Graph sparsification is the approximation of an arbitrary graph by a sparse graph. We explain what it means for one graph to be a spectral approximation of another and review the development of ...

Linear functions are used to model a broad range of real-world problems. The ability to solve linear equations and inequalities is an essential skill for analysing these models. This section covers ...

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 ...

Linear systems are the building blocks of countless real-world phenomena, from engineering to economics. This project explores the elegant methods used to solve these systems. The Gauss method is ...

Transforms a matrix into row echelon form (or reduced row echelon form) by applying a sequence of row operations, making it easier to solve for unknowns using backward substitution. Steps: Forward ...

Often it is necessary to look at several functions of the same independent variable. Consider the prior example where x, the number of items produced and sold, was the independent variable in three ...

Abstract: The line search has undergone numerous important improvements throughout the years, with many researchers concentrating on offering and developing developments that are suitable techniques ...