Brilliant

Life is full of all sorts of risks, chances, and gambles. With this course, you'll learn to analyze probabilistic scenarios and optimize your chances to win probabilistic games. By the end of this course, you’ll...

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...

Probability is full of counter-intuitive results and paradoxes. Challenge yourself by learning how to mathematically master some very surprising games and experiments including the Monty Hall game show, the Boy or Girl paradox, and the...

Learn how to beat the house! Or, if that's not possible, at least learn how much of an edge they have. In this course, you'll analyze three specific casino games: blackjack, craps, and poker. And,...

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...

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...

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...

This course was written in collaboration with former quantitative traders from two leading firms. In this course, we'll dive into statistical modeling, matrices, and Markov chains, and guide you through the powerful mathematics and statistics...

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...

This course is here to guide you through the "magic", revealing the thought processes that lead to clever solutions to beautiful problems. You’ll become a better mathematical problem-solver across several exciting topics, including algebra, geometry...

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...

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...

This course will teach you all of the fundamentals of trigonometry, starting from square one: the basic idea of similar right triangles. In the first sequences in this course, you'll learn the definitions of the...

Calculus is the mathematical study of things that change: cars accelerating, planets moving around the sun, economies fluctuating. To study these changing quantities, a new set of tools - calculus - was developed in the...

In a sense, differential calculus is local: it focuses on aspects of a function near a given point, like its rate of change there. Integral calculus complements this by taking a more complete view of...

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...

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...

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...

Change is deeply rooted in the natural world. Fluids, electromagnetic fields, the orbits of planets, the motion of molecules; all are described by vectors and all have characteristics depending on where we look and when....

Differential equations show up in just about every branch of science, including classical mechanics, electromagnetism, circuit design, chemistry, biology, economics, and medicine. From analyzing the simple harmonic motion of a spring to looking at t...