Mathematicians have devised a new way to solve higher-order polynomial equations, ushering in a 'dramatic revision of a basic ...

In a recent advance, a multi-disciplinary team of researchers developed a machine learning framework that adapts to changes ...

This project explores and implements a wide range of classical and advanced techniques in the field of numerical analysis and differential equations, combining symbolic ... and interpretation of each ...

A mathematician has built an algebraic solution to an equation that was once believed impossible to solve. A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge ...

Diophantus of Alexandria revolutionized algebra with Arithmetica, pioneering symbolic notation and abstract number theory.

A mathematician has solved a 200-year-old maths problem after figuring out a way to crack higher-degree polynomial equations ...

Multi-language suite for high-performance solvers of differential equations and scientific machine learning (SciML) components. Ordinary differential equations (ODEs), stochastic differential ...

We study the classical linear partial differential equations: Poisson's equation and the heat equation. We learn about representation formulas for solutions, maximum principles, and energy estimates.

This important book explains how the technique of Witten Laplacians may be useful in statistical mechanics. It considers the problem of analyzing the decay of correlations, after presenting its origin ...