diff --git a/pages/CSE559A/CSE559A_L1.md b/pages/CSE559A/CSE559A_L1.md
index 9ad90d9..a8d6c78 100644
--- a/pages/CSE559A/CSE559A_L1.md
+++ b/pages/CSE559A/CSE559A_L1.md
@@ -1,4 +1,4 @@
-# Lecture 1
+# CSE559A Lecture 1
 
 ## Introducing the syllabus
 
diff --git a/pages/CSE559A/CSE559A_L2.md b/pages/CSE559A/CSE559A_L2.md
index 532b204..462451b 100644
--- a/pages/CSE559A/CSE559A_L2.md
+++ b/pages/CSE559A/CSE559A_L2.md
@@ -1,4 +1,4 @@
-# Lecture 2
+# CSE559A Lecture 2
 
 ## The Geometry of Image Formation
 
diff --git a/pages/CSE559A/CSE559A_L3.md b/pages/CSE559A/CSE559A_L3.md
index 431e696..2f0a2e6 100644
--- a/pages/CSE559A/CSE559A_L3.md
+++ b/pages/CSE559A/CSE559A_L3.md
@@ -1,4 +1,4 @@
-# Lecture 3
+# CSE559A Lecture 3
 
 ## Image formation
 
diff --git a/pages/CSE559A/CSE559A_L4.md b/pages/CSE559A/CSE559A_L4.md
index 69567c4..ebc98a0 100644
--- a/pages/CSE559A/CSE559A_L4.md
+++ b/pages/CSE559A/CSE559A_L4.md
@@ -1,4 +1,4 @@
-# Lecture 4
+# CSE559A Lecture 4
 
 ## Practical issues with filtering
 
diff --git a/pages/CSE559A/CSE559A_L5.md b/pages/CSE559A/CSE559A_L5.md
index f925461..9ff86ae 100644
--- a/pages/CSE559A/CSE559A_L5.md
+++ b/pages/CSE559A/CSE559A_L5.md
@@ -1,4 +1,4 @@
-# Lecture 5
+# CSE559A Lecture 5
 
 ## Continue on linear interpolation
 
diff --git a/pages/CSE559A/CSE559A_L6.md b/pages/CSE559A/CSE559A_L6.md
index 44f1565..41e8322 100644
--- a/pages/CSE559A/CSE559A_L6.md
+++ b/pages/CSE559A/CSE559A_L6.md
@@ -1,4 +1,4 @@
-# Lecture 6
+# CSE559A Lecture 6
 
 ## Continue on Light, eye/camera, and color
 
diff --git a/pages/CSE559A/CSE559A_L7.md b/pages/CSE559A/CSE559A_L7.md
index 252ad04..faa94c4 100644
--- a/pages/CSE559A/CSE559A_L7.md
+++ b/pages/CSE559A/CSE559A_L7.md
@@ -1,4 +1,4 @@
-# Lecture 7
+# CSE559A Lecture 7
 
 ## Computer Vision (In Artificial Neural Networks for Image Understanding)
 
diff --git a/pages/CSE559A/CSE559A_L8.md b/pages/CSE559A/CSE559A_L8.md
index 93b26f7..cbb9906 100644
--- a/pages/CSE559A/CSE559A_L8.md
+++ b/pages/CSE559A/CSE559A_L8.md
@@ -1,4 +1,4 @@
-# Lecture 8
+# CSE559A Lecture 8
 
 Paper review sharing.
 
