diff --git a/module05/en.py_proj.tex b/module05/en.py_proj.tex
index 9c70b1d7..be47a199 100644
--- a/module05/en.py_proj.tex
+++ b/module05/en.py_proj.tex
@@ -24,8 +24,7 @@ \chapter*{Common Instructions}
   
   \item Your manual is the internet.
   
-  \item You can also ask questions in the \texttt{\#bootcamps} channel in the \href{https://42-ai.slack.com}{42AI}
-  or \href{42born2code.slack.com}{42born2code}.
+  \item You can also ask questions on the {https://discord.gg/8Vvb6QMCZq}{42AI} discord.
   
   \item If you find any issue or mistakes in the subject please create an issue on \href{https://github.com/42-AI/bootcamp_python/issues}{42AI repository on Github}.  
   
diff --git a/module05/en.subject.tex b/module05/en.subject.tex
index 4ab99615..a51aa1af 100644
--- a/module05/en.subject.tex
+++ b/module05/en.subject.tex
@@ -612,8 +612,8 @@ \section*{Instructions}
 def simple_predict(x, theta):
     """Computes the vector of prediction y_hat from two non-empty numpy.ndarray.
     Args:
-      x: has to be an numpy.ndarray, a vector of dimension m * 1.
-      theta: has to be an numpy.ndarray, a vector of dimension 2 * 1.
+      x: has to be an numpy.ndarray, a one-dimensional vector of size m.
+      theta: has to be an numpy.ndarray, a one-dimensional vector of size 2.
     Returns:
       y_hat as a numpy.ndarray, a vector of dimension m * 1.
       None if x or theta are empty numpy.ndarray.
@@ -694,7 +694,7 @@ \section*{Instructions}
 def add_intercept(x):
     """Adds a column of 1's to the non-empty numpy.array x.
     Args:
-      x: has to be a numpy.array of dimension m * n.
+      x: has to be a numpy.array. x can be a one-dimensional (m * 1) or two-dimensional (m * n) vector.
     Returns:
       X, a numpy.array of dimension m * (n + 1).
       None if x is not a numpy.array.
@@ -811,8 +811,8 @@ \section*{Instructions}
 def predict_(x, theta):
     """Computes the vector of prediction y_hat from two non-empty numpy.array.
     Args:
-      x: has to be an numpy.array, a vector of dimension m * 1.
-      theta: has to be an numpy.array, a vector of dimension 2 * 1.
+      x: has to be an numpy.array, a one-dimensional vector of size m.
+      theta: has to be an numpy.array, a two-dimensional vector of shape 2 * 1.
     Returns:
       y_hat as a numpy.array, a vector of dimension m * 1.
       None if x and/or theta are not numpy.array.
@@ -845,7 +845,7 @@ \section*{Examples}
 
 # Example 3:
 theta3 = np.array([[5], [3]])
-predict_(X, theta3)
+predict_(x, theta3)
 # Output:
 array([[ 8.], [11.], [14.], [17.], [20.]])
 
@@ -895,9 +895,9 @@ \section*{Instructions}
 def plot(x, y, theta):
     """Plot the data and prediction line from three non-empty numpy.array.
     Args:
-      x: has to be an numpy.array, a vector of dimension m * 1.
-      y: has to be an numpy.array, a vector of dimension m * 1.
-      theta: has to be an numpy.array, a vector of dimension 2 * 1.
+      x: has to be an numpy.array, a one-dimensional vector of size m.
+      y: has to be an numpy.array, a one-dimensional vector of size m.
+      theta: has to be an numpy.array, a two-dimensional vector of shape 2 * 1.
     Returns:
         Nothing.
     Raises:
@@ -986,7 +986,7 @@ \section*{Objective}
 
 Where:
 \begin{itemize}
-  \item $\hat{y}$ is a vector of dimension $m$, the vector of predicted values
+  \item $\hat{y}$ is a vector of dimension $m\times 1$, the vector of predicted values
   \item $y$ is a vector of dimension $m\times 1$, the vector of expected values
   \item $\hat{y}^{(i)}$ is the ith component of vector $\hat{y}$,
   \item $y^{(i)}$ is the ith component of vector $y$,
@@ -1011,8 +1011,8 @@ \section*{Instructions}
 	Description:
 		Calculates all the elements (y_pred - y)^2 of the loss function.
 	Args:
-      y: has to be an numpy.array, a vector.
-      y_hat: has to be an numpy.array, a vector.
+      y: has to be an numpy.array, a two-dimensional vector of shape m * 1.
+      y_hat: has to be an numpy.array, a two-dimensional vector of shape m * 1.
 	Returns:
 		J_elem: numpy.array, a vector of dimension (number of the training examples,1).
 		None if there is a dimension matching problem between X, Y or theta.
@@ -1027,8 +1027,8 @@ \section*{Instructions}
 	Description:
 		Calculates the value of loss function.
 	Args:
-      y: has to be an numpy.array, a vector.
-      y_hat: has to be an numpy.array, a vector.
+      y: has to be an numpy.array, a two-dimensional vector of shape m * 1.
+      y_hat: has to be an numpy.array, a two-dimensional vector of shape m * 1.
 	Returns:
 		J_value : has to be a float.
 		None if there is a dimension matching problem between X, Y or theta.
@@ -1063,8 +1063,8 @@ \section*{Examples}
 3.0
 
