Akalu Tefera

MultInt, a MAPLE Package for Multiple Integration by the WZ Method

We describe a MAPLE implementation, MultInt, of the continuous version of the WZ method. We also give various examples of how this package can be used to systematically generate proofs of identities (or recurrences) which involve multiple integrals of proper-hyperexponential functions. Moreover, by expressing a binomial coefficient sum as a hyperexponential contour or multi-contour integral, the package provides an alternative approach to sums.

Summation identities for representation of certain real numbers

We present identities used to represent real numbers of the form xum±yvn for appropriately chosen real numbers x, y, u, v and nonnegative integers m and n. We present the proofs of the identities by applying Zeilbergers algorithm.

A Wilf-Zeilberger Approach to Sums of Choi, Zörnig and Rathie

Abstract In this paper we present elegant and elementary proofs of identities that involve sums of the type in the title using Zeilbergers algorithm and the Wilf-Zeilberger proof style.

A NEW COMBINATORIAL IDENTITY

We prove a combinatorial identity which arose from considering the relation rp (x, y,z) = (x + y − z) p − (x p + y p − z p ) in connection with Fermats last theorem.

Freshman rules in calculus

In this note we present a class of functions (f, g) that satisfy ‘freshman rules’ in calculus.

ENHANCING CORE MATHEMATICS COURSES

ABSTRACT The Departments of Mathematics and Statistics at Grand Valley State University are engaged in a project to address the mathematical preparation of all its majors, including prospective elementary and secondary mathematics teachers. In this article, we describe how the mathematics and mathematics education faculty in our mathematics department formed a partnership and worked together to change two (Modern Algebra and Discrete Structures) of the six core mathematics courses that all mathematics majors take in order to make them more relevant for prospective teachers while at the same time maintaining core content and rigor for all majors. In particular, we have used the NSF-supported K-12 curricula projects and NCTM Standards-based materials as a foundation to create college-level mathematics activities. By using activities that incorporate and expand upon these K-12 materials, all majors are reminded of where they have encountered core mathematical concepts in previous courses, concepts are made more relevant as they are set in real-world or concrete settings, and prospective teachers are more motivated to learn the mathematics as they see how their coursework relates to the mathematics they will teach.

A NEW TRIPLE SUM COMBINATORIAL IDENTITY

(2.8)We now equate (2.4) and (2.8), removing the common summation terms, which givesthe identity.Remark 2.1. By using Wegschaider’s MultiSum, a computer algebra package whichis available from http://www.risc.uni-linz.ac.at/research/combinat/risc/software/,we found recurrence equations satisfied by the summand of our identity but we couldnot use them to give a short proof for our identity.References