Learn Mathematics for Data Science — Study Guide

Data Scientists use a combination of Mathematical and Statistical formulas to observe patterns and trends within data.

Learn Mathematics for Data Science — Study Guide
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Math is the heart of machine learning algorithms, and learning maths for data science is not an option.

The data science interviews are the toughest interviews to crack at FAANG companies and they give always the highest priority to candidates with a strong background in mathematical statistics and algorithms.

Data science is math-oriented and you need to be equipped with math skills to make strategic decisions while designing machine learning models.

As an aspiring Data Scientist, you must be familiar with important mathematical concepts and be able to think as mathematicians do. You need to learn the mathematical concepts for data science such as the gradient descent algorithm, backpropagation, linear and nonlinear functions, etc.

Good News is that you can learn how these algorithms work.

For the entry-level job roles, you don’t need the same depth of knowledge as senior data scientists or machine learning engineers. You need only to develop foundational skills as a practitioner.

We know the options out there; prerequisites and the math skills you need to land an entry-level data science job.

We also understand, it's very common for the beginners to feel intimidated by maths, but in reality you only need more time and practice to gain a thorough understanding.

If you’re terrified of mathematics or unwilling to solve an equation, you need encouragement. We highly recommend Naked Statistics by Charles Wheelan. This book is practical, easy to read and encouraging for straining forward to learn maths.

In this study guide, we explain the mathematical concepts you need to learn to master the key concepts of data science, along with high-quality learning resources.

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  • Statistics for Data Science
  • Math for Data Science
  • Statistics with Python
  • R and Statistics
  • Probability and Statistics
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Essential Mathematical Concepts for Data Science

Data scientists work in almost every industry and the one skill that unites them all is a solid understanding of mathematics. Whether they’re working on data analysis or implementing machine learning algorithms, maths is at the heart of all of them.

You will encounter these mathematical concepts in your data science career frequently.

We assume you do not have any background in mathematics.

Let's explore how much maths is required and the essential maths concepts you need to learn.


Arithmetic

Arithmetic is at the base of mathematics you need for data science and everything else. It is the simple study of numbers like addition, subtraction, multiplication, and division.

Make sure that you understand how a binary search algorithm uses logarithms to search faster. We can use binary search for debugging, and it's also helpful for the version controlling system.


Linear Algebra

Linear algebra is the study of vectors and linear functions.

  • Vectors are things you can add
  • Linear functions are functions of vectors that respect vector addition

Linear algebra takes arithmetic and supercharges it for the applications of data science such as image recognition, text analysis and also dimensionality reduction.

All data scientists should have a solid grasp of Linear algebra. It is the foremost topic of data science because machine learning often uses matrices to represent the data being analyzed.

Most data science interviewers test your matrix algebra and eigenvalues knowledge. Matrix algebra powers recommendation engines, like music recommendations on Spotify, friends suggestions on Facebook and product recommendations system on Amazon.

You don’t need to develop a high-level familiarity, but understanding of the principles is important because Linear algebra is an effective tool for implementing machine learning optimization.

Here are the important topics you need to be acquainted with for basic mathematical programming techniques.

  • Linear Systems and Gaussian Elimination
  • Vector and Spaces
  • Matrix Algebra
  • Transpose of a matrix
  • Inverse of a matrix
  • Trace of a matrix
  • Matrix Factorization
  • Dot product
  • Single Value Decomposition
  • Determinant and Eigens
  • Eigenvalues
  • Eigenvectors
  • Diagonalization

Learning algebra is hard and it can also be annoying to find the learning resources in the context of data science. Here are some of the best resources for learning Linear Algebra for data science.


Calculus

The calculus is an integral part of machine learning, used essentially for optimization techniques.

For data science, you only need to learn the basics of Differential and Integral Calculus, including functions, limits and continuity.

Data Science is the growing career and the knowledge of calculus plays a crucial role in many machine learning algorithms.

Calculus is essential for neural net and algorithms to increase their accuracy and performance.

