diff --git a/Book4_Ch20_Python_Codes/Bk4_Ch20_01.py b/Book4_Ch20_Python_Codes/Bk4_Ch20_01.py
deleted file mode 100644
index b59fb69..0000000
--- a/Book4_Ch20_Python_Codes/Bk4_Ch20_01.py
+++ /dev/null
@@ -1,97 +0,0 @@
-
-###############
-# Authored by Weisheng Jiang
-# Book 4  |  From Basic Arithmetic to Machine Learning
-# Published and copyrighted by Tsinghua University Press
-# Beijing, China, 2022
-###############
-
-# Bk4_Ch20_01.py
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-alphas = np.linspace(0, 2*np.pi, 100)
-
-# unit circle
-r = np.sqrt(1.0)
-
-z1 = r*np.cos(alphas)
-z2 = r*np.sin(alphas)
-
-Z = np.array([z1, z2]).T # data of unit circle
-
-# scale
-S = np.array([[2, 0],
-              [0, 0.5]])
-
-thetas = np.array([0, 30, 45, 60, 90, 120])
-
-for theta in thetas:
-
-    # rotate
-    print('==== Rotate ====')
-    print(theta)
-    theta = theta/180*np.pi
-    R = np.array([[np.cos(theta), -np.sin(theta)],
-                  [np.sin(theta),  np.cos(theta)]])
-    
-    # translate
-    c = np.array([2, 1])
-    X = Z@S@R.T + c;
-    
-    Q = R@np.linalg.inv(S)@np.linalg.inv(S)@R.T
-    print('==== Q ====')
-    print(Q)
-    LAMBDA, V = np.linalg.eig(Q)
-    print('==== LAMBDA ====')
-    print(LAMBDA)
-    print('==== V ====')
-    print(V)
-    
-    x1 = X[:,0]
-    x2 = X[:,1]
-    
-    fig, ax = plt.subplots(1)
-    ax.plot(z1, z2, 'b') # plot the unit circle
-    ax.plot(x1, x2, 'r') # plot the transformed shape
-    ax.plot(c[0],c[1],'xk') # plot the center
-    
-    ax.quiver(0,0,1,0,color = 'b',angles='xy', scale_units='xy',scale=1)
-    ax.quiver(0,0,0,1,color = 'b',angles='xy', scale_units='xy',scale=1)
-    ax.quiver(0,0,-1,0,color = 'b',angles='xy', scale_units='xy',scale=1)
-    ax.quiver(0,0,0,-1,color = 'b',angles='xy', scale_units='xy',scale=1)
-    
-    ax.quiver(0,0,c[0],c[1],color = 'k',angles='xy', scale_units='xy',scale=1)
-    
-    ax.quiver(c[0],c[1],
-              V[0,0]/np.sqrt(LAMBDA[0]),
-              V[1,0]/np.sqrt(LAMBDA[0]),color = 'r',
-              angles='xy', scale_units='xy',scale=1)
-    
-    ax.quiver(c[0],c[1],
-              V[0,1]/np.sqrt(LAMBDA[1]),
-              V[1,1]/np.sqrt(LAMBDA[1]),color = 'r',
-              angles='xy', scale_units='xy',scale=1)
-
-    ax.quiver(c[0],c[1],
-              -V[0,0]/np.sqrt(LAMBDA[0]),
-              -V[1,0]/np.sqrt(LAMBDA[0]),color = 'r',
-              angles='xy', scale_units='xy',scale=1)
-    
-    ax.quiver(c[0],c[1],
-              -V[0,1]/np.sqrt(LAMBDA[1]),
-              -V[1,1]/np.sqrt(LAMBDA[1]),color = 'r',
-              angles='xy', scale_units='xy',scale=1)
-    
-    plt.axvline(x=0, color= 'k', zorder=0)
-    plt.axhline(y=0, color= 'k', zorder=0)
-    
-    
-    ax.set_aspect(1)
-    plt.xlim(-2,4)
-    plt.ylim(-2,4)
-    plt.grid(linestyle='--')
-    plt.show()
-    plt.xlabel('$x_1$')
-    plt.ylabel('$x_2$')
diff --git a/Book4_Ch20_Python_Codes/Bk4_Ch20_02.py b/Book4_Ch20_Python_Codes/Bk4_Ch20_02.py
deleted file mode 100644
index 49c22ca..0000000
--- a/Book4_Ch20_Python_Codes/Bk4_Ch20_02.py
