Presburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose ...

Thus {f, g} represents the unordered pair of functions f and g. So will plot both f and g on the same graph. We don't care wich order it does them in so we can give f and g as an unordered pair.

Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly ...

Three hours of lecture/discussion per week. Algebraic operations on polynomials and rational functions as expressions, in equations, or inequalities. Graphing of linear and polynomial equations. An ...

Bernstein polynomial estimation provides a robust nonparametric technique for approximating both density and distribution functions. Based on the properties of Bernstein polynomials, which uniformly ...

The information presented here is intended to describe the course goals for current and prospective students as well as others who are interested in our courses. It is not intended to replace the ...

The mathematicians were trying to extend an illustrious result in their field, the Fundamental Theorem of Algebra. The astrophysicists were working on a fundamental problem in their field, the problem ...

A mathematician has solved a 200-year-old maths problem after figuring out a way to crack higher-degree polynomial equations without using radicals or irrational numbers. The method developed by ...

Long before robots could run or cars could drive themselves, mathematicians contemplated a simple mathematical question. They figured it out, then laid it to rest—with no way of knowing that the ...