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Cell[CellGroupData[{
Cell["Random Walks", "Title"],

Cell["\<\
AP 1601y
Columbia University\
\>", "Subsubtitle"],

Cell[CellGroupData[{

Cell["Introduction", "Section"],

Cell[TextData[{
 "In this notebook, we begin a study of random processes and statistical \
physics. We explore a simple model for diffusion by considering a simple",
 StyleBox[" ",
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 "model for the unbiased, ",
 ButtonBox["one-dimensional random walk",
  BaseStyle->"Hyperlink",
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    URL["http://mathworld.wolfram.com/RandomWalk1-Dimensional.html"], None}],
 ". Diffusion is the process by which a quantity (like particles, heat, or \
momentum) moves from a region of high concentration to low concretionary by a \
multi-step random process.  We also briefly introduce the concept of entropy, \
introduced by Rudolf Clausius in 1865."
}], "Text"]
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Cell[CellGroupData[{

Cell["Jacob Bernoulli", "Section"],

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Online biographies are available from ",
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Cell["One Dimensional Random Walks", "Section"],

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If we have a distribution of walkers (or \"particles\"), how does this \
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If we make a series expansion, this becomes the diffusion equation...\
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For two walkers and 10 steps, the probability that both will return to 0 \
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With 100 walkers and 10 steps, the probability of returning to the original \
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We can compute the entropy evolution of our random-walker simulation easily\
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