 x2 = np.array([0, 15, -9, 7, 12, 3, -21]).reshape(-1, 1)
-theta2 = np.array([[0.], [1.]]).reshape(-1, 1)
-y_hat2 = predict_(x3, theta3)
+theta2 = np.array(np.array([[0.], [1.]]))
+y_hat2 = predict_(x2, theta2)
 y2 = np.array([2, 14, -13, 5, 12, 4, -19]).reshape(-1, 1)
 
 # Example 3:
@@ -1141,8 +1141,8 @@ \section*{Instructions}
     """Computes the half mean squared error of two non-empty numpy.array, without any for loop.
     The two arrays must have the same dimensions.
     Args:
-      y: has to be an numpy.array, a vector.
-      y_hat: has to be an numpy.array, a vector.
+      y: has to be an numpy.array, a one-dimensional vector of size m.
+      y_hat: has to be an numpy.array, a one-dimensional vector of size m.
     Returns:
       The half mean squared error of the two vectors as a float.
       None if y or y_hat are empty numpy.array.
@@ -1159,8 +1159,8 @@ \section*{Examples}
 % --------------------------------- %
 \begin{minted}[bgcolor=darcula-back,formatcom=\color{lightgrey},fontsize=\scriptsize]{python}
 import numpy as np
-X = np.array([[0], [15], [-9], [7], [12], [3], [-21]])
-Y = np.array([[2], [14], [-13], [5], [12], [4], [-19]])
+X = np.array([0, 15, -9, 7, 12, 3, -21])
+Y = np.array([2, 14, -13, 5, 12, 4, -19])
 
 # Example 1:
 loss_(X, Y)
@@ -1206,9 +1206,9 @@ \section*{Instructions}
 def plot_with_loss(x, y, theta):
 """Plot the data and prediction line from three non-empty numpy.ndarray.
     Args:
-      x: has to be an numpy.ndarray, a vector of dimension m * 1.
-      y: has to be an numpy.ndarray, a vector of dimension m * 1.
-      theta: has to be an numpy.ndarray, a vector of dimension 2 * 1.
+      x: has to be an numpy.ndarray, one-dimensional array of size m.
+      y: has to be an numpy.ndarray, one-dimensional array of size m.
+      theta: has to be an numpy.ndarray, one-dimensional array of size 2.
     Returns:
         Nothing.
     Raises:
@@ -1334,8 +1334,8 @@ \section*{Instructions}
 	Description:
 		Calculate the MSE between the predicted output and the real output.
 	Args:
-        y: has to be a numpy.array, a vector of dimension m * 1.
-        y_hat: has to be a numpy.array, a vector of dimension m * 1.		
+        y: has to be a numpy.array, a two-dimensional vector of shape m * 1.
+        y_hat: has to be a numpy.array, a two-dimensional vector of shape m * 1.		
 	Returns:
 		mse: has to be a float.
 		None if there is a matching dimension problem.
@@ -1350,8 +1350,8 @@ \section*{Instructions}
 	Description:
 		Calculate the RMSE between the predicted output and the real output.
 	Args:
-	        y: has to be a numpy.array, a vector of dimension m * 1.
-        y_hat: has to be a numpy.array, a vector of dimension m * 1.		
+	        y: has to be a numpy.array, a two-dimensional vector of shape m * 1.
+        y_hat: has to be a numpy.array, a two-dimensional vector of shape m * 1.		
 	Returns:
 		rmse: has to be a float.
 		None if there is a matching dimension problem.
@@ -1366,8 +1366,8 @@ \section*{Instructions}
 	Description:
 		Calculate the MAE between the predicted output and the real output.
 	Args:
-        y: has to be a numpy.array, a vector of dimension m * 1.
-        y_hat: has to be a numpy.array, a vector of dimension m * 1.		
+        y: has to be a numpy.array, a two-dimensional vector of shape m * 1.
+        y_hat: has to be a numpy.array, a two-dimensional vector of shape m * 1.		
 	Returns:
 		mae: has to be a float.
 		None if there is a matching dimension problem.
@@ -1382,8 +1382,8 @@ \section*{Instructions}
 	Description:
 		Calculate the R2score between the predicted output and the output.
 	Args:
-        y: has to be a numpy.array, a vector of dimension m * 1.
-        y_hat: has to be a numpy.array, a vector of dimension m * 1.		
+        y: has to be a numpy.array, a two-dimensional vector of shape m * 1.
+        y_hat: has to be a numpy.array, a two-dimensional vector of shape m * 1.		
 	Returns:
 		r2score: has to be a float.
 		None if there is a matching dimension problem.
@@ -1412,8 +1412,8 @@ \section*{Examples}
 from math import sqrt
 
