How to build a 2N6027 PUT?
Disclaimer #1: This is not a direct answer to your question, as I've never used a PUT, nor I've read the book you've taken the exercise from. BUT I've attended a course about oscillators, and these may be workarounds for your problem. 
Disclaimer #2: You asked for transistor based solutions; this solution is op-amp based, but I found it clear enough. 
So, what do you need is a circuit with negative differential resistance in order to make an oscillator (and eventually other stuff). There are two main types of dipoles with that characteristic, and they're called 'S' and 'N' respectively, due to their I(V) characteristic.
Below is illustrated the difference between the two dipoles.

These dipoles can be used to create an oscillator with a passive dipole constituted by a RLC network. In order for the circuit to oscillate, the resistance has to be chosen in a way that its V-I curve intersects the 'S' characteristic in three points:

But back to the problem
Using an Op-amp, is quite easy to build a 'N' dipole, to achieve the same effect that you have with the PUT.

The analysis of this circuit, to demonstrate the function, can be done separately for the three operating regions of the Op-amp. The V(I) characteristic is:

$$ R_{eq} = \frac{V}{I} = - \frac{R_1 R_3}{R_2} $$
in the high-gain region of the Op-Amp.