How I First Heard About Calculus

An attempt to motivate a class of engineering students leads to insights both personal and pedagogical

The Nature of Numbers: Real Computing

While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both the computable real numbers and his famous ``Turing machine\u27\u27. The final part of this paper describes the computable real numbers in enough detail to supplement the usual undergraduate real analysis class. An appendix presents programs that implement the examples in the text

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Argonne National Laboratory Reports

The effects of curvature on steady states of chemical catalytic reactions are investigated by studying the cases of the catalytic particle being a spherical or cylindrical shell. Existence and stability of solutions are studied. It is shown that the solutions converge to the solutions for the catalytic slab when the curvature goes to 0 in each case

Numerical Partial Differential Equations in Scheme

I worked with the students in my one-semester graduate course CS615 "Numerical methods for partial differential equations" at Purdue University to write a set of routines to use the finite element method to solve elliptic and parabolic partial di#erential equations (PDEs). We used hacked versions of gcc-2.95.1, the Gambit-C 3.0 Scheme system by Marc Feeley, and the Meroon object system by Christian Queinnec as our software tools. We developed and ran the code on a Compaq DS20 clone with two 500 MHz Alpha 21264 processors and two GB of memory running RedHat 6.0. Our system performance is competitive with similar systems written in C or Fortran. The URL is http://www.math.purdue.edu/~lucier/615. We discuss the process of developing the software in this paper