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 ...

Partition functions, which enumerate the distinct ways a positive integer may be expressed as a sum of positive integers, have long captivated mathematicians due to their deep connections with number ...

Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...

For novices, functions are one of the most intimidating features of OpenOffice.org's Calc. Newcomers quickly learn that functions are a main feature of spreadsheets, but there are almost four hundred, ...

Concepts covered in this course include: standard functions and their graphs, limits, continuity, tangents, derivatives, the definite integral, and the fundamental theorem of calculus. Formulas for ...

A key part—though surely not the only part—of early-grades math is ensuring students get the basic arithmetic functions down and, beyond that, making sure they’re able to swiftly and automatically ...

All prerequisite courses must be passed with a grade of C- or better. For official course descriptions, please see the current CU-Boulder Catalog. MATH 3001 Analysis 1 Provides a rigorous treatment of ...

Scientists have developed and demonstrated the world's first programmable nanoprocessor. The groundbreaking prototype computer system represents a significant step forward in the complexity of ...