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Solving diophantine equations by factorization in number fields
Hrnčiar, Maroš ; Kala, Vítězslav (advisor) ; Příhoda, Pavel (referee)
Title: Solving diophantine equations by factorization in number fields Author: Bc. Maroš Hrnčiar Department: Department of Algebra Supervisor: Mgr. Vítězslav Kala, Ph.D., Mathematical Institute, University of Göttingen Abstract: The question of solvability of diophantine equations is one of the oldest mathematical problems in the history of mankind. While different approaches have been developed for solving certain types of equations, this thesis predo- minantly deals with the method of factorization over algebraic number fields. The idea behind this method is to express the equation in the form L = yn where L equals a product of typically linear factors with coefficients in a particular number field. Provided that several assumptions are met, it follows that each of the factors must be the n-th power of an element of the field. The structure of number fields plays a key role in the application of this method, hence a crucial part of the thesis presents an overview of algebraic number theory. In addition to the general theoretical part, the thesis contains all the necessary computations in specific quadratic and cubic number fields describing their basic characteristics. However, the main objective of this thesis is solving specific examples of equati- ons. For instance, in the case of equation x2 + y2 = z3 we...
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adaptation course as the class teacher's tool to get to know the class collective
TENKLOVÁ, Eliška
The thesis deals with the influence of class teacher's participation on the adaptation course to the teacher's knowledge of the pupils' collective. In the theoretical part, attention is paid to the concepts of experiential education and adaptation courses. Furthermore, it describes various types of adaptation course methodologies and suggests possibilities of class teacher's participation during the course. The research part describes a qualitative study with respondents who, as a class teacher, have undergone an adaptation course with their new class. The results of the research describe how class teachers perceive the adaptation course as a tool for their knowledge of pupils depending on their participation in the adaptation course.
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Solving diophantine equations by factorization in number fields
Hrnčiar, Maroš ; Kala, Vítězslav (advisor) ; Příhoda, Pavel (referee)
Title: Solving diophantine equations by factorization in number fields Author: Bc. Maroš Hrnčiar Department: Department of Algebra Supervisor: Mgr. Vítězslav Kala, Ph.D., Mathematical Institute, University of Göttingen Abstract: The question of solvability of diophantine equations is one of the oldest mathematical problems in the history of mankind. While different approaches have been developed for solving certain types of equations, this thesis predo- minantly deals with the method of factorization over algebraic number fields. The idea behind this method is to express the equation in the form L = yn where L equals a product of typically linear factors with coefficients in a particular number field. Provided that several assumptions are met, it follows that each of the factors must be the n-th power of an element of the field. The structure of number fields plays a key role in the application of this method, hence a crucial part of the thesis presents an overview of algebraic number theory. In addition to the general theoretical part, the thesis contains all the necessary computations in specific quadratic and cubic number fields describing their basic characteristics. However, the main objective of this thesis is solving specific examples of equati- ons. For instance, in the case of equation x2 + y2 = z3 we...
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Homophobic harassment and bullying in the school
Drbohlav, Lukáš ; Janošová, Pavlína (advisor) ; Vágnerová, Marie (referee)
This bachelory work is based on area, which is mapping homophobic bullying and harassment in classes at elementary and high schools. It shows it as psychologic area, which interdisciplinary exceeds to pedagogic area. Purpose of this work, in theoretic part, is to define different approaches for homosexuality, bisexuality, and transexuality from psychologic point, and clarify different homophobic prejudices, and negative attitude from students for this problem. It focuses at demarcation of different varieties of sexual orientation, and its diversity in society with regard to gender stereotypes. It also deals with specificity of homophobic bullying and harassment as a social pathologically phenomenon, which nowadays appears often at schools. Investigative part of this work should determine students' attitude to humans with non- heterosexual orientation and their imaginations of attitude forward these minorities in their social surrounding. Finally, it deals with bullying of these minorities. Keywords: Homophobia, homosexuality, gender, bullying, harassment, class group
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Enter a Gifted Child to School
Votrubová, Alena ; Hříbková, Lenka (advisor) ; Trpišovská, Dobromila (referee)
This bachelor thesis presents a case study of a gifted child under six years old entering a school. The aim is to identify the positive and negative aspects of a child's adaptation to school. My project focuses on the following research questions: 1. How a child under six years old adapts to a social group in the first class? 2. How does a child under six years old manage the demands of learning in the first class? To this purpose, I record the personality traits and social manifestations of the gifted child and relate them to the school teaching. Furthermore, I monitor the child's adaptation to the new environment, school work, teacher and peers. In the given case study, I observed the child in the classroom during the period September to December 2011 (in total 30 teaching hours) and conducted interviews with the classroom teacher, gifted child, and his parents. The data were processed qualitatively using grounded theory approach. The obtained findings were further analysed and confronted with the scientific literature. Data analysis showed that the observed child managed the learning requirements well and that his case resulted in successful premature training. The research also showed that the gifted child under six years old adapts well to the first grade social group, despite some minor...
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