  We calculate the symmetry energy of the nuclear matter by using the bottom-up
approach, so called hard wall model. To consider the nuclear matter, we
introduce the isospin for u- and d-quarks. We find that in the hard wall model,
the symmetry energy of the nuclear matter is proportional to the square of
nucleon density. We also study the symmetry energy of the quark matter in the
deconfining phase. Finally, we investigate the effect of the symmetry energy on
the Hawking-Page transition and show that at the given quark density, the
Hawking-Page transition temperature decreases due to the symmetry energy.
