typo-fixed: removed to many "must" employed

notes/sections/3.md

@@ -3,7 +3,7 @@
 ## Meson decay events generation
 
 A number of $N = 50000$ points on the unit sphere, each representing a
-particle detection event, must be generated according to then angular
+particle detection event, is to be generated according to then angular
 probability distribution function $F$:
 \begin{align*}
   F (\theta, \phi) = &\frac{3}{4 \pi} \Bigg[ 
@@ -105,7 +105,7 @@ a single point, the effect of this omission is negligible.
 
 ## Parameters estimation
 
-The sample must now be used to estimate the parameters $\alpha$, $\beta$ and
+The sample is now used to estimate the parameters $\alpha$, $\beta$ and
 $\gamma$ of the angular distribution $F$. The correct set will be referred to
 as {$\alpha_0$, $\beta_0$, $\gamma_0$}.
 

notes/sections/5.md

@@ -1,6 +1,6 @@
 # Exercise 5
 
-The following integral must be evaluated comparing different Monte Carlo
+The following integral is to be evaluated comparing different Monte Carlo
 techniques.
 
 \begin{figure}
@@ -39,7 +39,7 @@ being implemented in the GSL libraries `gsl_monte_plain`, `gsl_monte_miser` and
 ## Plain Monte Carlo
 
 When an integral $I$ over a $n-$dimensional space $\Omega$ of volume $V$ of a
-function $f$ must be evaluated, that is:
+function $f$ has to be evaluated, that is:
 $$
   I = \int\limits_{\Omega} dx \, f(x)
   \with V = \int\limits_{\Omega} dx
@@ -111,7 +111,7 @@ $$
 $$
 
 if an error of $\sim 1^{-n}$ is required, a number $\propto 10^{2n}$ of
-function calls must be executed, meaning that for $\sigma \sim 1^{-10}
+function calls should be executed, meaning that for $\sigma \sim 1^{-10}
 \rightarrow C = \SI{1e20}{}$, which would be impractical.
 
 
@@ -251,7 +251,7 @@ probability distribution $f$ itself, so that the points cluster in the regions
 that make the largest contribution to the integral.
 
 Remind that $I = V \cdot \langle f \rangle$ and therefore only $\langle f
-\rangle$ must be estimated. Consider a sample of $n$ points {$x_i$} generated
+\rangle$ is to be estimated. Consider a sample of $n$ points {$x_i$} generated
 according to a probability distribution function $P$ which gives thereby the
 following expected value:
 $$

notes/sections/6.md

@@ -2,7 +2,7 @@
 
 ## Generating points according to Fraunhöfer diffraction
 
-The diffraction of a plane wave thorough a round slit must be simulated by
+The diffraction of a plane wave through a round slit must be simulated by
 generating $N =$ 50'000 points according to the intensity distribution
 $I(\theta)$ on a screen at a great distance $L$ from the slit itself:
 
@@ -263,7 +263,7 @@ stored. This works for all lengths: when the length is even, the middle value
 is real. Thus, only $n$ real numbers are required to store the half-complex
 sequence (half for the real part and half for the imaginary).  
 If the bin width is $\Delta \theta$, then the DFT domain ranges from $-1 / (2
-\Delta \theta)$ to $+1 / (2 \Delta \theta$). The GSL functions aforementioned
+\Delta \theta)$ to $+1 / (2 \Delta \theta$). The aforementioned GSL functions 
 store the positive values from the beginning of the array up to the middle and
 the negative backwards from the end of the array (see @fig:reorder).  
 
@@ -321,7 +321,7 @@ shown in [@fig:results1; @fig:results2; @fig:results3].
 
 ## Unfolding with Richardson-Lucy
 
-The Richardson–Lucy (RL) deconvolution is an iterative procedure usually used
+The Richardson–Lucy (RL) deconvolution is an iterative procedure tipically used
 for recovering an image that has been blurred by a known point spread function.
 
 It is based on the fact that an ideal point source does not appear as a point
@@ -391,7 +391,7 @@ width of the original histogram, which is the one previously introduced in
 histogram deconvolved with the FFT method is in the middle and the one
 deconvolved with RL is located below.
 
-As can be seen, increasig the value of $\sigma$ implies a stronger smoothing of
+As can be seen, increasing the value of $\sigma$ implies a stronger smoothing of
 the curve. The FFT deconvolution process seems not to be affected by $\sigma$
 amplitude changes: it always gives the same outcome, which is exactly the
 original signal. In fact, the FFT is the analitical result of the deconvolution.
@@ -406,7 +406,7 @@ convolved is less smooth, it is less smooth too.
 
 The original signal is shown below for convenience.
 
-![Example of an intensity histogram.](images/fraun-original.pdf){#fig:original}
+![Example of an intensity histogram.](images/fraun-original.pdf)
 
 <div id="fig:results1">
 ![Convolved signal.](images/fraun-conv-0.05.pdf){width=12cm}

notes/sections/8.md

@@ -1 +1,4 @@
 # Bibliography
+
+The usage and a brief description of the theory underneath all the GLS functions
+employed in this report were found in [@GSL].