Why is computing competence important?

First of all, we need to define the term computing and what it contains.

Definition of computing. Computing means in this document solving scientific using computers. It covers numerical as well as symbolic computing. Computing is also about developing an understanding of the scientific process by enhancing the algorithmic thinking when solving problems.

Computing competence has always been a central part of the science and engineering education. Traditionally, such competence meant mastering mathematical methods to solve science problems - by pen and paper. In 2015, our candidates are expected to use all available tools to solve scientific problems; computers primarily, but also pen and paper. Below, we use the term algorithms in the broad meaning: mathematical methods to solve science problems, with and without computers.

Computing competence is about

derivation, verification, and implementation of algorithms
understanding what can go wrong with algorithms
overview of important, known algorithms
understanding how algorithms are used to solve mathematical problems
reproducible science and ethics
algorithmic thinking for gaining deeper insights about scientific problems

Algorithms involving pen and paper are traditionally aimed at what we often refer to as continuous models. Application of computers calls for approximate discrete models. Much of the development of methods for continuous models are now being replaced by methods for discrete models in science and industry, simply because much larger problem classes can be addressed with discrete models, often also by simpler and more generic methodologies. However, verification of algorithms and understanding their limitations requires much of the classical knowledge about continuous models.

So, why should basic university education undergo a shift from classical mathematics to modern computing?

The impact of the computer on mathematics is tremendous: science and industry now rely on solving mathematical problems through computing.
Computing increases the relevance in education by solving more realistic problems earlier.
Computing through programming is excellent training of creativity.
Computing enhances the understanding of abstractions and generalization.
Computing decreases the need for special tricks and tedious algebra, and shifts the focus to problem definition, visualization, and "what if" discussions.

The result is a deeper understanding of mathematical modeling. Not only is computing via programming a very powerful tool, it also a great pedagogical aid. We believe in the famous quote by Kristen Nygaard: "Programming is understanding".

For the mathematical training, there is one major new component among the arguments above: understanding abstractions and generalization. While many of the classical methods developed for continuous models are specialized for a particular problem or a narrow class of problems, computing-based algorithms are often developed for problems in a generic form and hence applicable to a large problem class.

Key principle in scientific modeling.

The power of the scientific method lies in identifying a given problem as a special case of an abstract class of problems, identifying general solution methods for this class of problems, and applying a general method to the specific problem (applying means, in the case of computing, calculations by pen and paper, symbolic computing, or numerical computing by ready-made and/or self-written software). This generic view on problems and methods is particularly important for understanding how to apply available, generic software to solve a particular problem.

Computing competence represents a central element in scientific problem solving, from basic education and research to essentially almost all advanced problems in modern societies. Computing competence is simply central to further progress. It enlarges the body of tools available to students and scientists beyond classical tools and allows for a more generic handling of problems. Focusing on algorithmic aspects results in deeper insights about scientific problems.

Today's project in science and industry tend to involve larger teams. Tools for reliable collaboration must therefore be mastered (e.g., version control systems, automated computer experiments for reproducibility, software and method documentation).