Let Q be an n x n symmetric matrix with integral entries and with det Q ≠ O, but not necesarily positive definite. We describe a generalized LLL algorithm to reduce this quadratic form. This algorithm ...

Some equations have letters on each side of the equals sign, for example: \(4(k + 7) = 12k - 4\). Solve this equation by rearranging all the letters onto one side of the equation and all numbers onto ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

Description There are five main sections: Algebra (vectors, complex numbers, matrices as transformations, solving equations using matrices, eigenvalues and eigenvectors); Analysis (Sequences, series, ...

Description There are five main sections: Algebra (vectors, complex numbers, matrices as transformations, solving equations using matrices, eigenvalues and eigenvectors); Analysis (Sequences, series, ...

Luis Caffarelli has won the 2023 Abel prize, unofficially called the Nobel prize for mathematics, for his work on a class of equations that describe many real-world physical systems, from melting ice ...