Several fixes.

Author: wcwitt

docs/src/gettingstarted/aceintro.md

@@ -42,14 +42,14 @@ Next, we form the $$N$$-correlations of the density, ``\rho^{\otimes N}`` and pr
    = \Big\langle \otimes_{t = 1}^N \phi_{n_t l_t m_t}, \rho^{\otimes N} \Big\rangle 
    = \prod_{t = 1}^N A_{n_t l_t m_t}.
 ```
-The reason to introduce these is that in the next step, the symmetrisation step the density project would loose all angular information while the ``N``-correlations retain most (though not all) of it. 
+The reason to introduce these is that in the next step, the symmetrisation step, the density project would lose all angular information while the ``N``-correlations retain most (though not all) of it. 
 
 ### Symmetrisation 
 
-Finally, we symmetrize the ``N``-correlations, by integrating over the ``O(3)``-Haar measure, 
+Finally, we symmetrise the ``N``-correlations, by integrating over the ``O(3)``-Haar measure, 
 ```math 
-  B_{\bm nlm} \propto 
-  \int_{O(3)} {\bm A}_{\bm nlm} \circ Q \, dQ 
+  B_{\mathbf{nlm}} \propto 
+  \int_{O(3)} {\bm A}_{\mathbf{nlm}} \circ Q \, dQ 
 ```
 Because of properties of the spherical harmonics one can write this as 
 ```math 
@@ -64,4 +64,4 @@ Notes:
 
 ### Linear Dependence
 
-The construction described above introduces a lot of linear dependence which is removed in the ACE basis construction in a mixed symbolic / numerical procedure. In the end we no longer index the symmetrized basis functions as ``B_{\bm nlm}`` but as ``B_{{\bm nl}i}`` with ``i`` indexing the linearly independent basis functions from the ``{\bm nl}`` block. 
+The construction described above introduces a lot of linear dependence which is removed in the ACE basis construction in a mixed symbolic / numerical procedure. In the end we no longer index the symmetrized basis functions as ``B_{\bm nlm}`` but as ``B_{\mathbf{nl}i}`` with ``i`` indexing the linearly independent basis functions from the ``\mathbf{nl}`` block.