CS Circles: An In-Browser Python Course for Beginners

Computer Science Circles is a free programming website for beginners that is designed to be fun, easy to use, and accessible to the broadest possible audience. We teach Python since it is simple yet powerful, and the course content is well-structured but written in plain language. The website has over one hundred exercises in thirty lesson pages, plus special features to help teachers support their students. It is available in both English and French. We discuss the philosophy behind the course and its design, we describe how it was implemented, and we give statistics on its use.Comment: To appear in SIGCSE 201

On the iteration of certain quadratic maps over GF(p)

AbstractWe consider the properties of certain graphs based on iteration of the quadratic maps x→x2 and x→x2−2 over a finite field GF(p)

Error Detection in Number-Theoretic and Algebraic Algorithms

CPU's are unreliable: at any point in a computation, a bit may be altered with some (small) probability. This probability may seem negligible, but for large calculations (i.e., months of CPU time), the likelihood of an error being introduced becomes increasingly significant. Relying on this fact, this thesis defines a statistical measure called robustness, and measures the robustness of several number-theoretic and algebraic algorithms. Consider an algorithm A that implements function f, such that f has range O and algorithm A has range O' where O⊆O'. That is, the algorithm may produce results which are not in the possible range of the function. Specifically, given an algorithm A and a function f, this thesis classifies the output of A into one of three categories: 1. Correct and feasible -- the algorithm computes the correct result, 2. Incorrect and feasible -- the algorithm computes an incorrect result and this output is in O, 3. Incorrect and infeasible -- the algorithm computes an incorrect result and output is in O'\O. Using probabilistic measures, we apply this classification scheme to quantify the robustness of algorithms for computing primality (i.e., the Lucas-Lehmer and Pepin tests), group order and quadratic residues. Moreover, we show that typically, there will be an "error threshold" above which the algorithm is unreliable (that is, it will rarely give the correct result)

Squares and overlaps in the Thue-Morse sequence and some variants

We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of 2) contains an overlap.http://www.numdam.org/item/ITA_2006__40_3_473_0

On the Iteration of Certain Quadratic Maps over GF(p)

We consider the properties of certain graphs based on iteration of the quadratic maps x ! x and x ! x 2 over a finite field GF(p)

Objective Scoring for Computing Competition Tasks

Computing competitions like the International Olympiad in Informatics (IOI) typically pose several problems that contestants are required to solve by writing a program. The program is tested automatically on several sets of input data to determine whether or not it computes the correct answer within specified time and memory limits. We consider the controversy of whether and how to award partial credit for programs that fail some of the tests. Using item response theory, we analyze the degree to which the scores from these automatic tests, separately and in various combinations, truly reflect the contestants ’ achievement.

Squares and overlaps in the Thue-Morse sequence and some variants

We consider the position and number of occurrences of squares in the Thue-Morse sequence, and show that the corresponding sequences are 2-regular. We also prove that changing any finite but nonzero number of bits in the Thue-Morse sequence creates an overlap, and any linear subsequence of the Thue-Morse sequence (except those corresponding to decimation by a power of 2) contains an overlap