The beauty of learning complex things is by breaking them down into smaller simple things. Nobody was born an expert, just like the writer did not become a data geek until after campus -- without even a Data Science background. Nevertheless, you should be in love with mathematics and coding to even appreciate the most difficult concepts in Data Science. To be a Data Science pro, you should be skilled in Statistics, Machine Learning,Deep Leaning; capable of knowing the right tools in those fields. Apparently, there is more to Data than collecting, preparing and cleaning using tools like MS Excel, R, SQL and Tableau that you will find in any Data Analytics course. Data Analytics answers questions pertaining descriptive, diagnostic and prescriptive analytics while Data Science involves an additional field known as predictive analytics.

I will make the argument that the disciplines of math and statistics have captured mainstream interest because of the growing availability of data, and we need math, statistics, and machine learning to make sense of it. Yes, we do have scientific tools, machine learning, and other automations that call to us like sirens. We blindly trust these "black boxes," devices, and softwares; we do not understand them but we use them anyway. While it is easy to believe computers are smarter than we are (and this idea is frequently marketed), the reality cannot be more the opposite. This disconnect can be precarious on so many levels.

Matrix decomposition, also called matrix factorization is the process of splitting a matrix into multiple pieces. In the context of data science, you can for instance use it to select parts of the data, aimed at reducing dimensionality without losing much information (as for instance in Principal Component Analysis, as you'll later in this post). Some operations are also more easily computed on the matrices resulting from the decomposition. In this article, you'll learn about the eigendecomposition of a matrix. One way to understand it is to consider it as a special change of basis (more details about change of basis in my last post).

In this article, you'll learn about Singular value decomposition (SVD), which is a major topic of linear algebra, data science, and machine learning. It is for instance used to calculate the Principal Component Analysis (PCA). You'll need some understanding of linear algebra basics (feel free to check the previous article and the book Essential Math for Data Science. You can only apply eigendecomposition to square matrices because it uses a single change of basis matrix, which implies that the initial vector and the transformed vector are relative to the same basis. You go to another basis with to do the transformation, and you come back to the initial basis with .

One way to understand eigendecomposition is to consider it as a change of basis. You'll learn in this article what is the basis of a vector space. You'll see that any vector of the space are linear combinations of the basis vectors and that the number you see in vectors depends on the basis you choose. Finally, you'll see how to change the basis using change of basis matrices. It is a nice way to consider matrix factorization as eigendecomposition or Singular Value Decomposition.

As you saw in Essential Math for Data Science, vectors are a useful way to store and manipulate data. You can represent them geometrically as arrows, or as arrays of numbers (the coordinates of their ending points). However, it can be helpful to create more complicated data structures – and that is where matrices need to be introduced. As vectors, matrices are data structures allowing you to organize numbers. They are square or rectangular arrays containing values organized in two dimensions: as rows and columns.

Calculus is a branch of mathematics that gives tools to study the rate of change of functions through two main areas: derivatives and integrals. In the context of machine learning and data science, you might use integrals to calculate the area under the curve (for instance, to evaluate the performance of a model with the ROC curve, or to calculate probability from densities. In this article, you'll learn about integrals and the area under the curve using the practical data science example of the area under the ROC curve used to compare the performances of two machine learning models. Building from this example, you'll see the notion of the area under the curve and integrals from a mathematical point of view (from my book Essential Math for Data Science). Let's say that you would like to predict the quality of wines from various of their chemical properties. You want to do a binary classification of the quality (distinguishing very good wines from not very good ones). You'll develop methods allowing you to evaluate your models considering imbalanced data with the area under the Receiver Operating Characteristics (ROC) curve.

In less than 3 hours, you can understand the theory behind modern artificial intelligence, and apply it with several hands-on examples. This is machine learning on steroids! Find out why everyone's so excited about it and how it really works – and what modern AI can and cannot really do. At the end, you will have a final challenge to create your own deep learning / machine learning system to predict whether real mammogram results are benign or malignant, using your own artificial neural network you have learned to code from scratch with Python. You will need some familiarity with Python and linear algebra to follow along, but if you have that experience, you will find that neural networks are not as complicated as they sound.

The full article also features courses that you could attend to learn the topics listed below, as well as numerous comments. We also added a few topics that we think are important and missing in the original article.

Here are the most popular posts in KDnuggets in September, based on the number of unique page views (UPV), and social share counts from Facebook, Twitter, and Addthis. Most Shareable (Viral) Blogs Among the top blogs, here are the 5 blogs with the highest ratio of shares/unique views, which suggests that people who read it really liked it. You Aren't So Smart: Cognitive Biases are Making Sure of It, by Matthew Mayo A Winning Game Plan For Building Your Data Science Team, by William Schmarzo What on earth is data science?, by Cassie Kozyrkov Everything You Need to Know About AutoML and Neural Architecture Search, by George Seif The Data Science of "Someone Like You" or Sentiment Analysis of Adele's Songs, by Preetish Panda How many data scientists are there and is there a shortage?, by Gregory Piatetsky Neural Networks and Deep Learning: A Textbook, by Charu Aggarwal 5 Resources to Inspire Your Next Data Science Project, by Conor Dewey Hadoop for Beginners, by Aafreen Dabhoiwala 6 Steps To Write Any Machine Learning Algorithm From Scratch: Perceptron Case Study, by John Sullivan Deep Learning for NLP: An Overview of Recent Trends, by Elvis Saravia (*) Ultimate Guide to Getting Started with TensorFlow, by Brian Zhang (*) How many data scientists are there and is there a shortage?, by Gregory Piatetsky Essential Math for Data Science: 'Why' and'How', by Tirthajyoti Sarkar Journey to Machine Learning - 100 Days of ML Code, by Avik Jain You Aren't So Smart: Cognitive Biases are Making Sure of It, by Matthew Mayo Neural Networks and Deep Learning: A Textbook, by Charu Aggarwal (*) You Aren't So Smart: Cognitive Biases are Making Sure of It, by Matthew Mayo How many data scientists are there and is there a shortage?, by Gregory Piatetsky You Aren't So Smart: Cognitive Biases are Making Sure of It, by Matthew Mayo A Winning Game Plan For Building Your Data Science Team, by William Schmarzo What on earth is data science?, by Cassie Kozyrkov Everything You Need to Know About AutoML and Neural Architecture Search, by George Seif The Data Science of "Someone Like You" or Sentiment Analysis of Adele's Songs, by Preetish Panda You Aren't So Smart: Cognitive Biases are Making Sure of It, by Matthew Mayo What on earth is data science?, by Cassie Kozyrkov