Author: Sanjay Goel, http://in.linkedin.com/in/sgoel
This is the fourth article in this 8 part series. The fifth part is
In the first decade, the computer science curriculum was lesser oriented towards business data processing needs. Interestingly, discrete structures and three courses in numerical methods were not considered as part of mathematics courses. Instead they were included as essential computer science courses. The ACM curriculum committee further suggested a minimum of six mathematics courses for undergraduate programs. The committee proposed essential inclusion of courses in related areas of mathematics, statistics, electrical engineering, philosophy, linguistics, industrial engineering, and management. Overspecialization at undergraduate level was discouraged by the committee, and it also encouraged the deep involvement of computer science faculty in computer applications. Scientific simulation and engineering calculation oriented applications encouraged to put a strong emphasis on numerical methods.
The strong emphasis on numerical methods decreased gradually through subsequent recommendations, and it was eliminated from the core in nearly all subsequent recommendations of the ACM, IEEE Computer society, as well as other bodies except International Federation of Information Processing (IFIP). Computing curricula  does not specify any minimum required weight of numerical techniques for any of the five computing discipline – computer science, computer engineering, information systems, software engineering, or information technology. It is not recommended even as an elective course for the later three disciplines.
On the other hand, discrete mathematics was increasingly being recognized as more central and fundamental for computer science than calculus [3-5]. There were proposals to teach discrete mathematics as the first mathematics course, and the model curriculum for liberal arts degree in computer science responded favorably [6-7]. In 2001, 76% faculty members are reported to have felt that discrete mathematics should be a prerequisite to data structures . However, many universities and institutions were slow to respond to this change. A survey  showed that even in late 1980s, nearly 30% universities and institutions in USA did not include discrete mathematics, and nearly 27% maintained numerical algorithms in the core curriculum of computer science.
Possibly because of IFIP influence, for quite some time, numerical techniques continued to be part of the core curriculum of many computing programs in India for some time. The current model curriculum recommended by the All India Council for Technical Education, India [10-11] has not included numerical mathematics as a core course for both the commonly offered undergraduate computing programs of engineering institutes: (1) computer science and engineering, (2) information technology. Unfortunately, discrete mathematics is excluded from the list of AICTE’s information technology curriculum.
Over the decades, with the advent of faster, cheaper, smaller, reliable, networked, and mobile hardware, as well as user friendly and multi-layered software, the computer applications have rapidly expanded much beyond the scope of computational science (numerical techniques, modeling and simulation, and operation research). Lethbridge [12-14] found that in the list of the most important twenty-five subject topics of the university curriculum, professional software engineers did not include a single topic of mathematic. Though computational science is recognized as an extremely valuable closely related discipline, the recommended core body of knowledge of computing curricula with specialization in computer science, computer engineering, software engineering, information systems, or information technology, do not include these courses any more [15-16].
Further, the ACM-AIS-IEEE joint report  has recommended a lowered minimum requirement for mathematical foundation for programs in software engineering, information systems, and information technology. ACM-IEEE joint curriculum recommendation on software engineering  has included only one topic of mathematics ‘discrete mathematics’ as part of the essential core. Recently, differentiating computer science from mathematics, Fant  argues that rather than computational issues, computer science is more concerned with issues related to creation and actualization of process expressions.
In my view, a strong foundation in calculus, differential equations, interpolation and approximation, linear algebra, probability, statistics, numerical methods, optimisation techniques, operation research, number theory, etc., certainly strengthens a student’s ability to design algorithms for a large variety of problems. However, traditional method of teaching mathematics that does not leverage students’ programming skills needs to be reviewed to make these courses more effective and relevant for students of software development. In my view, the teaching of these courses has to done with a very applied approach that necessarily includes good amount of programming work.
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 Karl M. Fant, Computer Science Reconsidered: The invocation models of process expression, John Wiley & Sons, USA, pp 1-10, 2007.