Typo fixes and small enhancements in week 3

Author: jussienko

docs/mooc/using-compiled-code/interfacing-c-with-cffi.md

@@ -174,3 +174,6 @@ bptr = ffi.cast("double *", ffi.from_buffer(b))
 
 lib.add(aptr, bptr, cptr, len(a))
 ~~~
+
+Beware that `aptr`, `bptr` and `cptr` resemble now in many ways C pointers,
+and if you deal carelessly with them you can get Segmentation faults!

docs/mooc/using-compiled-code/interfacing-c-with-cython.md

@@ -23,11 +23,11 @@ cdef extern void add(double *a, double *b, double *c, int n)
 ~~~
 
 one could call `add` function within that file. In addition, the actual
-library or source needs to be included in **setup.py** when building the
-extension module with Cython.
+library or source implementing the function needs to be included in 
+**setup.py** when building the extension module with Cython.
 
 With the above construct, Cython will add the declaration to the generated
-.c file. However, when using libraries it is preferrable to have the actual
+.c file. However, when using libraries it is preferable to have the actual
 library header included in the generated file. This can be achieved with the
 following construct:
 

docs/mooc/using-compiled-code/using-static-typing.md

@@ -119,8 +119,11 @@ types. More information can be found in the
 
 ## Static typing in Mandelbrot kernel
 
-Let's investigate possible speed-up by introducing static typing to the
-**kernel** function in the **mandelbrot.pyx** module.
+We did earlier a performance analysis of Mandelbrot fractal which revealed 
+that the **kernel** function in module **mandelbrot.py** was the most time
+critical one. Thus,  let's make **mandelbrot.py** into Cython module
+**mandelbrot.pyx** and introducing static typing to the function
+**kernel**.
 
 Pure Python version was:
 
@@ -151,7 +154,8 @@ def kernel(double zr, double zi, double cr, double ci, double lim, int cutoff):
     return count
 ~~~
 
-When measuring now the performance, we obtain the following results:
+When comparing the performance of pure Python and Cythonized versions, 
+we obtain the following results:
 
   - Pure Python:  0.57 s
   - Static type declarations in the kernel: 14 ms