RE:Analysis and Design of reinforced concrete slabs resting on various types of ground
I would recommend you start by completely familiarising yourself with the use of Yield line analysis as a design tool. A good starting point is the Reinforced Concrete Council publication "Practical Yield Line Design". This should help you gain the basic knowledge required to understand the principals which yield line analysis adopts.
Moving forward from this there are also numerous publications on the analyitical modelling of ground floor slabs, using springs with a definable stiffness for the ground, usually refered to as the modulus of subgrade reaction.
Having written a dissertation recently, they will probably be looking for you to demonstrate a progressive methodology within your work, starting simply e.g. simple hand calcs but leading to an FE model. I would also look at seeing if the University has access to any software programmes such as Ansys or Abacus, which shouldl enable the use of ground modelling along with the use of non-linear properties of concrete elements.