Essential Math for Data Science: Take Control of Your Data with Fundamental Linear Algebra, Probability, and Statistics

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The cross-entropy can’t be smaller than the entropy. Still in the right panel, you can see that, when the probability Q(x) is larger than P(x) (and thus associated with a lower amount of information), it is counterbalanced by the low weights (resulting in low weights and low information). These low weights will be compensated with larger weights in other probabilities from the distribution (resulting in large weights and large information). Most data roles are programming-based, except for a few like business intelligence, market analysis, product analyst, and others. What should you do after learning how to code? Are there topics that help you strengthen your foundations for data science? When you do the linear transformation associated with a matrix, we say that you apply the matrix to the vector. More concretely, it means that you calculate the matrix-vector product of the matrix and the vector. In this case, the matrix can sometimes be called a transformation matrix. For instance, you can apply a matrix A to a vector v with their product Av. A good way to understand the relationship between matrices and linear transformations is to actually visualize these transformations. To do that, you’ll use a grid of points in a two-dimensional space, each point corresponding to a vector (it is easier to visualize points instead of arrows pointing from the origin).

I am going to focus on technical data jobs that require expertise in at least one programming language. You can also use vectors to store data samples, for instance, store the height of ten people as a vector containing ten values. At the start of this year, I published a mind map on the Data Science learning roadmap (shown below). Many people found the roadmap useful, my article got translated into different languages, and a large number of folks thanked me for publishing it. Linear algebra is the branch of mathematics that studies vector spaces. You’ll see how vectors constitute vector spaces and how linear algebra applies linear transformations to these spaces. You’ll also learn the powerful relationship between sets of linear equations and vector equations, related to important data science concepts like least squares approximation. You’ll finally learn important matrix decomposition methods: eigendecomposition and Singular Value Decomposition (SVD), important to understand unsupervised learning methods like Principal Component Analysis (PCA). What are Vectors?Through the course of this book, you'll learn how to use mathematical notation to understand new developments in the field, communicate with your peers, and solve problems in mathematical form. You'll also understand what's under the hood of the algorithms you're using. So, I decided to give in and do it all myself. I have spent the last 3 months developing a curriculum that will provide a solid foundation for your career as a One of the most commonly used optimization algorithms — gradient descent–is an application of partial derivatives. As I delve deeper into the world of data science and machine learning, strengthening my mathematical foundation is just the beginning. "Essential Mathematics for Data Science" has provided me with a solid starting point. However, my learning journey continues, and I'm excited to explore these additional resources:

Use Python code and libraries like SymPy, NumPy, and scikit-learn to explore essential mathematical concepts like calculus, linear algebra, statistics, and machine learning There are exceptional resources to dive deep into Math but most of us are not made for it and you don't need to be a gold medalist in math to learn data science. What if you hate math and tutorials out there are either too basic tutorials or too deep? Could I recommend a compact yet comprehensive course on Math and Statistics? Choosing content wasn’t easy. There are certainly topics I wish I could have included such as how to build simulations as well as optimization algorithms in more depth. But I made machine learning the end goal of the book, and to get there I guided readers through foundational topics like linear algebra, calculus, and statistics which then feed into linear regression, logistic regression, and neural networks. The “build upon” approach worked quite nicely, and areas I couldn’t get to like optimization could at least get called out as other areas to explore, and I provide tons of resources throughout the book to learn more. I made a diligent effort as well to tie in real world examples and insights, as well as pitfalls to watch out for.Oh boy, the way I describe my book to friends and colleagues is “it’s what I wished I knew 12 years ago before data science and AI became a thing.” To characterize the binary entropy function, you’ll calculate the entropy of a biased coin described by various probability distributions (from heavily biased in favor of “tails” to heavily biased in favor of “heads”). However, vectors refer to various concepts according to the field they are used in. In the context of data science, they are a way to store values from your data. For instance, take the height and weight of people: since they are distinct values with different meanings, you need to store them separately, for instance using two vectors. You can then do operations on vectors to manipulate these features without losing the fact that the values correspond to different attributes. I talk about this extensively in my book, and you’ll probably not be surprised by my answer based on some previous answers I gave to other questions ; ) I think the the experienced programmer is going to do better in a majority of data science job listings out there, because most tasks in data science are unglamorous data wrangling and moving it from one place to another. Then there is a growing awkward need to put models in production, and a programmer is already going to know how to do this well. This is 95-99% of useful data science work.

There are practical reasons for why math is essential for folks who want a career as an ML practitioner, Data Scientist, or a Deep Learning Engineer. You'll Use Linear Algebra to Represent Data An image from the lecture on Vector Norms ( from this course)Chapter 6: Logistic Regression and Classification This chapter delves into logistic regression and classification, explaining concepts like R-squared, P-values, and confusion matrices. The discussion of ROC AUC and handling class imbalances is particularly useful.