The many-body problem arises in several disciplines in physics, both classical and quantum mechanical. One approach which has been particularly successful is perturbation theory. In atomic physics, Rayleigh-Schroedinger perturbation theory has been applied to second-order but going beyond that has been difficult owing to the rapid increase in the number of Feynman diagrams which arise with increasing order, and the corresponding need to sort and combine those diagrams to a form amenable to numeric computation. In this talk, a completely symbolic approach using the algebra of second-quantization, Wick's theorem, and the computer algebra system Mathematica, will be described and shown to be formally equivalent to the conventional use of Feynman diagrams. In addition, a second application of a symbolic program will be shown to perform the angular reduction of the Wigner 3-J terms, resulting in expressions which are then evaluated with a C-program and a parallel processing algorithm to form a fully automated approach. Complete, third-order, results will be shown to agree with experiment to about 1%, making this approach suitable for problems where such high precision is required. Finally, the application to parity violation in atoms will be briefly discussed, and the implications that such high-precision calculations, combined with experiment, have on the Standard Model.