Both novae and supernovae involve a lengthy chain of nuclear reactions. We observe the end products through optical, ultraviolet, and gamma-ray spectral lines. Five projects are specified to determine the initial chemical compositions in the exploding stars that will yield the final observed compositions. The main parameters of interest are initial oxygen and iron abundances, details of mass transfer onto the exploding star in a binary pair, and specific neutron donors in supernovae. The Earth and life thereon are composed mainly of elements made long ago in exploding stars. Many of the elements are made in supernovae, of which the new nearby supernova is one example. Recently the more ordinary novae have been recognized as important contributors to cosmic nuclear changes. Modern observations inform us in detail what elements are ejected from these exploding stars. The computing projects supported by this grant will elucidate the original conditions of the stars and the nuclear processes that lead to the observed elements. The results will clarify both the evolution of these stars and the cosmic evolution of the elements.