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As a data professional, you probably know that mathematics is fundamental to data science. Mathematics underpins data science: from understanding how data points are represented as vectors in a vector space to optimization algorithms that find the best parameters for a model and more.

Getting the hang of math fundamentals, therefore, can help you both in interviews and to get a deeper understanding of the algorithms that you implement. Here, we’ve compiled a list of free courses from Massachusetts Institute of Technology (MIT) on the following math topics:

- Linear algebra
- Calculus
- Statistics
- Probability

You can take these courses on the MIT OpenCourseWare platform. So make the most out of these courses and level up your data science expertise!

## 1. Linear Algebra

Besides being comfortable with high school math, linear algebra is by far the most important math topic for data science. The super popular Linear Algebra course by Prof. Gilbert Strang is one of the best math classes courses you can take. For this course and for the courses that follow, solve problem sets and attempt exams to test your understanding.

The course is structured into the following three main modules:

- Systems of equations Ax = b and the four matrix subspaces
- Least squares, determinants, and eigenvalues
- Positive definite matrices and applications

**Link**: Linear Algebra

## 2. Single Variable and Multivariable Calculus

A good understanding of calculus is important to become proficient with data science concepts. You should be comfortable with both single variable and multivariable calculus computing, derivatives partial derivatives, applying chain rule, and more. Here are two courses on single variable and multivariable calculus.

The Calculus I: Single Variable Calculus course covers:

- Differentiation
- Integration
- Coordinate systems and infinite series

Once you feel comfortable with single variable calculus, you can proceed to the Multivariable Calculus course that covers:

- Vectors and matrices
- Partial derivatives
- Double integrals and line integrals in the plane
- Triple integrals and surface integrals in 3D space

**Links to the courses**:

## 3. Probabilistic Systems Analysis and Applied Probability

Probability is yet another important math topic for data science, and a good foundation in probability is essential to ace mathematical modeling and statistical analysis and inference.

The Probabilistic Systems Analysis and Applied Probability course is a great resource that covers the following topics:

- Probability models and axioms
- Conditioning and Bayes rule
- Independence
- Counting
- Discrete and continuous random variables
- Continuous Bayes rule

**Link**: Probabilistic Systems Analysis and Applied Probability

## 4. Statistics for Applications

To become proficient in data science, you should have a good foundation in statistics. The Statistics for Applications course covers a lot of applied statistics concepts relevant in data science.

Here’s a list of topic covered:

- Parametric inference
- Maximum likelihood estimation
- Moments
- Hypothesis testing
- Goodness of fit
- Regression
- Bayesian statistics
- Principal component analysis
- Generalized linear models

If you are interested in exploring statistics in depth, check out 5 Free Courses to Master Statistics for Data Science.

**Link**: Statistics for Applications

## 5. Matrix Calculus for Machine Learning and Beyond

You should already be familiar with optimization from the courses on single and multivariable calculus. But in machine learning, you may run into large-scale optimization requiring matrix calculus and calculus on arbitrary vector spaces.

The Matrix Calculus for Machine Learning and Beyond will help you build on what you’ve learned in the linear algebra and calculus courses. This is, perhaps, the most advanced course on this list. But it can be very helpful if you plan on doing a graduate course in data science or would like to explore machine learning and research.

The following are some of the topics covered in this course:

- Derivatives as linear operators; linear approximations on arbitrary vectors space
- Derivatives of functions with matrix as input or output
- Derivatives of matrix factorizations
- Multi-dimensional chain rule
- Forward and reverse-mode manual an automatic differentiation

There are many other approximations and optimization algorithms you can explore too.

**Link**: Matrix Calculus for Machine Learning and Beyond

## Wrapping Up

If you ever want to master math for data science, this list of courses should suffice to learn everything you’d ever need—be it getting into machine learning research or an advanced degree in data science.

If you’re looking for a few more courses to learn math for data science, read 5 Free Courses to Master Math for Data Science.

** Bala Priya C** is a developer and technical writer from India. She likes working at the intersection of math, programming, data science, and content creation. Her areas of interest and expertise include DevOps, data science, and natural language processing. She enjoys reading, writing, coding, and coffee! Currently, she’s working on learning and sharing her knowledge with the developer community by authoring tutorials, how-to guides, opinion pieces, and more. Bala also creates engaging resource overviews and coding tutorials.

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