I'm writing my proposal at the moment; do I need a "Problem Statement" section? I'm confused with the Introduction and Problem Statement sections. They seem to be the same. Some authors just put the Problem Statement directly under the Introduction.

Help : (

the introduction should include the ideas required to understand the scenario of the research without serious regard of the problem. on the other hand, the problem statement should clearly state the problem that will be encountered in a particular situation. let's look at a simple example.

INTRODUCTION
one of the most popular problem in computational graph theory is finding the shortest path between two vertices. this can be achieved using djikstra's algorithm. the algorithm proceeds by ...
(the description of shortest path algorithm etc)

PROBLEM STATEMENT
the current shortest path algorithm requires a complete cycle to generate the shortest path. in a very large graph where the search can be terminated at any time, the algorithm would not be able to generate any solution, optimal or otherwise.
(shortest path algorithm is ok BUT it won't work in a situation where the size is very large and time is chaotic)

OBJECTIVE
develop a new algorithm that can be terminated at any time.
if the algorithm is allowed to complete the cycle, the result would be optimal.
if not, it would be sub-optimal, where optimality is proportionate to the time invested.
(what you intend to do to solve the aforementioned problem above)

hope it helps

ps : i'm assuming that u're doing research on graph theory given the reference u were looking for earlier.

statement of purpose? what do u mean?

problem statement is needed to clarify exactly what u intend to solve with ur research.

i usually explain the objectives in point form, followed by a paragraph to explain what the objective entails if need be. i usually explain the contribution in point form as well.

OBJECTIVE

1. develop new algorithm for x-computation
[paragraph to explain if need be]

2. evaluate performance of algorithm via monte carlo simulation
[paragraph ...]