The new spirit and urgency of converting the remaining research reactors from highly enriched uranium (HEU) to low-enriched fuel, combined with the prospects of new ultra-high-density fuels, provides the main impetus and defines the basic scientific objectives for this thesis. It is predictable that activities to convert existing research reactors will intensify in the near-term future, which in turn would simultaneously increase the need for corresponding neutronics calculations. Here, especially the analysis of the remaining high-flux reactors, which are most difficult to convert due to compact core geometries, may benefit from high-precision simulation tools to adequately set-up and study reactor parameters using complete three-dimensional core models. The scope of the present thesis is to support this process in providing a new computational tool for neutronics calculations (M3O), which is based on standard physics codes, while using the technical computing environment Mathematica as the primary user-interface. The use of such modern environments can be very convenient for a variety of reasons: their analytical capabilities allow for a broad range of calculations and data manipulation, while their interactive graphical user-interface facilitates intensive control of input parameters and interpretation of achieved results. At the same time, Monte Carlo methods play an increasing role in neutron transport and burnup analyses. In M3O, the Monte Carlo code MCNP is employed, which offers the potential for high-precision modeling and analysis. Both major components, Mathematica and MCNP, are also used in an optimization tool developed below and based on the linear programming technique to optimize reactor performance by variation of the fundamental core parameters. The potential (and limits) of monolithic fuels is largely unknown today. Even though the conversion of a large number of medium-flux reactors would be relatively straightforward, the performance of monolithic fuel with low-enrichment in high-flux reactors is less obvious. A second main objective of this thesis is therefore to study the neutronics performance of monolithic fuel for a specific type of high-flux reactors, namely the class of so-called single element reactors. These reactors can be considered to be the most difficult to convert to low-enriched fuel because they are characterized by very compact and inflexible core designs. Every existing reactor of this design still uses highly enriched uranium. In addition to a generic single element reactor, which is introduced for more fundamental purposes, the German research reactor FRM-II will be the primary test-case for the evaluation of monolithic fuel performance because it would be an obvious candidate to use this fuel in the future.