7 Steps to Mastering Math for Data Science

Image by Author | Created on Canva

Learning data science has become more accessible, thanks to all the free and high-quality resources out there. So if you are interested, you can teach yourself data science—learning and practicing—for free.

Learning programming languages and other tools and libraries can be simple. But you need to learn math foundations for data science as well. And this can be quite daunting if you do not come from a math or computer science background. But it's still doable.

Having a guide to help you go about learning math for data science can make things simpler. That is why we put together this guide to help you learn math for data science. Let's get started.

Step 1: Review Your Foundations in Algebra

It’s always easy to start with what you know. So start by reviewing the basics of algebra (which you should already be familiar with from school math).

You can review how to solve systems of equations, solve for unknowns, and graph functions.

What to Focus On

• Linear equations and inequalities: Learn how to solve equations with one or more variables and interpret the solutions.
• Functions and graphs: Understand different types of functions and how to graph them.
• Polynomials: Work with polynomial functions, which are used in various regression models to fit data points.
• Matrices and vectors: These are key in performing operations on datasets, especially in high-dimensional data. You can learn more when you focus on linear algebra.

Resources

• Data Science Math Skills | Coursera
• Algebra I | MIT OpenCourseWare

Step 2: Learn the Fundamentals of Calculus

Calculus is another important math tools for data science. It is essential for understanding data changes over time, modeling continuous data, and in optimization algorithms.

You should learn to differentiate a function with respect to one or more variables. Integration will come in handy when you learn probability and random variables—to find areas under curves—representing cumulative distribution functions or probability densities.

 What to Focus On

• Limits and continuity: Understand the concept of limits and continuity, and how they are used to understand the behavior of functions as inputs approach certain values.
• Differentiation: Learn how to calculate and interpret derivatives, which represent rates of change.
• Multivariable calculus: Expand your knowledge to functions with more than one variable, crucial for understanding complex models that involve multiple inputs.
• Integration: Understand the process of integration and how it’s used to calculate areas under curves.

Resources

• Calculus I: Single Variable Calculus | MIT OpenCourseWare
• Multivariable Calculus | MIT OpenCourseWare

Step 3: Get Comfortable with Linear Algebra

Linear algebra is integral to many algorithms in data science, including those used for dimensionality reduction (like PCA), data transformation, and more.

It provides the mathematical framework to work with datasets that have many dimensions and helps in the efficient storage and manipulation of data in high-dimensional spaces.

What to Focus On

• Vectors and vector spaces: Learn how to work with vectors, which are essential for representing data in high dimensions. Understanding vector spaces is necessary for data transformations and machine learning algorithms.
• Matrix operations: Master operations like matrix multiplication, inversion, and finding determinants, which are foundational for many machine learning models, especially in handling data transformations and multivariate analysis.
• Linear transformations: Understand how linear transformations are used to map data from one space to another.
• Eigenvalues and eigenvectors: Understanding eigen decomposition of square matrices and its significance. Especially in algorithms that reduce data dimensionality or extract features.

Resources

• 3blue1brown – Linear Algebra
• Linear Algebra | MIT OpenCourseWare

Step 4: Learn Discrete Math

You should take a (short) course in discrete math if you want to teach yourself computer science and data science.

It is particularly important in areas such as graph theory, cryptography, and combinatorial optimization. Discrete math helps you understand and solve problems in databases, computer algorithms, and network analysis.

What to Focus On

• Set theory: Learn the fundamentals of sets, including operations like union, intersection, and difference. Set theory is essential for understanding logic, functions, and relations in databases and algorithms.
• Combinatorics: Study techniques for counting, permutations, and combinations. This will be helpful in probability and algorithm analysis.
• Graph theory: Understand the properties of graphs (networks) and how they are used to model relationships between entities.
• Boolean algebra: Explore the basics of Boolean logic, which is foundational for designing and understanding algorithms, especially in decision-making processes.

Resources

• Mathematics for Computer Science | MIT OpenCourseWare
• Introduction to Discrete Mathematics for Computer Science | Coursera

Step 5: Learn Probability and Statistics

Probability and statistics allow you to make informed decisions based on data, model uncertainties, and test hypotheses. They are helpful foundational tools for predictive modeling, risk assessment, and data interpretation in data science.

From building probabilistic models to understanding data distributions, a strong grasp of these concepts is, therefore, essential.

What to Focus On

• Probability theory: Learn about the basics of probability, including conditional probability, Bayes' theorem, and independence.
• Random variables and probability distributions: Understand how different types of random variables (discrete and continuous) behave and how to model them using probability distributions such as Normal, Binomial, and Poisson distributions.
• Descriptive and inferential statistics: Master techniques for summarizing data (mean, median, mode, variance) and making inferences about populations based on sample data.
• Hypothesis testing: Learn how to perform and interpret hypothesis tests, which are used to make data-driven decisions by evaluating the evidence against a null hypothesis.

Resources

• Statistics with Python | Coursera
• Probability | Khan Academy

Step 6: Explore Optimization Techniques

You’ll run into optimization problems when working with machine learning algorithms and statistical models. Whether it’s finding the best parameters for a model or minimizing error rates, understanding optimization techniques allows you to improve the performance and efficiency of your models. As you work through optimization, you'll realize that you need to be comfortable with calculus and linear algebra.

What to Focus On

• Linear programming: Learn how to optimize linear functions subject to constraints.
• Gradient descent: Learn this fundamental optimization algorithm used to minimize loss functions in machine learning and deep learning models.
• Convex optimization: Understand the properties of convex functions and how you can formulate certain optimization problems to simplify.
• Constrained and unconstrained optimization: Learn the difference between optimization problems with and without constraints and how to solve them using appropriate algorithms.

Resources

• Convex Optimization | StanfordOnline
• Introduction to Convex Optimization | MIT OpenCourseWare

Step 7: Embrace Just-In-Time Learning

 
We’ve gone over the different math topics you need to know for data science. But you’ve also probably realized that it is not possible to become proficient in every math concept upfront. Once you’ve gained some foundational knowledge, you can learn the other concepts—just-in-time—as needed.

When faced with a specific problem, identify the mathematical techniques needed to solve it—whether it's a statistical method, optimization algorithm, or a matrix transformation—and learn those concepts on the fly.

Wrapping Up

And that’s a wrap!

I hope you find this guide on learning math for data science helpful. As mentioned, the list of everything you need to know seems super long. But you can always learn all the math you need when you’re working on a project.

Happy learning!
 
 

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.