Gone are the days when obscure, hour-long PowerPoints filled with complicated math results derived alone can win awards. The modern engineer must be communicative, creative, and collaborative to be successful. As a graduate student in neutronics, this can be especially challenging. My publications often center on subtle approximations to the neutron transport equation and their subsequent impact on simulation results. To avoid putting people to sleep during my presentations, I have developed a few techniques that help make it more exciting to talk about code. It all starts with identifying your audience and putting yourself in their shoes. There are three main categories of listener I run into: the uninitiated, the familiar, and the expert.

### The uninitiated listener

I typically talk to an initiated crowd at educational outreach events, during general-interest interviews, and at undergraduate seminars. To me, this group can be the hardest to speak to about math and programming. The first thing I do is let go of my ego. I might not get to the details of my thesis work because the uninitiated listener might not care to dive in that far. Instead, I spend a lot of time motivating the need for math and programming. I try to convince my listener that they wish they had my job.

When the time comes to present the neutron transport equation (I can’t totally avoid it because that *is* my work), I never use the written mathematical terms. My favorite method is to use concept boxes which illustrate the meaning of each term of the equation and emphasize the relationships between terms rather than the terms themselves, like in in the picture below. Especially in an educational outreach setting, I like to turn the neutron transport equation into a game. I ask the students to put themselves into the shoes of a neutron and imagine what things might happen to it during its life: it is born, it dies, it gets lost, it bumps into another material, etc. Then, we make a list of “gains” and “losses” to emphasize the impact of each term on the equation.

Once I have everyone on board with the neutron transport equation, I can afford to be vague about the changes I am making to it. I definitely don’t distinguish between the transport equation and the diffusion equation, and I get straight to the results. These results should be as visual as possible, illustrating how my technique is more accurate than others.

### The familiar listener

The familiar listener is a tricky category. Nestled somewhere between the novice and the expert, the familiar listener might be a nuclear engineer who has never written a line of code. On the other hand, they could be an avid programmer who has never seen the neutron transport equation. In this case, the presentation becomes a time-management issue since you will want to cover the material from multiple angles.

I often encounter familiar listeners at departmental seminars or computational conferences. A familiar listener will always try to fit what you are saying into the box of what they already know. And be careful; vocabulary that we use in our field could overlap but mean something else to the audience. For instance, in a nuclear setting, everyone has a firm idea of what Monte Carlo is. But Monte Carlo is actually a very general-purpose method used in many other fields. I always take the time to explain what I mean by Monte Carlo neutron transport at the start of my talk.

For a familiar audience, I allow myself to use mathematical terms for my equations, but I am careful to highlight changes and relationships very clearly (using color for example). I like to use analogies and focus on what terms are increasing, and what terms are decreasing. When it comes to describing algorithms, I can’t assume that the names of common algorithms are well-known, so I introduce them from scratch. I remain focused on results, and I leave a lot of room for questions since this is typically a very curious crowd.

### The expert listener

The expert listener is most common at small conferences and topical meetings. But don’t be fooled: a crowd of experts often has a few “familiar” listeners lurking as well, such as graduate students or someone who recently changed fields. Make sure you welcome these participants with enough background to learn something before you jump into the weeds.

When I give a talk to an expert crowd, I keep the motivation short and jump into the math fairly quickly. This gives me time to address the details that the audience will be interested in. I fully define all the mathematical terms, including the dependencies. For an expert, it’s important to know if a variable is spatially dependent for example. This doesn’t mean I abandon my visual aids such as color, arrows, and relationships.

Even experts can get lost if my talk isn’t organized, so it’s important not to jump around much. Sometimes, I will skip defining a numerical method if it’s widely known, but if I am presenting a change to an existing numerical method, I may define it in detail so that my change can be better understood.

### In general

No matter the audience, there are a few key things to keep in mind when presenting math: let them derive the equation (when appropriate), pause to allow them to check the math in their heads, and stay very consistent with notation.

Finally, we must address the cardinal sin of programmers (which I have been known to commit from time to time): including screen shots of your code in your slides. It’s hard to read; nobody knows what they are looking at or how to interpret it. Instead, present the algorithm in standard LaTeX form, or use a flowchart. The key is to be clear with which loops occur where, which the indentations of the algorithm or the circles in a flowchart do nicely (speaking of flowcharts, I am currently looking to up my flowchart game, and I’ve come across some free software that might help me do just that: inkscape and gperftools).

So, if you’re in a math-heavy research group and you’ve always felt disconnected from your audience, there are definitely a few things you can do to make your presentations more exciting! Take a step back and reflect on your audience. That might mean more work since you can’t use the same slide deck every time. But you’ll find the engagement of your audience to be well worth it! If you tend to fill your slides with math equations and numerical jargon, I suggest you remove all the math and put back in only what is absolutely necessary. Math can scare people away when it’s obscure. Instead, make sure your talk makes math look cool and fun, because you and I both know – we love doing this.

*Miriam Kreher is a PhD graduate student in the MIT Computational Reactor Physics Group, working with Prof. Ben Forget.
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*Published April 30, 2021*

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