Refactor code for improved readability and consistency across multiple Jupyter notebooks

- Added missing commas in various print statements and function calls for better syntax.
- Reformatted code to enhance clarity, including breaking long lines and aligning parameters.
- Updated function signatures to use float type for sigma parameters instead of int for better precision.
- Cleaned up comments and documentation strings for clarity and consistency.
- Ensured consistent formatting in plotting functions and data handling.

M1/Numerical Methods/TP2_DANJOU_Arthur.ipynb

@@ -17,7 +17,7 @@
    "source": [
     "import matplotlib.pyplot as plt\n",
     "import numpy as np\n",
-    "import scipy.stats as stats"
+    "from scipy import stats"
    ]
   },
   {
@@ -46,15 +46,12 @@
    "outputs": [],
    "source": [
     "def S(t, S0, mu, sigma, W):\n",
-    "    \"\"\"\n",
-    "    Solution exacte de l'EDS de Black-Scholes\n",
-    "    \"\"\"\n",
+    "    \"\"\"Solution exacte de l'EDS de Black-Scholes\"\"\"\n",
     "    return S0 * np.exp((mu - 0.5 * sigma**2) * t + sigma * W)\n",
     "\n",
     "\n",
     "def euler_maruyama(mu, sigma, T, N, X0=0.0):\n",
-    "    \"\"\"\n",
-    "    Simulation d'une EDS de Black-Scholes par la méthode d'Euler-Maruyama\n",
+    "    \"\"\"Simulation d'une EDS de Black-Scholes par la méthode d'Euler-Maruyama\n",
     "\n",
     "    Paramètres :\n",
     "        mu (float) : drift\n",
@@ -84,8 +81,7 @@
     "\n",
     "\n",
     "def plot_brownien(t, X, B=None):\n",
-    "    \"\"\"\n",
-    "    Plot la simulation d'Euler-Maruyama\n",
+    "    \"\"\"Plot la simulation d'Euler-Maruyama\n",
     "\n",
     "    Paramètres :\n",
     "        t (array-like) : tableau des temps\n",
@@ -169,8 +165,7 @@
     "\n",
     "\n",
     "def plot_convergence(S0, mu, sigma, T):\n",
-    "    \"\"\"\n",
-    "    Plot la convergence du schéma d'Euler-Maruyama\n",
+    "    \"\"\"Plot la convergence du schéma d'Euler-Maruyama\n",
     "\n",
     "    Paramètres :\n",
     "        S0 (int) : valeur initiale\n",
@@ -291,7 +286,7 @@
     "print(\n",
     "    \"La barrière a été franchie\"\n",
     "    if is_barrier_breached(X, B)\n",
-    "    else \"La barrière n'a pas été franchie\"\n",
+    "    else \"La barrière n'a pas été franchie\",\n",
     ")"
    ]
   },
@@ -335,8 +330,7 @@
     "    \"\"\"\n",
     "    if not is_barrier_breached(X, B):\n",
     "        return max(X[-1] - K, 0)\n",
-    "    else:\n",
-    "        return 0\n",
+    "    return 0\n",
     "\n",
     "\n",
     "def call_BS(x):\n",