideas that are impossible to convey without too many details.
So far, after reading the suggested materials for our class, my impression about given math talks are as follows:
(1) If your audience is well-acquainted with your work I think it is okay to go technical. My audience will be (brilliant) graduate students who may not be well-acquainted with my work, so I think it will be best to make the talk as leisurely as possible by (a) showing how my work relates to other fields, (b) spending some time on preliminary concepts and (c) illustrating these concepts as much as possible.
(2) Organization is a key element in delivering a good presentation. I think I’d be better off using the good ol’ format: Intro (context, notation, terminology, statement of the problem), Body (results and discussion) and Conclusion (what was achieved and what may be done next).
(3) Neither me nor my audience gains anything if I present anything too technical. So out with highly specialized results, especially those that rely strongly on concepts that I didn’t discuss. If a theorem needs to be proved, it’ll be probably best to give a sketch of the proof.
(4) A good rule of thumb on the number of slides is #minutes/2, which means that I have to prepare a presentation that is good for 15 slides. If I hadn’t read this advise, I would have made as many slides as I thought would be necessary. And the rule makes a lot of sense — more slides = more details = greater possibility that your audience will be lost along the way.
(5) It’s good to include an ample amount of illustrations. David Patterson writes, “Confucius says ‘A picture = 10K words,’ but Dijkstra says ‘Pictures are for weak minds.’ Who are you going to believe? Wisdom from the ages or the person who first counted goto’s?” (Aside: I loved gotos when I first learned LBasic, but I despised them when I learned R and C.)
(6) The basics: eye contact, clear (and engaging) voice, not reading what’s on the slides.
(7) In sum, the whole point of giving a talk is to convey the singular message, “This is what my work is all about, and I hope that you (a) find it interesting enough to Google one of the terminologies I have mentioned (b) think that my work is at least as interesting as yours.” The challenge with combinatorics, which is where my research is classified, is that it is particularly tricky to make results look interesting in front of a non-combinatorics audience. Math majors are trained to appreciate and recognize deep and elegant theorems, which combinatorics has none. (The Principle of Inclusion and Exclusion, for instance, is just equivalent to computing the inverse of a certain matrix.) Oh well, it can’t be helped. So this should be the least of my concern.
Then, again, my first question still begs itself — what should I include in my talk? Wait — I just submitted my abstract. ΩΤΦ*! Let’s see what I come up with tonight.
Image from http://zacthetoad.deviantart.com/art/Death-By-PowerPoint-88427711. Edited.