 # Example 1:
-x = np.array([0, 15, -9, 7, 12, 3, -21])
-y = np.array([2, 14, -13, 5, 12, 4, -19])
+x = np.array([[0], [15], [-9], [7], [12], [3], [-21]])
+y = np.array([[2], [14], [-13], [5], [12], [4], [-19]])
 
 # Mean squared error
 ## your implementation
diff --git a/module05/usefull_ressources.tex b/module05/usefull_ressources.tex
index 5a399c67..8dad22b8 100644
--- a/module05/usefull_ressources.tex
+++ b/module05/usefull_ressources.tex
@@ -16,36 +16,41 @@ \section*{Useful Ressources}
 
 You are strongly advise to use the following resource:
 \href{https://www.coursera.org/learn/machine-learning/home/week/1}{Machine Learning MOOC - Stanford}
-Here are the sections of the MOOC that are relevant for today's exercises: 
+These videos are available at no cost; simply log in, select "Enroll for Free", and choose "audit the course for free" in the popup window.
+The following sections of the course are pertinent to today's exercises: 
 
-\subsection*{Week 1}
+\subsection*{Week 1: Introduction to Machine Learning}
 
-\subsubsection*{Introduction}
+\subsubsection*{Supervised vs. Unsupervised Machine Learning}
 \begin{itemize}
-  \item What is Machine Learning? (Video + Reading)
-  \item Supervised Learning (Video + Reading)
-  \item Unsupervised Learning (Video + Reading)
-  \item Review (Reading + Quiz)
+  \item What is Machine Learning?
+  \item Supervised Learning Part 1
+  \item Supervised Learning Part 2
+  \item Unsupervised Learning Part 1
+  \item Unsupervised Learning Part 2
 \end{itemize}
     
-\subsubsection*{Linear Regression with One Variable}  
+\subsubsection*{Regression Model}  
 \begin{itemize}
-  \item Model Representation (Video + Reading)
-  \item Cost Function (Video + Reading)
-  \item Cost Function - Intuition I (Video + Reading)
-  \item Cost Function - Intuition II (Video + Reading)
+  \item Regression Model Part 1
+  \item Regression Model Part 2
+  \item Cost Function Formula
+  \item Cost Function Intuition
+  \item Visualizing the cost function
+  \item Visualizing Example
   \item \textit{Keep what remains for tomorow ;)}
 \end{itemize}
 
+\emph{All videos above are available also on this \href{https://youtube.com/playlist?list=PLkDaE6sCZn6FNC6YRfRQc_FbeQrF8BwGI&feature=shared}{Andrew Ng's YouTube playlist} from \#3 to \#14 includes}
+
 \newpage
 
 \subsubsection*{Linear Algebra Review}
 \begin{itemize}
-  \item Matrices and Vectors (Video + Reading)
-  \item Addition and Scalar Multiplication (Video + Reading)
-  \item Matrix Vector Multiplication (Video + Reading)
-  \item Matrix Matrix Multiplication (Video + Reading)
-  \item Matrix Multiplication Properties (Video + Reading)
-  \item Inverse and Transpose (Video + Reading)
-  \item Review (Reading + Quiz)
+  \item \href{https://www.youtube.com/watch?v=XMB__E658fQ}{Matrices and Vectors}
+  \item \href{https://www.youtube.com/watch?v=k1JGJhUGmBE}{Addition and Scalar Multiplication}
+  \item \href{https://www.youtube.com/watch?v=VIfykceJoZI}{Matrix Vector Multiplication}
+  \item \href{https://www.youtube.com/watch?v=JHZKyt0m1kc}{Matrix Matrix Multiplication}
+  \item \href{https://www.youtube.com/watch?v=wqM7O_ZUtCc}{Matrix Multiplication Properties}
+  \item \href{https://www.youtube.com/watch?v=IUf8HDyUeY0}{Inverse and Transpose}
 \end{itemize}
diff --git a/module06/en.py_proj.tex b/module06/en.py_proj.tex
index 9c70b1d7..be47a199 100644
--- a/module06/en.py_proj.tex
+++ b/module06/en.py_proj.tex
@@ -24,8 +24,7 @@ \chapter*{Common Instructions}
   
   \item Your manual is the internet.
   
