Summary: The closed, \(k=1\), FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the \(k=0\) case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semi-classical at some late time, the big-bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the ‘difficulties’ pointed out by Green and Unruh in the \(k=1\) case do not arise in a more systematic treatment. As in \(k=0\) models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the \(k=0\) case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna’s recent work addressed to computational physicists.