Editorial for the special issue on software support for teaching discrete mathematics
Valerie J. Harvey, Susan H. Rodger · Journal on Educational Resources in Computing · 2005
Discrete mathematics is routinely supported in certain programs beyond mathematics (as discrete mathematics or symbolic logic) and philosophy (as introductory logic or symbolic logic).Teaching discrete mathematics, which provides the basis for formal methods, is traditional in computer science (CS) and software engineering (SE), and is specified by the Accreditation Board for Engineering and Technology (ABET) computing accreditation criteria.In the September 2003 issue of Communications of the ACM, K. Devlin [Devlin 2003.],K. Bruce et al. [Bruce et al. 2003], and P. Henderson [Henderson 2003] all found that the form of mathematics of particular value to computer scientists and software engineers is discrete mathematics.The report of the ITICSE 2000 Working Group on Formal Methods in Education cites the role of discrete mathematics in formal methods and asserts that "without formal methods, the [software] engineering is non-existent or suspect" [Almstrum et al. 2000].This issue of JERIC covers a range of software support for teaching discrete mathematics, from fundamental presentations of logic, specification, and proofs, as proposed by John Cigas and Wen-Jun Hsin in reporting on the use of puzzles, to the teaching of advanced computer science with the Java program-verification tool reported on by Timothy Gegg-Harrison, and the techniques and resources described by Sutner for CDM, involving Mathematica and other tools.The need for software support begins with individual tools that can be used to teach, among other topics, logic, sets, and graphs, and proceeds to complex systems.To be useful, the most ambitious projects such as CSDM and program verification require complex systems.And, as Sutner points out (in the section of his article entitled "Afterlife"), for complex environments, it is necessary to provide for subsequent access to the material, for the problems of replicating the libraries, and for the computational behavior of a given system's computational context after a period of time.For the theory of computing, Ross describes a hypertextbook (in progress) which currently covers many topics in automata theory, including finite automata, regular expressions, regular grammars, context-free grammars, and parsing.The hypertextbook is built around Web technologies such as text, sound, pictures, slide shows, video, and active learning models.The idea is to allow students to experiment with concepts as they read the material.There have been various projects of this type, and they obviously