Sandra Fillebrown

Faster computation of Bernoulli numbers

Abstract Using the relationship between the Riemann zeta function and Bernoulli numbers, we develop an algorithm for the fast computation of Bernoulli numbers of high index. We present one algorithm to compute all Bernoulli numbers up to and including B 2 n , and a modified algorithm to compute B 2 n directly. We show that in both algorithms, all computations can be done using at most [2 n log 2 n ] bits and that the complexity of the first algorithm is O ( n 2 log n ) multiplications of numbers at most O ( n log n ) bits while that of the second is O ( n ) multiplications of numbers of at most O ( n log n ) bits.

Capstone: Why it Didn't Work for Us

Abstract Saint Josephs University, a small comprehensive university, implemented a one-credit capstone project for the mathematics major beginning in 2002. After expansion to three credits in 2007, the capstone, although successful, had unintended consequences. In 2010, for both programmatic and practical reasons, the department decided to remove the course from the program. This article describes that process and explains how the department met its program objectives through other means.

Courses on the Beauty of Mathematics: Our Version of General Education Mathematics Courses

Abstract This article describes various courses designed to incorporate mathematical proofs into courses for non-math and non-science majors. These courses, nicknamed “math beauty” courses, are designed to discuss one topic in-depth rather than to introduce many topics at a superficial level. A variety of courses, each requiring students to master mathematical proofs in the context of the field of study, is described briefly with details given for one.