In this thesis, we have considered two important problems, Boolean satisfiability (SAT) and derivative free optimization in the context of large scale quantum computers. In the first part, we survey well known classical techniques for solving satisfiability. We compute the approximate time it would take to solve SAT instances using quantum techniques and compare it with state-of-the heart classical heuristics employed annually in SAT competitions. In the second part of the thesis, we consider a few classically well known algorithms for derivative free optimization which are ubiquitously employed in engineering problems. We propose a quantum speedup to this classical algorithm by using techniques of the quantum minimum finding algorithm. In the third part of the thesis, we consider practical applications in the fields of bio-informatics, petroleum refineries and civil engineering which involve solving either satisfiability or derivative free optimization. We investigate if using known quantum techniques to speedup these algorithms directly translate to the benefit of industries which invest in technology to solve these problems. In the last section, we propose a few open problems which we feel are immediate hurdles, either from an algorithmic or architecture perspective to getting a convincing speedup for the practical problems considered.

The aim of this study is to investigate how and in which form students come in contact with practical applications in the upper secondary school course Chemistry B. The study is based upon the assumption that all learning is situated in a social environment. The theoretical framework is the design theory perspective, which entails an assumption that the pedagogical tools affect the knowledge content. The empiric materials in the study are collected through three methods: textbook analysis, classroom observations and questionnaires. Two groups of students and their teachers were observed during a section of the relevant course. The textbook analysis focuses upon the same course section in the textbooks of the two groups and compares these books with the relevant section in a third textbook. In addition, the two student groups responded to a questionnaire on their attitudes toward the subject of chemistry subject linked to its applications at a society level. The study shows that there are significant differences between the strategies which teachers and textbooks use in order to present and visualise practical applications of chemical theory. The context strategy is based upon the students’ own surroundings and uses real life application as a tool for the presentation of the principles of chemistry. According to this strategy, the knowledge content should be organised in such a way that the chemical principles are used to explain our surroundings. The process and product strategy, on the other hand focuses upon a scientific approach, in which science as a process and scientific products are most important. With this strategy, applications are used to illustrate and exemplify the knowledge content. The conclusion of this study is that neither different forms of presentation nor the presence of practical applications affect the students' attitude towards the subject. Furthermore, practical applications are not a significant part of the students' learning strategies.

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