-  \item You can also ask questions in the \texttt{\#bootcamps} channel in the \href{https://42-ai.slack.com}{42AI}
-  or \href{42born2code.slack.com}{42born2code}.
+  \item You can also ask questions on the {https://discord.gg/8Vvb6QMCZq}{42AI} discord.
   
   \item If you find any issue or mistakes in the subject please create an issue on \href{https://github.com/42-AI/bootcamp_python/issues}{42AI repository on Github}.  
   
diff --git a/module06/en.subject.tex b/module06/en.subject.tex
index 9b45eb96..27ea083e 100644
--- a/module06/en.subject.tex
+++ b/module06/en.subject.tex
@@ -297,7 +297,7 @@ \section*{Instructions}
     """Computes a gradient vector from three non-empty numpy.array, without any for loop.
        The three arrays must have compatible shapes.
     Args:
-      x: has to be a numpy.array, a matrix of shape m * 1.
+      x: has to be a numpy.array, a vector of shape m * 1.
       y: has to be a numpy.array, a vector of shape m * 1.
       theta: has to be a numpy.array, a 2 * 1 vector.
     Return:
@@ -630,11 +630,11 @@ \section*{Examples}
 import pandas as pd
 import numpy as np
 from sklearn.metrics import mean_squared_error
-from mylinearregression import MyLinearRegression as MyLR
+from my_linear_regression import MyLinearRegression as MyLR
 
 data = pd.read_csv("are_blue_pills_magic.csv")
-Xpill = np.array(data[Micrograms]).reshape(-1,1)
-Yscore = np.array(data[Score]).reshape(-1,1)
+Xpill = np.array(data['Micrograms']).reshape(-1,1)
+Yscore = np.array(data['Score']).reshape(-1,1)
 
 linear_model1 = MyLR(np.array([[89.0], [-8]]))
 linear_model2 = MyLR(np.array([[89.0], [-6]]))
diff --git a/module06/usefull_ressources.tex b/module06/usefull_ressources.tex
index a0d84c99..a1bce088 100644
--- a/module06/usefull_ressources.tex
+++ b/module06/usefull_ressources.tex
@@ -15,20 +15,36 @@ \section*{Useful Ressources}
 
 You are strongly advise to use the following resource:
 \href{https://www.coursera.org/learn/machine-learning/home/week/1}{Machine Learning MOOC - Stanford}
-Here are the sections of the MOOC that are relevant for today's exercises: 
+These videos are available at no cost; simply log in, select "Enroll for Free", and choose "audit the course for free" in the popup window.
+The following sections of the course are pertinent to today's exercises: 
 
-\subsection*{Week 1}
+\subsection*{Week 1: Introduction to Machine Learning}
 
-\subsubsection*{Linear Regression with One Variable}
+\subsubsection*{Train the model with Gradient Descent}
 \begin{itemize}
-  \item Gradient Descent (Video + Reading)
-  \item Gradient Descent Intuition (Video + Reading)
-  \item Gradient Descent For Linear Regression (Video + Reading)
-  \item Review (Reading + Quiz)
+  \item Gradient descent
+  \item Implementing gradient descent
+  \item Gradient descent intuition
+  \item Learning rate
+  \item Gradient descent for linear regression
+  \item Running gradient descent
 \end{itemize}
     
-\subsection*{Week 2}
-\subsubsection*{Multivariate Linear Regression}  
+\subsection*{Week 2: Regression with multiple input variables}
+
+\subsubsection*{Multiple linear Regression}  
+\begin{itemize}
+  \item Multiple features
+  \item Vectorization part1 (optional)
+  \item Vectorization part2 (optional)
+\end{itemize}
+
+\subsubsection*{Gradient descent in practice}  
 \begin{itemize}
-  \item Gradient Descent in Practice 1 - Feature Scaling (Video + Reading)
+  \item Feature scaling part 1
+  \item Feature scaling part 2
 \end{itemize}
+
+\emph{All videos above are available also on this \href{https://youtube.com/playlist?list=PLkDaE6sCZn6FNC6YRfRQc_FbeQrF8BwGI&feature=shared}{Andrew Ng's YouTube playlist} from #15 to #21 includes, #25 and #26}
+
+