Teaching Mathematics to Computer Scientists: Reflections and a Case Study

Mathematics, despite being the foundation of computer science, is nowadays often considered a totally separate subject. The fact that many jobs in computer science do not explicitly require any specific mathematical knowledge posed questions about the importance of mathematics within computer science undergraduate curricula. In many educational systems a prior high school knowledge of mathematics is often not a mandatory requirement to be enrolled into a degree of computer science. On the other hand, several studies report that mathematics is important to computer scientists since it provides essential analytical and critical skills and since many professional and research tasks in computer science require an in-depth understanding of mathematical concepts. From this assumption, this article proposes an analysis of the cohort of computer science' students, with a specific reference to British Universities, and identifies some challenges that lecturers of mathematical subjects normally face. On the basis of this analysis this article proposes two teaching techniques to promote effective learning. The proposed techniques aim at addressing the diversity of cohorts in terms of mathematical background and skepticism from part of the cohort of students to consider mathematics as an essential element of their education. Numerical results indicate the validity and effectiveness of the proposed teaching techniques

Evolutionary computation for software testing

A variety of products undergo a transformation from a pure mechanical design to more and more software and electronic components. A polarized example are watches. Several decades ago they have been purely mechanical. Modern smart watches are almost completely electronic devices which heavily rely on software. Further, a smart watch offers a lot more features than just the information about the current time. This change had a crucial impact on how software is being developed. A first attempt to control the rising complexity was to move to agile development practices such as extreme programming or scrum. This rise in complexity is not only affecting the development process but also quality assurance and software testing. If a product contains more and more features then this leads to a higher number of tests necessary to ensure quality standards. Furthermore agile development practices work in an iterative manner which leads to repetitive testing that puts more effort on the testing team. We aimed within the thesis to ease the pain of testing. Thereby we examined a series of subproblems that arise. A key complexity is the number of test cases. We intended to reduce the number of test cases before they are executed manually or implemented as automated tests. Thereby we examined the test specification and based on the requirements coverage of the individual tests, we were able to identify redundant tests. We relied on a novel metaheuristic called GCAIS which we improved upon iteratively. Another task is to control the remaining complexity. Testing is often time crucial and an appropriate subset of the available tests must be chosen in order to get a quick insight into the status of the device under test. We examined this challenge in two different testing scenarios. The first scenario is located in semi-automated testing where engineers execute a set of automated tests locally and closely observe the behaviour of the system under test. We extended GCAIS to compute test suites that satisfy different criteria if provided with sufficient search time. The second use case is located in fully automated testing in a continuous integration (CI) setting. CI focuses on frequent software build cycles which also include testing. These builds contain a testing stage which greatly emphasizes speed. Thus there we also have to compute crucial tests. However, due to the nature of the process we have to continuously recompute a test suite for each build as the software and maybe even the test cases at hand have changed. Hence it is hard to compute the test suite ahead of time and these tests have to be determined as part of the CI execution. Thus we switched to a computational lightweight learning classifier system (LCS) to prioritize and select test cases. We integrated a series of innovations we made into an LCS known as XCSF such as continuous priorities, experience replay and transfer learning. This enabled us to outperform a state of the art artificial neural network which is used by companies such as Netflix. We further investigated how LCS can be made faster using parallelism. We developed generic approaches which may run on any multicore computing device. This is of interest for our CI use case as the build server's architecture is unknown. However, the methods are also independent of the concrete LCS and are not linked to our testing problem. We identified that many of the challenges that need to be faced in the CI use case have been tackled by Organic Computing (OC), for example the need to adapt to an ever changing environment. Hence we relied on OC design principles to create a system architecture which wraps the LCS developed and integrates it into existing CI processes. The final system is robust and highly autonomous. A side-effect of the high degree of autonomy is a high level of automatization which fits CI well. We also gave insight on the usability and delivery of the full system to our industrial partner. Test engineers can easily integrate it with a few lines of code and need no knowledge about LCS and OC in order to use it. Another implication of the developed system is that OC's ideas and design principles can also be employed outside the field of embedded systems. This shows that OC has a greater level of generality. The process of testing and correcting found errors is still only partially automated. We make a first step into automating the entire process and thereby take an analogy to the concept of self-healing of OC. As a first proof of concept of this school of thought we take a look at touch interfaces. There we can automatically manipulate the software to fulfill the specified behaviour. Thus only a minimalistic amount of manual work is required