Dendrologia, [kreikkaa]

Invocatio: KREIKKAA alpha, omega.

De fortuna et casu

Invocatio: KREIKKAA Alpha, omega.

De infantibus supposititiis

Invocatio: KREIKKAA Alpha, omega.

Olfactus natura

Invocatio: KREIKKAA Alpha, omega.

De confessione Evae, ex Gen. IV, 1

Invocatio: [Alpha et Omega].

Unitas transcendentalis

Invocatio: KREIKKAA Alpha, omega.

De stellis, & earum affectionibus

Invocatio: KREIKKAA Alpha, omega.

Strena metaphysica

Invocatio: [Alpha Omega].

De sangvisuga

Invocatio: KREIKKAA Alpha & omega.

De astrologia judiciaria

Invocatio: [Alpha et Omega].

Species intelligibilis

Invocatio: Alpha, Omega.

Grammatica Fennica

Ilmajoen rovastin Bartholdus Vhaelin (1667-1723) laatima suomen kielen kielioppi julkaistiin hänen kuolemansa jälkeen käsikirjoituksen pohjalta. Tässä kielen kuvauksessa esitetään mm. nominien sijamuodot, verbien taivutus, vokaalisointu ja astevaihtelu lähes nykyaikaisella tavalla. Vhael antaa tietoja myös ääntämisestä ja Suomen murteista. GRAMMATICA painettiin muuttamattomana uudestaan vielä vuonna 1821.

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

Beyond the obvious : three acts in educational drama

Researching research is not a common theme in educational drama. Nor is the educational drama process from a participant perspective a typical focus of research, at least not if the participants are disabled. Yet this is the theme of this thesis, a drama in three acts. The aim of this thesis is to describe, analyse, and discuss both the ways in which research within educational drama can be carried out and represented, and the experiences of the participants of the educational drama process. The theoretical framework that steers the research process is built up of two pairs of frames, each of them, like Russian nesting dolls, containing further frames. The first frame, relating to the outcomes of conducting research in educational drama, comprises philosophical, representational, and personal theories. As the second question asks what educational drama is, the subject related frame is built up of pedagogical, drama educational, and aesthetic theories. The study in its entirety follows the structure of the researcher’s hermeneutical learning process and takes the form of a journey starting from what is familiar, stretching towards what is new and different, and finally returning back to the beginning with a new view on what was there at the start. The thesis consists of two separate but related studies. The first, a familiar study conducted earlier, Alpha in Act I, was carried out among upper secondary school pupils. In the second, the new and therefore unfamiliar study, Omega in Act III, the participants are adult individuals who are physically and communicatively disabled. In between these two Acts an element of “Verfremdung” where the Alpha study is systematically scrutinized as the purpose is to teach and to manage the reader to think. Meta-discussions on the philosophical issues of the study are conducted throughout the text, parallel to the empirical parts. The outcomes of the first research question show that philosophical, methodical, and representational consistency is crucial for research. While this may sound like stating the obvious, this has nevertheless not always been considered fact, especially not within qualitative research. The outcomes further stress that representational issues are also to be recognized when presenting non-rational aspects of educational drama. By wording the world, through the use of visualising language, the surplus of meanings of educational drama can be, as they are within this study, made visible, sensible, and almost tangible, not only cognitively understandable. The outcomes of the second question point to the different foci of the studies, with Alpha focusing on the rationally retold experiences and Omega focusing on nonrational experiences. The outcomes expose educational drama as a learning process comprising doing, reflecting, and being. The doing aspect communicates the concrete efforts in creating a piece of theatre, while the being aspect relates experiences of being as situated, embodied and sensuous, reciprocal, empowering, aesthetic and artistic, and existential. Reflection is the twine that runs throughout the process and connects both doing and being. In summary, the outcomes could be formulated as “learning from learning how to make theatre”.

Qualitative Characteristics and Quantitative Measures of Solution's Reliability in Discrete Optimization: Traditional Analytical Approaches, Innovative Computational Methods and Applicability

The purpose of this thesis is twofold. The first and major part is devoted to sensitivity analysis of various discrete optimization problems while the second part addresses methods applied for calculating measures of solution stability and solving multicriteria discrete optimization problems. Despite numerous approaches to stability analysis of discrete optimization problems two major directions can be single out: quantitative and qualitative. Qualitative sensitivity analysis is conducted for multicriteria discrete optimization problems with minisum, minimax and minimin partial criteria. The main results obtained here are necessary and sufficient conditions for different stability types of optimal solutions (or a set of optimal solutions) of the considered problems. Within the framework of quantitative direction various measures of solution stability are investigated. A formula for a quantitative characteristic called stability radius is obtained for the generalized equilibrium situation invariant to changes of game parameters in the case of the H¨older metric. Quality of the problem solution can also be described in terms of robustness analysis. In this work the concepts of accuracy and robustness tolerances are presented for a strategic game with a finite number of players where initial coefficients (costs) of linear payoff functions are subject to perturbations. Investigation of stability radius also aims to devise methods for its calculation. A new metaheuristic approach is derived for calculation of stability radius of an optimal solution to the shortest path problem. The main advantage of the developed method is that it can be potentially applicable for calculating stability radii of NP-hard problems. The last chapter of the thesis focuses on deriving innovative methods based on interactive optimization approach for solving multicriteria combinatorial optimization problems. The key idea of the proposed approach is to utilize a parameterized achievement scalarizing function for solution calculation and to direct interactive procedure by changing weighting coefficients of this function. In order to illustrate the introduced ideas a decision making process is simulated for three objective median location problem. The concepts, models, and ideas collected and analyzed in this thesis create a good and relevant grounds for developing more complicated and integrated models of postoptimal analysis and solving the most computationally challenging problems related to it.