In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a ...

Learning calculus can be a daunting task for many students. As one of the most important areas of mathematics, calculus is ...

Among other things, the course includes elementary linear algebra, the solution of equation systems, the theory of functions of several variables ... models formulate linear models in a compact ...

Our physics expert picks his top-five equations, plus a scheme to supply US power needs with a bucket of baseballs. Thanks, Einstein!

What you think is important, but what you do matters more. This simple formula describes the best way to change your ...

Executive function describes a set of cognitive processes and mental skills that help an individual plan, monitor, and successfully execute their goals. The “executive functions,” as they’re ...

The gradient of the determinant is ∇(det A) = det(A)A⁻ᵀ (course notes chapter 7) an amazing trick by Mathias (1996): f([A dA; 0I A]) = [f(A) f′(A)[dA]; 0I f(A)] (in Julia notation) for any ...

This course is a continuation of high school calculus, but goes deeper into the theoretical foundations and develops the methods further in order to deal with more complicated cases. The course also ...

We are a research team at Columbia University in the City of New York. Our Principal Investigator is Renata M. Wentzcovitch. Our research is devoted to computational quantum mechanical studies of ...