White dwarf asteroseismology offers the opportunity to probe the structure and composition of stellar objects governed by relatively simple physical principles. The observational requirements of asteroseismology have been addressed by the development of the Whole Earth Telescope, but the analysis procedures still need to be refined before this technique can yield the complete physical insight that the data can provide. We have applied an optimization method utilizing a genetic algorithm to the problem of fitting white dwarf pulsation models to the observed frequencies of the most thoroughly characterized helium-atmosphere pulsator, GD 358. The free parameters in this initial study included the stellar mass, the effective temperature, the surface helium layer mass, the core composition, and the internal chemical profile. For many years, astronomers have promised that the study of pulsating white dwarfs would ultimately lead to useful information about the physics of matter under extreme conditions of temperature and pressure. The optimization approach developed in this dissertation has allowed us to finally make good on that promise by exploiting the sensitivity of our models to the core composition. We empirically determine that the central oxygen abundance in GD 358 is 84 +/- 3 percent. We use this value to place a preliminary constraint on the C12(alpha,gamma)O16 nuclear reaction cross-section of S_300 = 295 +/- 15 keV barns. We find a thick helium layer solution for GD 358 that provides a better match to the data than previous fits, and helps to resolve a problem with the evolutionary connection between PG 1159 stars and DBVs. [abridged]

Ph.D. thesis. Summary to appear in PASP (October 2001). HTML version and full-resolution figures available at http://whitedwarf.org/metcalfe/