Thermal physics. Entropy's functional dependecy

[rar0308]

Homework Statement

I'm reading Kittel&kroemer's Thermal physics. How can I know Entropy's functional dependency?
Author assume entropy's functional dependecy without explanations and derive some equaltities. So I can't follow it.

N the number of particles. U Energy of the system. V. volume of the system $\tau$ fundamental temperature
$\sigma(N,U)$, $\sigma(\tau,V) etc...$

Homework Equations

The Attempt at a Solution

 

[George Jones]

On what page(s) does this occur?

 

[rar0308]

2nd edition p66~p67, p43. "" is what author says.
p66 "The number of states and thus the entropy depend only on U and on V, for fixed number of particles," I don't know why the number of states depend on on U and V.
In chapter2 multiplicity thus entropy is function of U and N. p43 "The entropy may depend on additional independent variables" I don't know in what circumstance the entropy depend on what variables.
p67 "If we denote these interdependent values of dU and dV by $(\delta U)_{\sigma}$ and $(\delta V)_{\sigma}$, the entropy change will be zero." I don't know why it's possible to assume constant entropy and make U and V be interdependent.