  We investigate properties of carbon-oxygen white dwarfs with respect to the
composite uncertainties in the reaction rates using the stellar evolution
toolkit, Modules for Experiments in Stellar Astrophysics (MESA) and the
probability density functions in the reaction rate library STARLIB. These are
the first Monte Carlo stellar evolution studies that use complete stellar
models. Focusing on 3 M$_{\odot}$ models evolved from the pre main-sequence to
the first thermal pulse, we survey the remnant core mass, composition, and
structure properties as a function of 26 STARLIB reaction rates covering
hydrogen and helium burning using a Principal Component Analysis and Spearman
Rank-Order Correlation. Relative to the arithmetic mean value, we find the
width of the 95\% confidence interval to be $\Delta M_{{\rm 1TP}}$ $\approx$
0.019 M$_{\odot}$ for the core mass at the first thermal pulse,
$\Delta$$t_{\rm{1TP}}$ $\approx$ 12.50 Myr for the age, $\Delta \log(T_{{\rm
c}}/{\rm K}) \approx$ 0.013 for the central temperature, $\Delta
\log(\rho_{{\rm c}}/{\rm g \ cm}^{-3}) \approx$ 0.060 for the central density,
$\Delta Y_{\rm{e,c}} \approx$ 2.6$\times$10$^{-5}$ for the central electron
fraction, $\Delta X_{\rm c}(^{22}\rm{Ne}) \approx$ 5.8$\times$10$^{-4}$,
$\Delta X_{\rm c}(^{12}\rm{C}) \approx$ 0.392, and $\Delta X_{\rm
c}(^{16}\rm{O}) \approx$ 0.392. Uncertainties in the experimental
$^{12}$C($\alpha,\gamma)^{16}\rm{O}$, triple-$\alpha$, and
$^{14}$N($p,\gamma)^{15}\rm{O}$ reaction rates dominate these variations. We
also consider a grid of 1 to 6 M$_{\odot}$ models evolved from the pre
main-sequence to the final white dwarf to probe the sensitivity of the
initial-final mass relation to experimental uncertainties in the hydrogen and
helium reaction rates.
