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 ...

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 ...

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 ...

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 ...

Randolph Grace receives funding from the Marsden Fund, administered by the Royal Society of New Zealand. University of Canterbury provides funding as a member of The Conversation AU. University of ...