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2 changes: 1 addition & 1 deletion SUMMARY.md
Original file line number Diff line number Diff line change
Expand Up @@ -20,7 +20,7 @@
* [Multiplication as a Convolution](contents/convolutions/multiplication/multiplication.md)
* [Convolutions of Images (2D)](contents/convolutions/2d/2d.md)
* [Convolutional Theorem](contents/convolutions/convolutional_theorem/convolutional_theorem.md)
* [Probability Distributions](contents/probability/distributions/distributions.md)
* [Probability Distributions](contents/probability_distributions/distributions.md)
* [Tree Traversal](contents/tree_traversal/tree_traversal.md)
* [Euclidean Algorithm](contents/euclidean_algorithm/euclidean_algorithm.md)
* [Monte Carlo](contents/monte_carlo_integration/monte_carlo_integration.md)
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4 changes: 2 additions & 2 deletions contents/metropolis/metropolis.md
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@@ -1,7 +1,7 @@
# The Metropolis Algorithm

The [Monte Carlo Integration](../monte_carlo_integration/monte_carlo_integration.html) method uses random numbers to approximate the area of pretty much any shape we choose.
The Metropolis algorithm {{ "metropolis1953equation" | cite }} is a slightly more advanced Monte Carlo method which uses random numbers to approximate a [probability distribution](../probability/distributions/distributions.md):
The Metropolis algorithm {{ "metropolis1953equation" | cite }} is a slightly more advanced Monte Carlo method which uses random numbers to approximate a [probability distribution](../probability_distributions/distributions.md):

$$
P(\mathbf{x}) = \frac{f(\mathbf{x})}{\displaystyle\int_D f(\mathbf{x})d\mathbf{x}},
Expand Down Expand Up @@ -42,7 +42,7 @@ $$
P(\mathbf{x}) = \frac{\displaystyle \exp\left[{\displaystyle\frac{-E(\mathbf{x})}{T} } \right]} {Q},
$$

where the numerator is called the __Boltzmann factor__, and $$Q$$ is the [normalization constant](../probability/distributions/distributions.md),
where the numerator is called the __Boltzmann factor__, and $$Q$$ is the [normalization constant](../probability_distributions/distributions.md),

$$
Q = \int_D \exp\left[{\displaystyle\frac{-E(\mathbf{x})}{T} } \right] d\mathbf{x}.
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