Started intro in theory/methods documentation.

docs/source/methods/introduction.rst

@@ -4,7 +4,37 @@
 Introduction
 ============
 
+The physical process by which a population of particles evolves over time is
+governed by a number of `probability distributions`_. For instance, given a
+particle traveling through some material, there is a probability distribution
+for the distance it will travel until its next collision (an exponential
+distribution). Then, when it collides with a nucleus, there is associated
+probability of undergoing each possible reaction with that nucleus. While the
+behavior of any single particle is unpredictable, the average behavior of a
+large population of particles originating from the same source is well defined.
+
+If the probability distributions that govern the transport of a particle are
+known, the process of single particles randomly streaming and colliding with
+nuclei can be simulated directly with computers using a technique known as
+`Monte Carlo`_ simulation. If enough particles are simulated this way, the
+average behavior can be determined to within arbitrarily small statistical
+error, a fact guaranteed by the `central limit theorem`_. To be more precise,
+the central limit theorem tells us that the variance of the sample mean of some
+physical parameter being estimated with Monte Carlo will be inversely
+proportional to the number of realizations, i.e. the number of particles we
+simulate:
+
+.. math::
+
+    \sigma^2 \propto \frac{1}{N}.
+
+where :math:`\sigma^2` is the variance of the sample mean and :math:`N` is the
+number of realizations.
+
 ---------------------
 Criticality Algorithm
 ---------------------
 
+.. _probability distributions: http://en.wikipedia.org/wiki/Probability_distribution
+.. _Monte Carlo: http://en.wikipedia.org/wiki/Monte_Carlo_method
+.. _central limit theorem: http://en.wikipedia.org/wiki/Central_limit_theorem