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Introduction into the topic of sequences at the secondary school of book culture in a motivating way
Bay, Petra ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The aim of the thesis is to present the potential of constructivist approaches to teach sequences at high school, with special attention to the problems leading to generalisation. You will read about critical points in the process of generalisation which occurred in TIMSS and PISA international studies and which were examined in the teaching experiment. The question of motivation to learn mathematics is an essential part of this thesis as well as it is an essential part of constructivist approaches to teaching. Two chapters at the beginning analyze school curricular documents, science articles, school textbooks and TIMSS and PISA international studies which formed the theoretical frame of the teaching experiment. The teaching experiment is based on Hejný's theory of generic models and on constructivist approaches to teaching which are introduced in the third chapter. Chapter four which describes the teaching experiment and pre-experiment is the main part of the thesis. It brings inspiration how to deal with the critical points in the process of generalisation and how to motivate pupils to learn mathematics. Key words sequence, generalisation, mathematisation, motivation, approaches to teaching, constructivism
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Artificial Neural Networks and Their Usage For Knowledge Extraction
Petříčková, Zuzana ; Mrázová, Iveta (advisor) ; Procházka, Aleš (referee) ; Andrejková, Gabriela (referee)
Title: Artificial Neural Networks and Their Usage For Knowledge Extraction Author: RNDr. Zuzana Petříčková Department: Department of Theoretical Computer Science and Mathema- tical Logic Supervisor: doc. RNDr. Iveta Mrázová, CSc., Department of Theoretical Computer Science and Mathematical Logic Abstract: The model of multi/layered feed/forward neural networks is well known for its ability to generalize well and to find complex non/linear dependencies in the data. On the other hand, it tends to create complex internal structures, especially for large data sets. Efficient solutions to demanding tasks currently dealt with require fast training, adequate generalization and a transparent and simple network structure. In this thesis, we propose a general framework for training of BP/networks. It is based on the fast and robust scaled conjugate gradient technique. This classical training algorithm is enhanced with analytical or approximative sensitivity inhibition during training and enforcement of a transparent in- ternal knowledge representation. Redundant hidden and input neurons are pruned based on internal representation and sensitivity analysis. The performance of the developed framework has been tested on various types of data with promising results. The framework provides a fast training algorithm,...
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Smoothness of Functions Learned by Neural Networks
Volhejn, Václav ; Musil, Tomáš (advisor) ; Straka, Milan (referee)
Modern neural networks can easily fit their training set perfectly. Surprisingly, they generalize well despite being "overfit" in this way, defying the bias-variance trade-off. A prevalent explanation is that stochastic gradient descent has an implicit bias which leads it to learn functions that are simple, and these simple functions generalize well. However, the specifics of this implicit bias are not well understood. In this work, we explore the hypothesis that SGD is implicitly biased towards learning functions that are smooth. We propose several measures to formalize the intuitive notion of smoothness, and conduct experiments to determine whether these measures are implicitly being optimized for. We exclude the possibility that smoothness measures based on first derivatives (the gradient) are being implicitly optimized for. Measures based on second derivatives (the Hessian), on the other hand, show promising results. 1
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Artificial Neural Networks and Their Usage For Knowledge Extraction
Petříčková, Zuzana ; Mrázová, Iveta (advisor) ; Procházka, Aleš (referee) ; Andrejková, Gabriela (referee)
Title: Artificial Neural Networks and Their Usage For Knowledge Extraction Author: RNDr. Zuzana Petříčková Department: Department of Theoretical Computer Science and Mathema- tical Logic Supervisor: doc. RNDr. Iveta Mrázová, CSc., Department of Theoretical Computer Science and Mathematical Logic Abstract: The model of multi/layered feed/forward neural networks is well known for its ability to generalize well and to find complex non/linear dependencies in the data. On the other hand, it tends to create complex internal structures, especially for large data sets. Efficient solutions to demanding tasks currently dealt with require fast training, adequate generalization and a transparent and simple network structure. In this thesis, we propose a general framework for training of BP/networks. It is based on the fast and robust scaled conjugate gradient technique. This classical training algorithm is enhanced with analytical or approximative sensitivity inhibition during training and enforcement of a transparent in- ternal knowledge representation. Redundant hidden and input neurons are pruned based on internal representation and sensitivity analysis. The performance of the developed framework has been tested on various types of data with promising results. The framework provides a fast training algorithm,...
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Introduction into the topic of sequences at the secondary school of book culture in a motivating way
Bay, Petra ; Vondrová, Naďa (advisor) ; Kvasz, Ladislav (referee)
The aim of the thesis is to present the potential of constructivist approaches to teach sequences at high school, with special attention to the problems leading to generalisation. You will read about critical points in the process of generalisation which occurred in TIMSS and PISA international studies and which were examined in the teaching experiment. The question of motivation to learn mathematics is an essential part of this thesis as well as it is an essential part of constructivist approaches to teaching. Two chapters at the beginning analyze school curricular documents, science articles, school textbooks and TIMSS and PISA international studies which formed the theoretical frame of the teaching experiment. The teaching experiment is based on Hejný's theory of generic models and on constructivist approaches to teaching which are introduced in the third chapter. Chapter four which describes the teaching experiment and pre-experiment is the main part of the thesis. It brings inspiration how to deal with the critical points in the process of generalisation and how to motivate pupils to learn mathematics. Key words sequence, generalisation, mathematisation, motivation, approaches to teaching, constructivism
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