diff --git a/lecture1/exercise_0_python.ipynb b/lecture1/exercise_0_python.ipynb
index a453cea92a1b71ab2827f6196073935b275c5f45..9e55c7577a5205ddae4e0fe2a526f101b52ad3cc 100644
--- a/lecture1/exercise_0_python.ipynb
+++ b/lecture1/exercise_0_python.ipynb
@@ -10,7 +10,7 @@
     "\n",
     "Welcome to this warm-up tutorial! Let's take a look at some highlights of Python!\n",
     "\n",
-    "Please execute the whole notebook now by clicking on Cell->Execute All in the menubar. In the following, cells starting with TODOs and ending with a ```?``` are tasks to be solved individually.\n",
+    "Please execute the whole notebook now by clicking on Execution->Execute All in the menubar. In the following, cells starting with TODOs and ending with a ```?``` are tasks to be solved individually.\n",
     "\n",
     "Let's start with the usual **hello world** program:"
    ]
@@ -319,7 +319,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a457a29",
+   "id": "db6f86f8",
    "metadata": {},
    "source": [
     "### Task: <a class=\"tocSkip\"> \n",
@@ -387,7 +387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f42ae0f",
+   "id": "3c16d62e",
    "metadata": {},
    "source": [
     "These functions can be also called recursively -- for this, we can take a look at the factorial function:"
@@ -600,7 +600,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "274853db",
+   "id": "78db6018",
    "metadata": {},
    "source": [
     "### Task: <a class=\"tocSkip\">\n",
@@ -791,7 +791,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "739732e5",
+   "id": "2af74b4a",
    "metadata": {},
    "outputs": [
     {
diff --git a/lecture1/exercise_0_pytorch.ipynb b/lecture1/exercise_0_pytorch.ipynb
index 6e53369f2b1120184d7f56ce0bf53c48f00a91ef..b3572a1dda19df133b4c5d92ebac83c9b19d2ff2 100644
--- a/lecture1/exercise_0_pytorch.ipynb
+++ b/lecture1/exercise_0_pytorch.ipynb
@@ -114,7 +114,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "42d65b3f",
+   "id": "0e583095",
    "metadata": {},
    "source": [
     "**Conversion** from and to ```numpy``` is also supported in an intuitive way:"
@@ -123,7 +123,7 @@
   {
    "cell_type": "code",
    "execution_count": 5,
-   "id": "4ff55ee1",
+   "id": "c285066e",
    "metadata": {},
    "outputs": [
     {
@@ -157,7 +157,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "b41c3f17",
+   "id": "bf9b99ed",
    "metadata": {},
    "outputs": [
     {
@@ -198,7 +198,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7392c21",
+   "id": "4f283cd2",
    "metadata": {},
    "source": [
     " A key **difference in syntax** however is that ```pytorch``` knows the ```axis``` keyword as ```dim```:"
@@ -207,7 +207,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "ae7c557f",
+   "id": "3fe72fbc",
    "metadata": {},
    "outputs": [
     {
@@ -233,18 +233,18 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd7f9110",
+   "id": "f01db24d",
    "metadata": {},
    "source": [
     "### Task <a class=\"tocSkip\">\n",
     "Implement the mean-square difference function in pytorch:\n",
-    "    $$ L(x, y) = \\sum_i \\frac{(x_i-y_i)^2}{N}$$"
+    "$ L(x, y) = \\sum_i \\frac{(x_i-y_i)^2}{N}$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "8e87425d",
+   "id": "d674de00",
    "metadata": {},
    "outputs": [
     {
diff --git a/lecture1/exercise_0_tensorflow.ipynb b/lecture1/exercise_0_tensorflow.ipynb
index 33db1a3e7410fd1cc710a6ca3448a0cf993f1560..9fefdf58a6ff00f3dfa254c5b7309b1fb05e51f6 100644
--- a/lecture1/exercise_0_tensorflow.ipynb
+++ b/lecture1/exercise_0_tensorflow.ipynb
@@ -190,7 +190,7 @@
   {
    "cell_type": "code",
    "execution_count": 6,
-   "id": "57455b4b",
+   "id": "58c8bd1d",
    "metadata": {},
    "outputs": [
     {
@@ -222,7 +222,7 @@
   {
    "cell_type": "code",
    "execution_count": 7,
-   "id": "6413d2a9",
+   "id": "dd02b475",
    "metadata": {},
    "outputs": [
     {
@@ -244,18 +244,18 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3d32f8a4",
+   "id": "cb3f2c1a",
    "metadata": {},
    "source": [
     "### Task: <a class=\"tocSkip\">\n",
     "Implement the mean-square difference function in tensorflow:\n",
-    "    $$ L(x, y) = \\sum_i \\frac{(x_i-y_i)^2}{N}$$"
+    "$ L(x, y) = \\sum_i \\frac{(x_i-y_i)^2}{N}$"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 8,
-   "id": "7aec09c9",
+   "id": "d925efd7",
    "metadata": {},
    "outputs": [
     {