diff --git a/homework_04_logistic_regression/homework/README.md b/homework_04_logistic_regression/homework/README.md
index 271a005..bbe04d0 100644
--- a/homework_04_logistic_regression/homework/README.md
+++ b/homework_04_logistic_regression/homework/README.md
@@ -22,11 +22,11 @@ g(z_i)=g(\theta_i^T \mathbf{x})=\frac{e^{\theta_i^T\mathbf{x}}}{\sum\limits_{j=1
 $$
 构造似然函数，若有$m$个训练样本：
 $$
-\begin{align}
-L(\Theta)&=p(\mathbf{y}|\mathbf{X};\Theta) \\
-& = \prod\limits_{i=1}^{m} p(y^{i}|\mathbf{x}^{i};\Theta) \\
+\begin{aligned}
+L(\Theta)&=p(\mathbf{y}|\mathbf{X};\Theta) \\\\
+& = \prod\limits_{i=1}^{m} p(y^{i}|\mathbf{x}^{i};\Theta) \\\\
 & = \prod_{i=1}^m h_{\theta_i}(\mathbf{x})
-\end{align}
+\end{aligned}
 $$
 对似然函数取对数，转换为：
 $$
@@ -35,21 +35,21 @@ $$
 对$log(h_{\theta_i}(\mathbf{x}))$求导得到：
 $$
 \frac{\partial{log(h_{\theta_i}(\mathbf{x}))}}{\partial{z_k}}=\begin{cases}
-1-h_{\theta_k}(\mathbf{x}) & \text{ if } k=i \\
+1-h_{\theta_k}(\mathbf{x}) & \text{ if } k=i \\\\
 -h_{\theta_k}(\mathbf{x}) & else
 \end{cases}
 $$
 转换后的似然函数对$\theta$求偏导，在这里我们以只有一个训练样本的情况为例：
 $$
-\begin{align}
-\frac{\partial}{\partial\theta_k}l(\Theta)&=\frac{\partial l(\Theta)}{\partial{z_k}}\cdot \frac{\partial z_k}{\partial \theta_k} \\
+\begin{aligned}
+\frac{\partial}{\partial\theta_k}l(\Theta)&=\frac{\partial l(\Theta)}{\partial{z_k}}\cdot \frac{\partial z_k}{\partial \theta_k} \\\\
 &=(y_k-h_{\theta_k}(\mathbf{x}))\mathbf{x}
-\end{align}
+\end{aligned}
 $$
 上式中$y_k$的表达式如下：
 $$
 y_k=\begin{cases}
-1 & \text{ if } k=i \\
+1 & \text{ if } k=i \\\\
 0 & else
 \end{cases}
 $$