+++ /dev/null
@@ -1,56 +0,0 @@
-
-###############
-# Authored by Weisheng Jiang
-# Book 4  |  From Basic Arithmetic to Machine Learning
-# Published and copyrighted by Tsinghua University Press
-# Beijing, China, 2022
-###############
-
-# Bk4_Ch20_02.py
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-alphas = np.linspace(0, 2*np.pi, 100)
-
-# unit circle
-r = np.sqrt(1.0)
-
-z1 = r*1/np.cos(alphas)
-z2 = r*np.tan(alphas)
-
-Z = np.array([z1, z2]).T # data of unit circle
-
-# scale
-S = np.array([[1, 0],
-              [0, 1]])
-
-thetas = np.array([0, 30, 45, 60, 90, 120])
-
-for theta in thetas:
-
-    # rotate
-    print('==== Rotate ====')
-    print(theta)
-    theta = theta/180*np.pi
-    R = np.array([[np.cos(theta), -np.sin(theta)],
-                  [np.sin(theta),  np.cos(theta)]])
-
-    X = Z@S@R.T;
-    
-    x1 = X[:,0]
-    x2 = X[:,1]
-    
-    fig, ax = plt.subplots(1)
-    ax.plot(z1, z2, 'b') # plot the unit circle
-    ax.plot(x1, x2, 'r') # plot the transformed shape
-
-    plt.axvline(x=0, color= 'k', zorder=0)
-    plt.axhline(y=0, color= 'k', zorder=0)
-    ax.set_aspect(1)
-    plt.xlim(-3,3)
-    plt.ylim(-3,3)
-    plt.grid(linestyle='--')
-    plt.show()
-    plt.xlabel('$x_1$')
-    plt.ylabel('$x_2$')
diff --git a/Book4_Ch20_Python_Codes/Bk4_Ch20_03.py b/Book4_Ch20_Python_Codes/Bk4_Ch20_03.py
deleted file mode 100644
index db073f1..0000000
--- a/Book4_Ch20_Python_Codes/Bk4_Ch20_03.py
+++ /dev/null
@@ -1,50 +0,0 @@
-
-###############
-# Authored by Weisheng Jiang
-# Book 4  |  From Basic Arithmetic to Machine Learning
-# Published and copyrighted by Tsinghua University Press
-# Beijing, China, 2022
-###############
-
-# Bk4_Ch20_03.py
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-a = 1.5
-b = 1
-
-x1 = np.linspace(-3,3,200)
-x2 = np.linspace(-3,3,200)
-xx1,xx2 = np.meshgrid(x1,x2)
-
-fig, ax = plt.subplots()
-
-theta_array = np.linspace(0,2*np.pi,100)
-
-plt.plot(a*np.cos(b*np.sin(theta)),b*np.sin(b*np.sin(theta)),color = 'k')
-
-colors = plt.cm.RdYlBu(np.linspace(0,1,len(theta_array)))
-
-for i in range(len(theta_array)):
-    
-    theta = theta_array[i]
-    
-    p1 = a*np.cos(theta)
-    p2 = b*np.sin(theta)
-    
-    tangent = p1*xx1/a**2 + p2*xx2/b**2 - p1**2/a**2 - p2**2/b**2
-    
-    colors_i = colors[int(i),:]
-    
-    ax.contour(xx1,xx2,tangent, levels = [0], colors = [colors_i])
-
-plt.axis('scaled')
-ax.set_xlim(-3,3)
-ax.set_ylim(-3,3)
-ax.spines['top'].set_visible(False)
-ax.spines['right'].set_visible(False)
-ax.spines['bottom'].set_visible(False)
-ax.spines['left'].set_visible(False)
-ax.axvline(x=0,color = 'k')
-ax.axhline(y=0,color = 'k')
diff --git a/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py b/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py
deleted file mode 100644
index 325db63..0000000
--- a/Book4_Ch20_Python_Codes/Streamlit_Bk4_Ch20_04.py
+++ /dev/null
@@ -1,132 +0,0 @@
-
-###############
-# Authored by Weisheng Jiang
-# Book 4  |  From Basic Arithmetic to Machine Learning
