What are the areas a student must focus before entering the computational biology research?

Pretty much any biology can be made computational. Now as it is called "computational" I hope you can do some programming, for that's what it is going to be about.

For gene stuff I think databases and algorithms are important, for they deal with big data. This is an area I know little about, but it seems what other people have been suggesting are mainly useful here (i.e. basic sort algorithms, databases).

Systems biology on the other hand is often more concerned with somewhat specific, smaller systems (how genes inhibit, promote, and interact with each other). One typically models what are essentially chemical reactions. So in a way it is about expanding the Michaelis-Menten equilibrium kinetics to smaller populations with noise. There are many ways to approach this problem, numerically the most popular one is perhaps the Gillespie method. Mastering this along with enzyme (chemical) reaction rate constants is not difficult supposing you remember your differential equations.

Now a lot of the people involved in the programme seemed to have a physics background, and accordingly they had publications on membranes, the favorite model toy of biophysicists. A lot of interesting questions to ask about membranes are related to their elastic behaviour; how much energy does it take to bend and how much do thermal fluctuations cause it to do so, as a textbook example. This is most typically done by the use of the so called Helfrich Hamiltonian. To be able to analyze these, you'd have to remind yourself of equilibrium thermodynamics: Free energy, the equipartition theorem, and the fluctuation-dissipation theorem come to mind. From mathematical tools you'd need Fourier analysis and calculus of variations (i.e. Euler-Lagrange). Still related to membranes is phase separation and basically all of thermodynamics in general. Learning and coding the Ising model gets you a long way in this regard. Hydrodynamics, too, are important not only to membranes, but to a lot of research in computational biology in general. Finally I'd like to point out that DNA is often also related to statistical mechanics, thermodynamics and hydrodynamics, the most simple models of its stretching are in fact based on the Ising model (and polymer physics).

Finally, you have intense computational modeling of small biological structures. Perhaps most computational work on proteins is about homology modeling and here you might be using tools from quantum physics and chemistry, so knowing some of the terminology there might be useful (say at the level of what Hartree-Fock is, what DFT stands for, and what are pi orbitals). More often than not, these results are parametrized to a classical force field, and run using a molecular dynamics simulation. Coding up a simple MD program (say of three planets attracting one another) should again be a simple task. Some keywords here, if you want to delve deeper, might be AMBER, CHARMM, GROMACS (these are programs that are used with biomolecular simulations, and while learning to use them is a whole other matter, their manuals and tutorials might help you understand what they are about).

Now I did take a very particular route down from genes to single molecules in my explanation here, and there are many things that I did not touch upon (given that my background is in physics, not biology nor in data science, a major pillar in anything computational). In particular, I did not discuss active processes, something that is of course very important in biology: This is why I referenced (equilibrium) thermodynamics so many times above, and it can really only be used in equilibrium. Nevertheless, it is difficult to understand nonequilibrium without first being introduced to equilibrium. I, however, think that given the interests of the researchers affiliated with the programme, some of the topics I mentioned above may well come up. Do also note that I did, in places, go quite a bit into the technical detail, something you might not be willing to do due to the time constraints.

Finally, I'd like to mention Coursera.org, for they have had several offerings of systems biology and the like, so you might find that a useful resource.