The lack of knowledge of calculus will be an obstacle for many data science job roles and you must gain the basic familiarity important concepts for machine learning algorithms, such as gradient descent algorithm and backpropagation.

Calculus is far from being the hardest when compared to linear algebra. Here are the fundamental concepts you need to learn:

  • Limits
  • Differential Calculus
  • Integral Calculus
  • Multivariable Calculus

For most data science job roles, it’s only important to understand the basic principles of calculus, and how they affect your models. Here are some of the best resources to learn calculus for data science.


How Much Math Do You Need to Learn for Data Science

Data Science is an intimidating subject and Learning Mathematics for Data Science on your own can be a daunting experience.

Math is not always the requirement for data scientists, but we really need it for machine learning algorithms and deep learning models.

A degree in mathematics is helpful—but not required. All you need is an online course or a book that provides a mathematical foundation in the context of data science.

The advancing of machine learning algorithms through math can be difficult. We recommend learning the basics of Linear algebra and calculus, but first you should be intimately familiar with statistics for data science.

As a data science aspirant, it’s important to keep in mind that the mathematical statistics is very crucial for building efficient and reliable machine learning models. You should therefore devote adequate time to study the mathematical theory behind common machine learning algorithms.

There are countless online courses that will teach you the math skills for data science. We have done the heavy lifting for you and compiled the high-quality learning resources (books and courses) from experienced instructors and notable data science educators.


Math for Data Science Books

Whether you’re a complete novice or an experienced programmer, we have compiled the best referential math books that will suit both newcomers and veterans alike who are looking to improve their understanding of data science.


Math for Data Science Courses

These Math Courses will edify you with the core skills that you need as a data scientist for machine learning.

Note: These courses are not in any order.

1. Linear Algebra for Data Science in R

In this course, you’ll learn to work with vectors and matrices, solve matrix-vector equations, understand perform eigenvalue/eigenvector analyses, and use principal component analysis.

This course is created by Eric Eager, who is a Data Scientist at Pro Football Focus.
Algebra for Data Science
Image by DataCamp

Is it right for you?

This course is suitable for learners with a background in R programming and knowledge of high-school-level mathematics.

By the end, you will have an advanced familiarity with Linear algebra used in data science.


2. Linear Algebra For Machine Learning

This course teaches the linear algebra concepts behind machine learning systems like neural networks and training deep learning models.

Deep learning is one the most requested data science skills, and this course is excellent for learning the key ideas to understand linear systems and apply concepts to machine learning techniques.

Linear Algebra for Data Science
Image by Dataquest

Is it right for you?

This is an excellent course to learn linear algebra topics essential for data science.

You will learn Matrix Algebra calculus fundamentals for data science and machine learning.

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3. Introduction to Calculus

This course is excellent for learning to develop and practice methods of differential calculus with applications and integral calculus.

This course, designed by The University of Sydney, emphasises the key ideas of precalculus and the historical motivation for calculus.
Calculus for Data Science
Image by Coursera

Is it right for you?

This intermediate-level course is perfect for learning the threshold concepts in foundational mathematics

By the end, you will have advanced familiarity with the applications of mathematics in engineering, science and business.


4. Matrix Methods

In this course, you will learn the basics of Matrix Methods, matrix-matrix multiplication, solving linear equations, orthogonality, and more.

This course is designed by The University of Minnesota and delivered via Coursera.
Data Science Math Course
Image by Coursera

Is it right for you?

This course assumes basic knowledge of high-school level maths and Python programming.

By the end, you will become highly prepared for learning advanced data science courses.

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GO TO — Matrix Methods

5. Data Science Math Skills

Duke University designed this course to equip learners with the basic math knowledge required to be successful in advanced data science courses.

This course is excellent for learners who have basic math skills but may not have taken algebra or pre-calculus.

Data Science Math Skills
Image by Coursera

Is it right for you?

If you want to learn the math that data science is built upon, then this beginner-level course will enlighten you with no extra complexity.

