Input field not showing up in Distance Matrix In QGIS 2.0?
There is no way to detect an arbitrary MITM, because there are several techniques to perform them.
However, most MITM attacks on Ethernet or WLAN use ARP spoofing to redirect traffic. There are tools to detect ARP spoofing, these should indicate most MITM attacks. See e.g. the Wikipedia page for some tools.
Get your feet wet in applied math to make sure you'll like it. Apparently there is no applied math program where you are now, but you can still do this, through a combination of self study and courses offered in your own and in other departments. Look at some applied math programs at other universities to get a flavor for the variety involved, and to give you some ideas of what sorts of courses to look for. Programming skills are not required for all areas of applied math but can really come in handy for some.
When you're ready to ask for recommendations, be honest, just say that you are hopeful an applied math degree will make you more employable.
I assume you'll want to pursue this process with some transition time, during which you'll continue working to some extent with your current program including your research project.... If so, please find some people to interact with remotely, in your area.
You can't just say "0.001 is a very small number, therefore there are very few electrons in the conduction band." Is 0.001 really a small number? Well, compared to 1, it's a small number, but compared to 0.0000001, it's an enormous number!!
As it happens, there is an enormous density of conduction band states, so even if only 1/1000th of them is occupied, the semiconductor still has a large number of electrons.
A good starting point is to use the figure of 0.001 to try to figure out mathematically how far the fermi level is below the conduction band. How many eV? Then draw the fermi level at the appropriate place in the bandgap. Look at the picture, then you can answer the question of whether the semiconductor is p-type or n-type.
By the way, I don't want you to think that your original reasoning was stupid. In fact, there's nothing wrong with having a qualitative discussion of a physical system, using terms like "big" or "small". It's an extremely important skill! But you can't have those kinds of discussions until you have some rough ideas about "how big is big" and "how small is small". Working through some examples numerically is a good way to develop that sense. Then later on, you'll be able to answer this question (and similar questions) correctly off the top of your head, without doing any calculations. So use math for now, but keep thinking visually and qualitatively about what you're learning when you do those calculations. :-D
I won't want walk through all the quantitative details here: It's a homework problem which is beneficial to do yourself. :-D