David M. Bressoud

Some identities for terminating q-series

We present the following sequence of polynomial identities: is the Gaussian polynomial denned to be zero for m m > N , one for m = 0 or N and

A generalization of the Rogers-Ramanujan identities for all moduli

Abstract The Rogers-Ramanujan identities have been extended to odd moduli by B. Gordon and to moduli of the form 4 k + 2 by G. Andrews. We demonstrate and prove an extension to all even moduli, and provide a theorem which holds for all moduli.

Change of base in bailey pairs

Versions of Baileys lemma which change the base from q to q2 or q3 are given. Iterates of these versions give many new versions of multisum Rogers-Ramanujan identities.

The calculus student: insights from the Mathematical Association of America national study

In fall 2010, the Mathematical Association of America undertook the first large-scale study of postsecondary Calculus I instruction in the United States, employing multiple instruments. This report describes this study, the background of the students who take calculus and changes from the start to the end of the course in student attitudes towards mathematics and intention to continue in mathematics.

Extension of the partition sieve

Abstract We demonstrate the correspondence which lies behind certain partition identities used by Andrews in his partition sieve. This leads to an extension of his methods and a generalization of his results.

An easy proof of the Rogers-Ramanujan identities

Abstract A proof of the Rogers-Ramanujan identities is presented which is brief, elementary, and well motivated; the “easy” proof of whose existence Hardy and Wright had despaired. A multisum generalization of the Rogers-Ramanujan identities is shown to be a simple consequence of this proof.

Identities in combinatorics III: Further aspects of ordered set sorting

Given two multi-sets of non-negative integers, we define a measure of their common values called the crossing number and then use this concept to provide a combinatorial interpretation of the q-Hahn polynomials and combinatorial proofs of the q-analogs of the Pfaff-Saalschutz summation and the Sheppard transformation.

Linearization and Related Formulas for q-Ultraspherical Polynomials

A new proof is given for Rogers’ linearization formula for the q-ultraspherical polynomials. This proof leads to several new formulas relating q-ultraspherical polynomials. The principal result yields the following formula for the ultraspherical polynomials,

Generalized Rogers-Ramanujan bijections

C_n^\lambda (x)

The impact of instructor pedagogy on college calculus students’ attitude toward mathematics

, when q approaches 1: \[ \left( {1 - 2rx + r^2 } \right)^{ - \lambda } \left( {1 - 2sx + s^2 } \right)^{ - \lambda } = \sum_{m,n = 0}^\infty {\left( {\begin{array}{*{20}c} {m + n} \\ n \\ \end{array} } \right)} \frac{{\Gamma (\lambda + m)\Gamma (\lambda + n)}}{{\Gamma (\lambda )\Gamma (\lambda + m + n)}}r^m s^n {}_2 F_1 \left[ {\begin{array}{*{20}c} {\lambda ,2\lambda + m + n} \\ {\lambda + m + n + 1} \\ \end{array} ;rs} \right]C_{m + n}^\lambda (x).\]