By the end, you will gain familiarity with the unfamiliar ideas and gain skills in Bayes’ Theorem, Bayesian Probability, Probability and Probability Theory.


6. Matrix Algebra for Engineers

This course aims to equip learners with sufficient mathematical maturity and problem-solving skills.

This course is offered by The Hong Kong University of Science and Technology and delivered via Coursera.
Mathematics for Data Science
Image by Coursera

Is it right for you?

This course is suitable for intermediate-level learners who want to understand the basics of matrix algebra.

By the end, you will have gained a solid understanding of matrices, systems of Linear Equations, Vector Spaces, Eigenvalues and eigenvectors.


7. Calculus: Single Variable ( 5-Parts )

This course series is designed by The University of Pennsylvania and delivered via Coursera.

Through a series of lectures, you’ll dig much deeper to understand Single Variable Calculus and functions, differentiation, integration, and applications.

Math for Data Science
Image by Coursera

Is it right for you?

This series is suitable for learners with high-school level knowledge of mathematics.

After the successful completion of this course, you’ll become highly prepared to take advanced mathematics and data science courses.


8. Differential Equations for Engineers

This course is excellent for learning about differential equations, both basic theory and applications.

This course is designed by The Hong Kong University of Science and Technology, and taught by Professor Jeffrey R. Chasnov.
Mathematics for Data Science
Image by Coursera

Is it right for you?

This course is suitable for intermediate learners and learners aspiring to work as Data Scientists.

By the end, you will have an advanced familiarity with Ordinary Differential Equation, Partial Differential Equation (PDE), and Engineering Mathematics.


Extra Helpful Courses


9. Game Theory

This course aims to solidify learners' understanding of game theory and the mathematical modeling of strategic interaction among rational and irrational agents.

This high-rated course is designed by Stanford University and The University of British Colombia and delivered via Coursera.
Math for Data Science
Image by Coursera

Is it right for you?

This beginner-level course is suitable for anyone and if you have a basic knowledge of maths, then you’ll surely get ahead faster.

By the end, you’ll have a good understanding of Game Theory, Backward Induction, Bayesian Game, and Problem Solving.

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GO TO — Game Theory

10. Introduction to Mathematical Thinking

This course will edify you with the lifelong skills to solve all the real-world, science and even mathematical problems.

This brisk course is designed by Stanford University to equip learners with the cognitive skills to think the way professional mathematicians do.
Math for Data Science Course
Image by Coursera

Is it right for you?

This intermediate-level course assumes a background in maths, at least of high school level.

By the end, you will have gained advanced familiarity in Number Theory and Real Analysis.


11. Introduction to Logic

This is another high-rated course from Stanford University that aims to provide a thorough introduction to logic from a computational perspective

You will learn to encode information in logical sentences and understand logic technology and its applications in mathematics, science, engineering, and more.

Math for Data Science Courses
Image by Coursera

Is it right for you?

This course is suitable for intermediate level learners who have a basic understanding of computational mathematics.

By the end, you will be equipped with skills in Relational Algebra, Problem Solving, Propositional Calculus and Mathematical Logic.

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12. Game Theory II: Advanced Applications

You will learn the design interactions between agents and understand social choice theory, mechanism design, and auctions.

This course is designed by The University of British Columbia and Stanford University.
Data Science Math Courses
Image by Coursera

Is it right for you?

This advanced course is suitable for learners with college-level knowledge in mathematics.

By the end of this course, you will have become highly prepared for working on data science projects.


Conclusion

Data is a powerful resource and most Fortune 500 companies are still pushing for harnessing the power of data science and machine learning.

The field of data science is growing and market experts expect a lot of advancements in the future, pay the way for the high demands of skilled data scientists. Hope this article helped you to learn about the essential mathematics for data science that can help you start a career as a data scientist.

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Notable Mention

We strongly recommend 3blue1brown’s channel on YouTube.

It's simply good to learn algebra and calculus.
Linear Algebra
Calculus