diff --git a/lecture13_15/handout_13.ipynb b/lecture13_15/handout_13.ipynb
index 43d9bc4..1ac3ee2 100644
--- a/lecture13_15/handout_13.ipynb
+++ b/lecture13_15/handout_13.ipynb
@@ -2,29 +2,29 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Iteration 0, Loss: 466.56000000000006\n",
-      "Iteration 20, Loss: 5.32959636083938\n",
-      "Iteration 40, Loss: 0.41191523404899866\n",
-      "Iteration 60, Loss: 0.031836212079467595\n",
-      "Iteration 80, Loss: 0.002460565465389601\n",
-      "Iteration 100, Loss: 0.000190172825660145\n",
-      "Iteration 120, Loss: 1.4698126966451542e-05\n",
-      "Iteration 140, Loss: 1.1359926717815175e-06\n",
-      "Iteration 160, Loss: 8.779889800154524e-08\n",
-      "Iteration 180, Loss: 6.7858241357822796e-09\n",
+      "Iteration 0, Loss: 0.0\n",
+      "Iteration 20, Loss: 0.0\n",
+      "Iteration 40, Loss: 0.0\n",
+      "Iteration 60, Loss: 0.0\n",
+      "Iteration 80, Loss: 0.0\n",
+      "Iteration 100, Loss: 0.0\n",
+      "Iteration 120, Loss: 0.0\n",
+      "Iteration 140, Loss: 0.0\n",
+      "Iteration 160, Loss: 0.0\n",
+      "Iteration 180, Loss: 0.0\n",
       "Final weights:\n",
-      " [[-0.00698895 -0.01397789 -0.02096684 -0.02795579]\n",
-      " [ 0.25975286  0.11950572 -0.02074143 -0.16098857]\n",
-      " [ 0.53548461  0.27096922  0.00645383 -0.25806156]]\n",
+      " [[0. 0. 0. 0.]\n",
+      " [0. 0. 0. 0.]\n",
+      " [0. 0. 0. 0.]]\n",
       "Final biases:\n",
-      " [-0.00698895 -0.04024714 -0.06451539]\n"
+      " [0. 0. 0.]\n"
      ]
     }
    ],
@@ -114,7 +114,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.2"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,
diff --git a/lecture13_15/notes_13.ipynb b/lecture13_15/notes_13.ipynb
index 83114b4..7dc7486 100644
--- a/lecture13_15/notes_13.ipynb
+++ b/lecture13_15/notes_13.ipynb
@@ -368,6 +368,99 @@
    "source": [
     "# Backpropagation of a Layer"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Iteration 0, Loss: 466.56000000000006\n",
+      "Iteration 20, Loss: 5.329595763793193\n",
+      "Iteration 40, Loss: 0.41191524253483786\n",
+      "Iteration 60, Loss: 0.03183621475376345\n",
+      "Iteration 80, Loss: 0.002460565405431671\n",
+      "Iteration 100, Loss: 0.0001901729121621426\n",
+      "Iteration 120, Loss: 1.4698120139337557e-05\n",
+      "Iteration 140, Loss: 1.1359948840900371e-06\n",
+      "Iteration 160, Loss: 8.779778427447647e-08\n",
+      "Iteration 180, Loss: 6.785903626216421e-09\n",
+      "Final weights:\n",
+      " [[-0.00698895 -0.0139779  -0.02096685 -0.0279558 ]\n",
+      " [ 0.25975286  0.11950571 -0.02074143 -0.16098857]\n",
+      " [ 0.53548461  0.27096922  0.00645383 -0.25806156]]\n",
+      "Final biases:\n",
+      " [-0.00698895 -0.04024714 -0.06451539]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "\n",
+    "# Initial inputs\n",
+    "inputs = np.array([1, 2, 3, 4])\n",
+    "\n",
+    "# Initial weights and biases\n",
+    "weights = np.array([\n",
+    "    [0.1, 0.2, 0.3, 0.4],\n",
+    "    [0.5, 0.6, 0.7, 0.8],\n",
+    "    [0.9, 1.0, 1.1, 1.2]\n",
+    "])\n",
+    "\n",
+    "biases = np.array([0.1, 0.2, 0.3])\n",
+    "\n",
+    "learning_rate = 0.001\n",
+    "\n",
+    "# Add the derivative function to the ReLU class\n",
+    "class Activation_ReLU:\n",
+    "    def forward(self, inputs):\n",
+    "        return np.maximum(0, inputs)\n",
+    "    \n",
+    "    def derivative(self, inputs):\n",
+    "        return np.where(inputs > 0, 1, 0)\n",
+    "    \n",
+    "relu = Activation_ReLU()\n",
+    "\n",
+    "num_iterations = 200\n",
+    "\n",
+    "# Training loop\n",
+    "# A single layer of 3 neurons, each with 4 inputs\n",
+    "# The neuron layer is then fed into a ReLU activation layer\n",
+    "for iteration in range(num_iterations):\n",
+    "    # Forward pass\n",
+    "    neuron_outputs = np.dot(weights, inputs) + biases\n",
+    "    relu_outputs = relu.forward(neuron_outputs)\n",
+    "    \n",
+    "    # Calculate the squared loss assuming the desired output is a sum of 0. Trivial but just an example\n",
+    "    final_output = np.sum(relu_outputs)\n",
+    "    loss = final_output**2\n",
+    "\n",
+    "    # Backward pass\n",
+    "    dL_dfinal_output = 2 * final_output\n",
+    "    dfinal_output_drelu_output = np.ones_like(relu_outputs)\n",
+    "    drelu_output_dneuron_output = relu.derivative(neuron_outputs)\n",
+    "\n",
+    "    dL_dneuron_output = dL_dfinal_output * dfinal_output_drelu_output * drelu_output_dneuron_output\n",
+    "\n",
+    "    # Get the gradient of the Loss with respect to the weights and biases\n",
+    "    dL_dW = np.outer(dL_dneuron_output, inputs)\n",
+    "    dL_db = dL_dneuron_output\n",
+    "\n",
+    "    # Update the weights and biases\n",
+    "    weights -= learning_rate * dL_dW\n",
+    "    biases -= learning_rate * dL_db\n",
+    "\n",
+    "    # Print the loss every 20 iterations\n",
+    "    if iteration % 20 == 0:\n",
+    "        print(f\"Iteration {iteration}, Loss: {loss}\")\n",
+    "\n",
+    "# Final weights and biases\n",
+    "print(\"Final weights:\\n\", weights)\n",
+    "print(\"Final biases:\\n\", biases)\n"
+   ]
   }
  ],
  "metadata": {