Maths courses

Linear algebra is pervasive in just about all modern scientific subjects, including physics, mathematics, computer science, electrical engineering, economics, and aeronautical engineering. You’ll learn about its applications in computer graphics, si...

Random variables and their distributions are the best tools we have for quantifying and understanding unpredictability. This course covers their essential concepts as well as a range of topics aimed to help you master the...

Problem solving requires creativity, intuition, knowledge, and skill. It also requires practice. This course dives deep into four mathematical explorations, each of which quickly goes beyond 'rote' learning, challenging you to explore patterns an...

Statistics starts from data and then asks what was used to generate it. Learning the building blocks — median, mode, range, variance, and standard deviation — will help you analyze graphs, determine statistical significance, and...

Drum vibrations, heat flow, the quantum nature of matter, and the dynamics of competing species are just a few real-world examples involving advanced differential equations. These models and many others from across the sciences, engineering,...

Reckoning with infinity is one of the major accomplishments of mathematics. Start with basic counting and work your way up to the many types of infinity, culminating in the profundity of Cantor's theorem. Explore the...

How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate...

Explore the fundamental concepts of three-dimensional geometry: What strangely-shaped 3D pieces can result from slicing up 3D polyhedra with planes? What flat polygons can fold up into 3D shapes? If you're running around on the...

Where will a cannonball land after firing? How does a harmonograph create art? How can logarithm scales help us represent the universe? Through motivating questions and interactive graphing, you’ll learn pre-calculus without relying on memorizatio...

Explore how algebra works and why it matters, and build a strong foundation of skills across many algebra topics including equations, rates, ratios, and sequences. By the end of this course, you’ll know both traditional...

This course is for those who want to fully master Algebra with complex numbers at an advanced level. The prize at the end will be combining your newfound Algebra skills in trigonometry and using complex...

We make many day-to-day decisions without seeing the big picture. Sometimes things turn out in our favor, sometimes not. Scientists, engineers, and other technically-minded people also make judgments using limited information. However, their field...

Linear algebra plays a crucial role in many branches of applied science and pure mathematics. This course covers the core ideas of linear algebra and provides a solid foundation for future learning. Using geometric intuition...

Our math journey starts with fractions, percents, and ratios in everyday contexts. Interactive problems and intuitive visuals will help you see numeric quantities and their relationships in a new light. By revisiting topics ranging from...

In this unit, we will learn about the fundamentals of differential calculus and why they are important for data science. First, we will analyze functions using the concepts of limits and derivatives. After a conceptual...

Use diagrams and words to explore the very start of algebra, with puzzles and intuition guiding the way. By the end of the course, you'll be able to simplify expressions and solve equations using methods...

This course covers a wide range of theorems in classical Euclidean geometry. You'll start by deriving the Central Angle Theorem and Thales' Theorem, then move on to the Power of a Point Theorem, and conclude...

Via intriguing problems and competition-style practice, we’ll guide you through your training from start to finish. Improve your speed and accuracy while gaining an appreciation for how fun math can be. Upon completion, you’ll have...

Change is an essential part of our world, and calculus helps us quantify it. The change that most interests us happens in systems with more than one variable: weather depends on time of year and...

Calculus has such a wide scope and depth of application that it's easy to lose sight of the forest for the trees. This course takes a bird's-eye view, using visual and physical intuition to present...