-# Published and copyrighted by Tsinghua University Press
-# Beijing, China, 2022
-###############
-
-
-
-import streamlit as st
-import plotly.graph_objects as go
-import sympy
-import numpy as np
-from scipy.stats import multivariate_normal
-
-def bmatrix(a):
-    """Returns a LaTeX bmatrix
-
-    :a: numpy array
-    :returns: LaTeX bmatrix as a string
-    """
-    if len(a.shape) > 2:
-        raise ValueError('bmatrix can at most display two dimensions')
-    lines = str(a).replace('[', '').replace(']', '').splitlines()
-    rv = [r'\begin{bmatrix}']
-    rv += ['  ' + ' & '.join(l.split()) + r'\\' for l in lines]
-    rv +=  [r'\end{bmatrix}']
-    return '\n'.join(rv)
-
-with st.sidebar:
-    
-    st.latex(r'''
-             \Sigma = \begin{bmatrix}
-    \sigma_1^2 & 
-    \rho \sigma_1 \sigma_2 \\
-    \rho \sigma_1 \sigma_2 & 
-    \sigma_2^2
-    \end{bmatrix}''')
-    
-    
-    st.write('$\sigma_1$')
-    sigma_1 = st.slider('sigma_1',1.0, 2.0, step = 0.1)
-
-    st.write('$\sigma_2$')
-    sigma_2 = st.slider('sigma_2',1.0, 2.0, step = 0.1)
-    
-    st.write('$\u03C1$')
-    rho_12 = st.slider('rho',-0.9, 0.9, step = 0.1)
-        
-#%%
-
-st.latex(r'''
-   f(x) = \frac{1}{\sqrt{2\pi} \sigma} 
-          \exp\left( -\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{\!2}\,\right)
-          ''')
-  
-st.latex(r'''
-   f(x) = \frac{1}{\left( 2 \pi \right)^{\frac{D}{2}} 
-          \begin{vmatrix}
-          \Sigma 
-          \end{vmatrix}^{\frac{1}{2}}} 
-          \exp\left( 
-         -\frac{1}{2}
-          \left( x - \mu \right)^{T} \Sigma^{-1} \left( x - \mu \right)
-          \right)
-          ''')
-          
-#%%
-x1 = np.linspace(-3,3,101)
-x2 = np.linspace(-3,3,101)
-
-xx1, xx2 = np.meshgrid(x1,x2)
-pos = np.dstack((xx1, xx2))
-
-Sigma = [[sigma_1**2, rho_12*sigma_1*sigma_2], 
-         [rho_12*sigma_1*sigma_2, sigma_2**2]]
-rv = multivariate_normal([0, 0], 
-                         Sigma)
-PDF_zz = rv.pdf(pos)
-
-#%%
-
-Sigma = np.array(Sigma)
-
-D,V = np.linalg.eig(Sigma)
-D = np.diag(D)
-
-st.latex(r'''\Sigma = \begin{bmatrix}%s & %s\\%s & %s\end{bmatrix}''' 
-         %(sigma_1**2, 
-           rho_12*sigma_1*sigma_2, 
-           rho_12*sigma_1*sigma_2, 
-           sigma_2**2))
-st.latex(r'''\Sigma = V \Lambda V^{T}''')
-st.latex(bmatrix(Sigma) + '=' + 
-         bmatrix(np.around(V, decimals=3)) + '@' + 
-         bmatrix(np.around(D, decimals=3)) + '@' + 
-         bmatrix(np.around(V.T, decimals=3)))
-
-#%% Plot 3D surface
-
-fig_surface = go.Figure(go.Surface(
-    x = x1,
-    y = x2,
-    z = PDF_zz,
-    colorscale= 'RdYlBu_r'))
-fig_surface.update_layout(
-    autosize=False,
-    width=500,
-    height=500)
-st.plotly_chart(fig_surface)
-
-#%% Plot 2D contour
-
-fig_contour = go.Figure(
-    go.Contour(
-        z=PDF_zz,
-        x=x1,
-        y=x2,
-        colorscale= 'RdYlBu_r'
-    ))
-
-fig_contour.update_layout(
-    autosize=False,
-    width=500,
-    height=500)
-
-st.plotly_chart(fig_contour)       
-        
-        
-        
-    
\ No newline at end of file