For over a decade studies of the strong interaction in extremely dense nuclear environments have been done at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory. It is hypothesized that colliding two beams of Au nuclei at relativistic speeds creates an environment of hot dense nuclear matter where the quarks and gluons inside the nucleus, which are normally confined within the protons and neutrons, become deconfined into a soup called the quark-gluon plasma. Since direct observation of this short-lived phase is impossible, many sophisticated analysis techniques attempt to study the early interactions via the final state particles. What has emerged from analyses of the data are two, contradictory paradigms for understanding the results. On the one hand the colliding quarks and gluons are thought to strongly interact and reach thermal equilibrium. The other view is that primary parton-parton scattering leads directly to jet fragmentation with little effect from re-scattering. It is in principle possible to distinguish and perhaps falsify one or both of these models of relativistic heavy ion collisions via the analysis of two-particle correlations among all charged particles produced in [mathematical symbols] = 200 GeV Au+Au collisions at the STAR experiment at RHIC. This dissertation presents studies of two-particle correlations, whose derivation can be traced back to Pearson's correlation coefficient, in transverse momentum and angular space. In momentum space a broad peak is observed extending from 0.5-4.0 GeV/c which, as a function of nuclear overlap, remains at a fixed position while monotonically increasing in amplitude. Comparisons to theoretical models suggests this peak is from jet fragmentation. In a complementary study the momentum distribution of correlations in ([eta],[phi]) space is investigated. The momentum distribution of correlated pairs that contribute to the peak near the origin, commonly associated with jet fragmentation, is peaked around 1.5 GeV/c and does not soften with increased centrality. These measurements present important aspects of the available six dimensional correlation space and provide definitive tests for theoretical models. Preliminary findings do not appear to support the hypothesis of a strongly interacting QGP where back-to-back jets are expected to be significantly suppressed.