This article discusses the key elements of the Data Science Technology course offered to postgraduate students enrolled in the Master of Data Science program. This course complements the existing curriculum by providing the skills to handle the Big Data platform and tools, in addition to data science activities. We tackle the discussion about this course based on three main requirements, which are related to the need to exploit the key skills from two dimensions, namely, Data Science and Big Data, and the need for a cluster-based computing platform and its accessibility. We address these requirements by presenting the course design and its assessments, the configuration of the computing platform, and the strategy to enable flexible accessibility. In terms of course design, the offered course contributes to several innovative elements and has covered multiple key areas of the data science body of knowledge and multiple quadrants of the job and skills matrix. In the case of the computing platform, a stable deployment of a Hadoop cluster with flexible accessibility, triggered by the pandemic situation, has been established. Furthermore, through our experience with the implementation of the cluster, it has shown the ability of the cluster to handle computing problems with a larger dataset than the one used for the semesters within the scope of the study. We also provide some reflections and highlight future improvements.