@@ -78,10 +78,3 @@ $$
 $$
 
 #### General backpropagation algorithm
-
-
-
-
-
-
-
diff --git a/pages/CSE559A/CSE559A_L9.md b/pages/CSE559A/CSE559A_L9.md
new file mode 100644
index 0000000..2eb9594
--- /dev/null
+++ b/pages/CSE559A/CSE559A_L9.md
@@ -0,0 +1,102 @@
+# CSE559A Lecture 9
+
+## Continue on ML for computer vision
+
+### Backpropagation
+
+#### Computation graphs
+
+SGD update for each parameter
+
+$$
+w_k\gets w_k-\eta\frac{\partial e}{\partial w_k}
+$$
+
+$e$ is the error function.
+
+#### Using the chain rule
+
+Suppose $k=1$, $e=l(f_1(x,w_1),y)$
+
+Example: $e=(f_1(x,w_1)-y)^2$
+
+So $h_1=f_1(x,w_1)=w^T_1x$, $e=l(h_1,y)=(y-h_1)^2$
+
+$$
+\frac{\partial e}{\partial w_1}=\frac{\partial e}{\partial h_1}\frac{\partial h_1}{\partial w_1}
+$$
+
+$$
+\frac{\partial e}{\partial h_1}=2(h_1-y)
+$$
+
+$$
+\frac{\partial h_1}{\partial w_1}=x
+$$
+
+$$
+\frac{\partial e}{\partial w_1}=2(h_1-y)x
+$$
+
+For the general cases,
+
+$$
+\frac{\partial e}{\partial w_k}=\frac{\partial e}{\partial h_K}\frac{\partial h_K}{\partial h_{K-1}}\cdots\frac{\partial h_{k+2}}{\partial h_{k+1}}\frac{\partial h_{k+1}}{\partial h_k}\frac{\partial h_k}{\partial w_k}
+$$
+
+Where the upstream gradient $\frac{\partial e}{\partial h_K}$ is known, and the local gradient $\frac{\partial h_k}{\partial w_k}$ is known.
+
+#### General backpropagation algorithm
+
+The adding layer is the gradient distributor layer.
+The multiplying layer is the gradient switcher layer.
+The max operation is the gradient router layer.
+
+![Images of propagation](https://static.notenextra.trance-0.com/CSE559A/General_computation_graphs_for_MLP.png)
+
+Simple example: Element-wise operation (ReLU)
+
+$f(x)=ReLU(x)=max(0,x)$
+
+$$
+\frac{\partial z}{\partial x}=\begin{pmatrix}
+\frac{\partial z_1}{\partial x_1} & 0 & \cdots & 0 \\
+0 & \frac{\partial z_2}{\partial x_2} & \cdots & 0 \\
+\vdots & \vdots & \ddots & \vdots \\
+0 & 0 & \cdots & \frac{\partial z_n}{\partial x_n}
+\end{pmatrix}
+$$
+
+Where $\frac{\partial z_i}{\partial x_j}=1$ if $i=j$ and $z_i>0$, otherwise $\frac{\partial z_i}{\partial x_j}=0$.
+
+When $\forall x_i<0$ then $\frac{\partial z}{\partial x}=0$ (dead ReLU)
+
+Other examples on ppt.
+
+## Convolutional Neural Networks
+
+### Basic Convolutional layer
+
+#### Flatten layer
+
+Fully connected layer, operate on vectorized image.
+
+With the multi-layer perceptron, the neural network trying to fit the templates.
+
+![Flatten layer](https://static.notenextra.trance-0.com/CSE559A/Flatten_layer.png)
+
+#### Convolutional layer
+
+Limit the receptive fields of units, tiles them over the input image, and share the weights.
+
+Equivalent to sliding the learned filter over the image , computing dot products at each location.
+
+![Convolutional layer](https://static.notenextra.trance-0.com/CSE559A/Convolutional_layer.png)
+
+Padding: Add a border of zeros around the image. (higher padding, larger output size)
+
+Stride: The step size of the filter. (higher stride, smaller output size)
+
+### Variants 1x1 convolutions, depthwise convolutions
+
+### Backward pass
diff --git a/pages/CSE559A/_meta.js b/pages/CSE559A/_meta.js
index ed50190..b79d0b8 100644
--- a/pages/CSE559A/_meta.js
+++ b/pages/CSE559A/_meta.js
@@ -11,4 +11,5 @@ export default {
     CSE559A_L6: "Computer Vision (Lecture 6)",
     CSE559A_L7: "Computer Vision (Lecture 7)",
     CSE559A_L8: "Computer Vision (Lecture 8)",
+    CSE559A_L9: "Computer Vision (Lecture 9)",
 }
diff --git a/pages/Math416/Math416_L1.md b/pages/Math416/Math416_L1.md
index 6163d5f..6597f2b 100644
--- a/pages/Math416/Math416_L1.md
+++ b/pages/Math416/Math416_L1.md
@@ -1,4 +1,4 @@
-# Lecture 1
+# Math416 Lecture 1
 
 ## Chapter 1: Complex Numbers
 
diff --git a/pages/Math416/Math416_L2.md b/pages/Math416/Math416_L2.md
index 2246204..5bdc07b 100644
--- a/pages/Math416/Math416_L2.md
+++ b/pages/Math416/Math416_L2.md
@@ -1,4 +1,4 @@
-# Lecture 2
+# Math416 Lecture 2
 
 ## Review?
 
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