The diploma thesis deals with ways of teaching combinatorics at a secondary school. Specifically, I analyzed selected mathematics textbooks for secondary schools in terms of introducing concepts and operations of combinatorics and in terms of types of tasks used. I carried out interviews with six secondary school mathematics teachers and observations of their lessons in order to describe their method of teaching combinatorics. Using results of tests written by these teachers' pupils, I examined whether and how their solving strategies and errors might be influenced by their teachers' approach to teaching combinatorics. Finally, I compared my results with the existing results of mathematics education research on pupils' combinatorial reasoning. The work is divided into four chapters; the first three are theoretical (curricular documents for selected schools, analysis of textbooks on combinatorics in terms of the implementation of combinatorial concepts and operations, selected research about pupils' solving strategies and errors for combinatorial problems, methods of checking the correctness of their solutions. and the impact of ways of teaching combinatorics on pupils' performance). Chapter 4 focuses on my own research which consists of interviews with teachers, observations of lessons on combinatorics, the...

Deposition of nanoscale thickness films is ubiquitous in micro- and nano-scale device manufacturing. Current techniques such as spin-coating and chemical vapor deposition are designed to create only uniform thin films, and can be wasteful in material consumption. They lack the ability to adaptively prescribe desired film thickness profiles. This dissertation presents a novel inkjet-based zero-waste polymer deposition process referred to as Jet and Coat of Adaptive Sustainable Thin Films or J-CAST. The core of this process is built on an experimentally validated multi-scale fluid evolution model, based on extensions of lubrication theory. This model involves a nano-scale fluid film sandwiched between two flat plates: a compliant superstrate and a rigid substrate, with spatial topography on both surfaces. Accounting for the flexural elasticity of the compliant superstrate, and describing the temporal evolution of the fluid film in the presence of different boundary conditions reveals that instead of seeking process equilibrium, non-equilibrium transients should be exploited to guide film deposition. This forms the first core concept behind the process. This concept also enables robust full-wafer processes for creation of uniform films as well as nanoscale films with prescribed variation of thickness at mm-scale spatial wavelengths. The use of inkjets enables zero-waste adaptive material deposition with the preferred drop volumes and locations obtained from an inverse optimization formulation. This forms the second core concept behind the process. The optimization is based on the prescribed film thickness profile and typically involves >100,000 integer parameters. Using simplifying approximations for the same, three specific applications have been discussed - gradient surfaces in combinatorial materials science and research, elliptical profiles with ~10km radius of curvature for X-ray nanoscopy applications and polishing of starting wafer surfaces for mitigation of existing nanotopography. In addition, the potential of extending the demonstrated process to high throughput roll-roll systems has also been mentioned by modifying the model to incorporate the compliance of the substrate along with that of the superstrate. / text