Abstract.It is well known that Discrete Fourier Transform (DFT) techniques may be used to multiply large integers. We introduce the concept of Discrete Weighted Transforms (DWTs) which, in certain situations, substantially improve the speed of multiplication by obviating costly zero-padding of digits. In particular, when arithmetic is to be performed modulo Fermât Numbers 22"1 + 1 , or Mersenne Numbers 29 -1 , weighted transforms effectively reduce FFT run lengths. We indicate how these ideas can be applied to enhance known algorithms for general multiplication, division, and factorization oflarge integers.

We report the results of a year-long experiment in the use of robots to teach computer science. Our data set compares results from over 800 students on identical tests from both robotics and nonrobotics-based laboratory sessions. We also examine the effectiveness of robots in encouraging students to select computer science or computer engineering as a field of study. Our results are negative: test scores were lower in the robotics sections than in the nonrobotics ones, nor did the use of robots have any measurable effect on students' choice of discipline. We believe the most significant factor that accounts for this is the lack of a simulator for our robotics programming system. Students in robotics sections must run and debug their programs on robots during assigned lab times, and are therefore deprived of both reflective time and the rapid compile-run-debug cycle outside of class that is an important part of the learning process. We discuss this and other issues, and suggest directions for future work.

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We present one approach to teaching basic computer science concepts with robotics, using an Ada interface to Lego Mindstorms™ 1 . We show simple problems put to students with no programming experience, discuss the solutions, and for each concept explain the advantages of using robots to teach it.

This article presents an Ada interface to the Lego Mindstorms TM RCX "brick", the core element of a commercial product that emerged from a collaboration between the Lego Corporation and MIT's Media Laboratory. Since its arrival on the market in 1998, it has considerable interest in the computing community: a variety of operating systems and language interfaces are available for it, all provided free of charge by people who simply wanted to find out how the RCX workedThe interface described here is in use at the Air Force Academy as part of an experiment in computer science education. Students with no prior programming background are given a pre-built Mindstorms robot and a series of programming challenges, which they then attempt to implement using Ada. Our hope is that the experience of programming robots will provide an effective, efficient, and enjoyable method for conveying essential computer science concepts. We are currently attempting to assess its effectiveness, and hope to present our results at a future date.