Mathematics for Data Scientist: Necessary Sections

Mathematics is the cornerstone of Data Science. Although some theorems, axioms, and formulas seem too abstract and far from practice, in fact, without them it is impossible to truly deeply analyze and systematize huge data arrays.

The following areas of mathematics are important for a Data Science specialist:

• statistics;
• probability theory;
• mathematical analysis;
• linear algebra.

In a previous article, “Data Science: Entry-Level Books,” Plarium Krasnodar experts recommended literature on Python programming, as well as on visualization of results and machine learning. In this article, they offer a selection of math materials and books useful in Data Science.

Statistics and probability theory

It is difficult to overestimate the importance of knowledge of statistics for Data Scientist at any level. All classic machine learning is based on statistical learning. Moreover, standard A / B tests are based on it.

Sources for inspiration:



All of Statistics
Larry Wasserman

As the author writes: "This book is for people who want to learn probability and statistics quickly."

The book gives all the basic provisions of probability theory and statistics.



Basics of statistics (3 parts)
Stepik educational platform

Statistics course for beginners. Covers all elementary concepts.



Statistics Fundamentals Succinctly Katharine
Alexis Kormanik

In a previous articleThis book has already been recommended, but repeating will not be amiss. :-)

In the first sections, the basic definitions are given with illustrations and comments, the last reveals the significance of T- and Z-tests. The materials are presented in an accessible language, with the minimum necessary mathematical apparatus. This guide is an excellent introduction to statistics from a practical point of view.



Probability Theory and Mathematical Statistics
N. Sh. Kremer The

textbook is aimed at economists; therefore, the complexity and depth of concepts does not shock the beginner in Data Science. Suitable for learning the basics before diving into specialized literature.



Probability Theory and Mathematical Statistics
A. I. Kibzun, E. R. Goryainova, A. V. Naumov, A. N. Sirotin

This basic course provides deeper insights than the previous one. In addition to
theory, it includes practical tasks and reference materials.



Basic concepts of probability theory and mathematical statistics
M. Ya. Kelbert, Yu. M. Sukhov

A great option for those who are already familiar with the topic and want to get deeper knowledge.

Mathematical analysis

At first glance, this direction is needed more within the walls of universities, but without it it will not be possible to deal with backpropagation or to master a deep learning course in a qualitative way.

Filling in the gaps in statistics, it's time to start studying the materials in this section. And there are a great many of them.



Calculus
edX

A course from the Massachusetts Institute of Technology, consisting of 3 parts:

• Calculus 1A: Differentiation - a course on finding a derivative, its geometric interpretation and physical meaning.
• Calculus 1B: Integration - a course on finding the integral, its relationship with the derivative and application in engineering design, scientific analysis, probability theory and statistics.
• Calculus 1C: Coordinate Systems & Infinite Series - a course on calculating curves, coordinate systems, approximating functions to polynomials and infinite series. All this is necessary to build mathematical models of the real world.

Calculus One
Coursera educational platform

The course is aimed at beginners, but a convenient presentation of material will help refresh the memory of experienced Data Scientist.



Khan Academy
Educational platform

A variety of materials presented on the resource are perfect for starting a study of mathematics, programming and computer science.



Calculus
James Stewart

The book is famous for its carefully designed content and fairly simple language.



The course of mathematical analysis
L. D. Kudryavtsev

For those who want to get more fundamental knowledge about differential and integral calculus, series theory, functional and harmonic analysis.

You can also pay attention to two courses from MIT:

1. Single Variable Calculus - a course for independent study of differentiation, integral calculus and infinite series.
2. Multivariable Calculus is another course for independent study of differentiation, as well as integral and vector calculus of functions of several variables.

Linear algebra

Without this section of mathematics, it will not be possible to develop machine learning methods, simulate the behavior of various objects, or optimize the clustering process and reduce the dimensionality of data descriptions.



Linear Algebra
Georgi E. Shilov

The textbook contains a well-developed material. The book is suitable for studying an introductory course in linear algebra.



Linear Algebra
V. A. Ilyin, E. G. Poznyak

This textbook was written on the basis of lectures by teachers of the Physics Department of Moscow State University. All materials are presented in an accessible language and are suitable for in-depth study of the basic theories of linear algebra.

And finally, another recommendation is the MIT Linear Algebra training course . He reveals the theory of matrices and the positions of linear algebra.