diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb
index bae231ee293ba5a32f95504444dd5123e66034ba..b72b8e52b8f1d34b469d6cd51720858627755c1c 100644
--- a/module2/exo1/toy_notebook_en.ipynb
+++ b/module2/exo1/toy_notebook_en.ipynb
@@ -1,32 +1,12 @@
 {
  "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid syntax (<ipython-input-1-a53cacb01e8c>, line 1)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-1-a53cacb01e8c>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    1 On the computation of π\u001b[0m\n\u001b[0m       ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
-     ]
-    }
-   ],
-   "source": [
-    "1 On the computation of π\n",
-    "1.1 Asking the maths library\n",
-    "My computer tells me that π is approximatively"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 1 On the computation of π\n",
-    "## 1.1 Asking the maths library\n",
-    "My computer tells me that π is approximatively"
+    "# On the computation of $\\pi$\n",
+    "## Asking the maths library\n",
+    "My computer tells me that $\\pi$ is *approximatively*"
    ]
   },
   {
@@ -51,8 +31,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 1.2 Buffon’s needle\n",
-    "Applying the method of Buffon’s needle, we get the approximation"
+    "## Buffon's needle\n",
+    "Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
    ]
   },
   {
@@ -84,9 +64,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 1.3 Using a surface fraction argument\n",
-    "A method that is easier to understand and does not make use of the sin function is based on the\n",
-    "fact that if X ∼ U(0, 1) and Y ∼ U(0, 1), then P[X2 + Y2 ≤ 1] = π/4 (see \"Monte Carlo method\" on Wikipedia). The following code uses this approach:"
+    "## Using a surface fraction argument\n",
+    "A method that is easier to understand and does not make use of the $\\sin$ function is based on the fact that if $X\\sim U(0,1)$ and $Y\\sim U(0,1)$, then $P[X^2+Y^2\\leq 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
    ]
   },
   {
@@ -126,8 +105,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "It is then straightforward to obtain a (not really good) approximation to π by counting how\n",
-    "many times, on average, X2 + Y2 is smaller than 1:"
+    "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1:"
    ]
   },
   {