Title: Financial Mathematics in Czech textbooks from the Marchet's Reform Author: Martin Melcer Department: Department of Mathematics Education Supervisor: doc. RNDr. Martina Bečvářová, Ph.D. Abstract: The PhD thesis presents a comprehensive view of the development and the position of financial mathematics in Czech textbooks and collections particularly those used in high schools with consideration of the political situation in our country. The analysed period from 1908, i.e. from the Marchet's Reform, to the present is divided into five principal stages. In each stage textbooks covering financial mathematics instruction in all types of secondary schools are chosen. This shows the level and extent of the presentation, the complexity of the given tasks and problems and the way in which they are integrated into the textbooks or the syllabus, more precisely. At first the basic general characteristics of the textbooks are presented followed by a detailed description of partial topics of study which are then analysed thoroughly and mutually compared. The conclusions of the PhD thesis reflect the current situation of financial mathematics instruction and offer ways leading to the improvement in the level of financial literacy of our citizens. Keywords: financial mathematics, principal, interest, debt, annuity,...

The thesis is devoted to ancient Indian mathematics; it describes the mathe- matical knowledge, computational techniques and methods for solving various ari- thmetic, algebraic and geometric problems that the Indians knew and used. The thesis follows the development of Indian mathematics from the oldest knowledge contained in ancient Vedic texts to the knowledge originated from the classic me- dieval arithmetic and algebraic works. This is the first comprehensive text written in Czech which contains the translation of original problems and analysis of their solutions in the current mathematical formulation and symbolism. The sources are mainly English translations of ancient Sanskrit texts and their commentaries.

The aim of this thesis is to elaborate a set of tasks that will have increasing difficulty and will lead pupils to the skill of solving problems designed for gifted students. The action research will focus on the student's work with the proposed tasks. In the theoretical part, attention will be paid to the available literature on the teaching of mathematics to exceptionally gifted pupils.

This diploma thesis briefly introduces the concept of inquiry based teaching mathematics. In inquiry based teaching, emphasis is placed primarily on the active activity of the pupil, the aim of which is to discover a certain reality. This activity mainly involves solving problems and finding the right paths to achieve the right goal. We can call this path to a goal as a research. The inquiry process involves observing, formulating questions, identifying information, designing possible processes, and verifying them. In this educational method, the role of the teacher is not to pass the facts to the pupils, but to target them and to supervise the correctness of their practices. We can understand the teacher here as a guide, adviser or assistant on the path to the goal (discovery). In the thesis a few examples of mathematics of elementary and secondary schools are given, in which the inquiry based approach is applied. Mathematics in the given examples is not complicated, emphasis is put on the practical use. In the examples interdisciplinary relationships are developed as well, which is an important part of the inquiry based teaching. In each example, additional questions are provided.

This Thesis deals with mathematical inequalities, their use in mathematics and applications to thermodynamics. The main emphasis is placed on proofs of inequalities and solving examples. The following thing explains the mathematical concept such as norm or metric, needed to understand these procedures, and also some of basic concepts of thermodynamics. To understand this Thesis the knowledge of analysis and thermodynamics is required.

The subject of the diploma thesis is the creation of study material relating the subject of theory of dividing for students trained to be teachers at primary school. In the first part of the thesis I am concentrating on theory of mentioned problem. The main target of the thesis in the second part is the collection of exercises for the students. In the third part of these I am checking the level of knowledge in the subject of divisions in natural numbers with ten years old autistics student that I take care during school instruction. The results of these tests are mentioned in the thesis.

In the introductory part of the dissertation I deal with mathematics for the first classes of elementary schools and applicability for computers in education. The main part contains the methodical manual which helps teachers with orientation in the interactive textbook that I wrote and which describes the work with particular exercises. The next part is aimed for material verification in practice. In conclusion I evaluate results and analyze observations from the experiment.

The thesis deals with the use of calculators as a teaching aid in mathematics education in primary school, and its contribution to the development of mental arithmetic and construction of numerical concepts. The thesis is a collection of activities designed for an application of the calculator on interactive whiteboard. It contains an interesting task to explore the world of numbers and arithmetic operations. The collection is designed for teachers who want to diversify the mathematics education for students.

The aim of the thesis is to create a set of examples from mathematics using MS Excel spreadsheet, which could be used for teaching mathematics in primary schools. Pupils practice their work from this spreadsheet calculator and also enrich their knowledge of mathematics for its practical use. This set will be used to practice graphs, functions, financial mathematics, patterns, probability, and another. All these examples will be tested in educational practice.

This diploma thesis deals with Elica DALEST applications, which are a part of the DALEST project (Developing Active Learning Environment for Stereometry). The goal of the project is to create a suitable tool for teaching stereometry. This thesis deals with 7 out of 13 applications which are part of the DALEST project. The goal of my thesis is to create materials which can be used for presentation of features of Dalest applications to mathematics teachers. Instructional videos are part of the thesis and can be found on the enclosed CD. One of the goals of my thesis is to present created materials to elementary schools teachers in practice.