diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb
index 099535058959d3066b91f31dce519c8b454be424..ad7d073916d76fa1069e36f7153680a031d57ee6 100644
--- a/module2/exo1/toy_notebook_en.ipynb
+++ b/module2/exo1/toy_notebook_en.ipynb
@@ -4,8 +4,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 1. On the computation of $\\pi$\n",
-    "## 1.1 Asking the maths library\n",
+    "# On the computation of $\\pi$\n",
+    "## Asking the maths library\n",
     "My computer tells me that $\\pi$ is *approximately*"
    ]
   },
@@ -64,8 +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 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:"
+    "# 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:"
    ]
   },
   {
@@ -95,7 +95,7 @@
     "x = np.random.uniform(size=N, low=0, high=1)\n",
     "y = np.random.uniform(size=N, low=0, high=1)\n",
     "\n",
-    "accept = (x*x+y*y) < 1\n",
+    "accept = (x*x+y*y) <= 1\n",
     "reject = np.logical_not(accept)\n",
     "\n",
     "fig, ax = plt.subplots(1)\n",
@@ -108,7 +108,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "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:"
+    "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:"
    ]
   },
   {