In EE/EC/CS departments, there are certain fields that are theory-based (like the algo or complexity groups), ones that lean towards systems implementation (OS, programming languages, etc) and others have a component of both (like networking).

In such a field like networking, there are professors who work on hard-core math modelling (example) and people who work on implementation and protocol design (example). From what I glean from my own paper-reading experience, the natures of these papers are as different as chalk and cheese: the math papers seem to look for ways to cast the problem in a mathematical framework and try to derive their results from such a set-up, while the implementation-oriented papers conceive of some algorithm and a protocol (based solely on logical argument rather than any rigorous mathematical premise) and present the results of their software simulations.

While on paper people argue there is no divide between theory and practice, at least to me the approach towards research differs widely between faculty members in the same field and department. Now to my questions:

- How important is math emphasis in an applied field like networking? Industry work is almost always simulation-based from whatever I have seen. After all, networks are there to be implemented and deployed, so why bother about probabilistic modelling?
- When there are two modes of research in a particular field, will the PhD student's approach play a role in faculty recruitment?
- Is there a widespread notion of one being superior to another? I know of professors and students who widely emphasise math and pooh-pooh "S-BAA: simulation based on arbitrary algorithm" type of papers.

## 1 Answer

How important is math emphasis in an applied field like networking? Industry work is almost always simulation-based from whatever I have seen. After all, networks are there to be implemented and deployed, so why bother about probabilistic modelling and research? In other words, why should an engineering department award a degree to a thesis where the problem has an engineering cause, but everything is simply applied math?

In these fields, math is a tool, as coding or lab experiment. Even if you have a full mathematical analysis of a protocol, you have to conduct experiments, because real life is not one of our - too simple - models. Why bother on probabilistic modelling? because we have to find ideas for designing algorithms, hoping that the performance in the real world will be somehow related to those in the formal model.

When there are two modes of research in a particular field, will the PhD student's approach play a role in faculty recruitment?

Yes it almost always will. You apply in a team, probably the team is inclined in some of the ways, and want either to make the team even stronger wrt an approach or, to the contrary, to open itself to other ways of thinking. I also remember my own recruitment, where the fact that I am in the middle (maths + experiments) was a big plus for me- since people assumed that I will be able to speak to a lot of people in the lab, from theory to practical people (and that's what happened).

Is there a widespread notion of one being superior to another? I know of professors and students who widely emphasise math and pooh-pooh "S-BAA: simulation-based on arbitrary algorithm" type of papers.

At the end, only one thing is important: making things that work. You will always find people that think that the theoretical approach (resp. the experimental approach) is superior to the experimental approach (resp. the theoretical approach). Both are wrong, what we want is usable (in real conditions) algorithms with guarantees (controlled error, correctness, etc.), how we achieve this goal is interesting for us, but not the main point of our research (** recall that the question is about engineering research**).