diff --git a/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb b/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb
index c2fe012..3ca132d 100644
--- a/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb
+++ b/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb
@@ -1,18 +1,16 @@
 {
   "cells": [
     {
-      "attachments": {},
       "cell_type": "markdown",
       "metadata": {
-        "colab_type": "text",
-        "id": "view-in-github"
+        "id": "view-in-github",
+        "colab_type": "text"
       },
       "source": [
         "<a href=\"https://colab.research.google.com/github/udlbook/udlbook/blob/main/Notebooks/Chap01/1_1_BackgroundMathematics.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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       "cell_type": "markdown",
       "metadata": {
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@@ -41,7 +39,6 @@
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       "cell_type": "markdown",
       "metadata": {
         "id": "WV2Dl6owme2d"
@@ -49,11 +46,11 @@
       "source": [
         "**Linear functions**<br> We will be using the term *linear equation* to mean a weighted sum of inputs plus an offset. If there is just one input $x$, then this is a straight line:\n",
         "\n",
-        "\\begin{equation}y=\\beta+\\omega x,\\end{equation} \n",
+        "\\begin{equation}y=\\beta+\\omega x,\\end{equation}\n",
         "\n",
         "where $\\beta$ is the y-intercept of the linear and $\\omega$ is the slope of the line. When there are two inputs $x_{1}$ and $x_{2}$, then this becomes:\n",
         "\n",
-        "\\begin{equation}y=\\beta+\\omega_1 x_1 + \\omega_2 x_2.\\end{equation} \n",
+        "\\begin{equation}y=\\beta+\\omega_1 x_1 + \\omega_2 x_2.\\end{equation}\n",
         "\n",
         "Any other functions are by definition **non-linear**.\n",
         "\n",
@@ -99,7 +96,7 @@
         "ax.plot(x,y,'r-')\n",
         "ax.set_ylim([0,10]);ax.set_xlim([0,10])\n",
         "ax.set_xlabel('x'); ax.set_ylabel('y')\n",
-        "plt.show\n",
+        "plt.show()\n",
         "\n",
         "# TODO -- experiment with changing the values of beta and omega\n",
         "# to understand what they do.  Try to make a line\n",
@@ -107,7 +104,6 @@
       ]
     },
     {
-      "attachments": {},
       "cell_type": "markdown",
       "metadata": {
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@@ -192,7 +188,6 @@
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@@ -236,7 +231,6 @@
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       "cell_type": "markdown",
       "metadata": {
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@@ -279,7 +273,6 @@
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     },
     {
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       "cell_type": "markdown",
       "metadata": {
         "id": "3LGRoTMLU8ZU"
@@ -293,7 +286,6 @@
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     {
-      "attachments": {},
       "cell_type": "markdown",
       "metadata": {
         "id": "7Y5zdKtKZAB2"
@@ -325,11 +317,10 @@
         "ax.plot(x,y,'r-')\n",
         "ax.set_ylim([0,100]);ax.set_xlim([-5,5])\n",
         "ax.set_xlabel('x'); ax.set_ylabel('exp[x]')\n",
-        "plt.show"
+        "plt.show()"
       ]
     },
     {
-      "attachments": {},
       "cell_type": "markdown",
       "metadata": {
         "id": "XyrT8257IWCu"
@@ -345,7 +336,6 @@
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-      "attachments": {},
       "cell_type": "markdown",
       "metadata": {
         "id": "R6A4e5IxIWCu"
@@ -373,11 +363,10 @@
         "ax.plot(x,y,'r-')\n",
         "ax.set_ylim([-5,5]);ax.set_xlim([0,5])\n",
         "ax.set_xlabel('x'); ax.set_ylabel('$\\log[x]$')\n",
-        "plt.show"
+        "plt.show()"
       ]
     },
     {
-      "attachments": {},
       "cell_type": "markdown",
       "metadata": {
         "id": "yYWrL5AXIWCv"
@@ -397,8 +386,8 @@
   ],
   "metadata": {
     "colab": {
-      "include_colab_link": true,
-      "provenance": []
+      "provenance": [],
+      "include_colab_link": true
     },
     "kernelspec": {
       "display_name": "Python 3 (ipykernel)",
@@ -420,4 +409,4 @@
   },
   "nbformat": 4,
   "nbformat_minor": 0
-}
+}
\ No newline at end of file