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Implementation of Statistical Functions Using HLS
Šinaľ, Peter ; Martínek, Tomáš (referee) ; Dvořák, Milan (advisor)
The aim of this thesis was to design and implement selected statistical functions used in technical analysis. I focused on moving averages, Black-Schles model for calculating option prices and Indicator Delta. These functions are through HLS transformed into an appropriate description for programmable FPGA. During the transformation process, emphasis is on low latency and resource consumption. Created solutions demonstrate the potential of HLS. They show complexity of the technical analysis and hardware requirements. Achieved results show high accuracy in the simulations. Deviation from the reference value is approximately 6,615*10e-3. The results also indicate thet that reducing latency does not necessarily cause an increase in the consumption of resources on the chip.
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Elementary mathematics from an advanced standpoint
Kučera, Jiří ; Bečvář, Jindřich (advisor) ; Staněk, Jakub (referee)
Mine thesis is written for self-study of secondary school graduates students which prepare for the mathematically oriented high schools. It clarifies theoretical approach to mathematics. It was chosen topics exponents, square roots, logarithms and equations that contain these objects for this purpose. For this reason students are given the opportunity to gain stance to university mathematics knowledge that should be known from high school. In addition, his work allows him to enlarge knowledge of those topics and learn heavier and unusual examples.
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Basic notions of the calculus by Newton, Berkely and their followers
Mixa, Lukáš ; Kvasz, Ladislav (advisor) ; Dvořák, Petr (referee)
Seventeenth century is important not only for mathematics but for European social development in general. This thesis offers an overview about development of mathematics in the seventeenth century England. I present only those mathematical discoveries, which were relevantfor the work of Isaac Newton. In the first part I show the construction of logarithms by John Napier, Henry Briggs and Gregory Saint-Vincent. The second part is dedicated to methods of tangents and quadrature. I describe works of Pierre Fermat, John Wallis and Isaac Barrow. In the third part is shown how Isaac Newton used the mentioned findings for the development of the calculus. I use this example to demonstrate, that historical approach offers an illustrative connection between geometry, algebra and mathematical analysis and can be used in teaching. Keywords: Logarithm, tangent, quadrature, fluxion, fluent, calculus
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Defining the exponential function and logarithm
Franc, Tomáš ; Bárta, Tomáš (advisor) ; Veselý, Jiří (referee)
In this diploma thesis we will introduce six de nitions of the natural exponential function and ve de nitions of the natural logarithmic function. We will prove the de nitions' correctness, derive basic properties of both funcions and show the equivalence of all de nitions for each function. We will see how these funcions are de ned in some textbooks for universities and in textbooks for grammar schools. We will discuss the bene ts and drawbacks of all de nitions and will use the criteria such as required theory and difficulty or length of proofs. At the end of the thesis we will make some recommendations regarding de ning these functions at high schools and universities and we will give several suggestions for an additional research.
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Euler's number in calculus
RÁLKOVÁ, Lucie
The main aim of my thesis on the topic of "Euler's number in mathematical analysis" is to create an overview of the Euler numbers in calculus. This essay in the first part deals with the rise of the number e, in other parts of the current use of calculus. Purpose of this work is the insight students of secondary schools and universities to problems Euler numbers and to better understand the importance of e not only in mathematics.
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Basic notions of the calculus by Newton, Berkely and their followers
Mixa, Lukáš ; Kvasz, Ladislav (advisor) ; Dvořák, Petr (referee)
Seventeenth century is important not only for mathematics but for European social development in general. This thesis offers an overview about development of mathematics in the seventeenth century England. I present only those mathematical discoveries, which were relevantfor the work of Isaac Newton. In the first part I show the construction of logarithms by John Napier, Henry Briggs and Gregory Saint-Vincent. The second part is dedicated to methods of tangents and quadrature. I describe works of Pierre Fermat, John Wallis and Isaac Barrow. In the third part is shown how Isaac Newton used the mentioned findings for the development of the calculus. I use this example to demonstrate, that historical approach offers an illustrative connection between geometry, algebra and mathematical analysis and can be used in teaching. Keywords: Logarithm, tangent, quadrature, fluxion, fluent, calculus
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|
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Elementary mathematics from an advanced standpoint
Kučera, Jiří ; Bečvář, Jindřich (advisor) ; Staněk, Jakub (referee)
Mine thesis is written for self-study of secondary school graduates students which prepare for the mathematically oriented high schools. It clarifies theoretical approach to mathematics. It was chosen topics exponents, square roots, logarithms and equations that contain these objects for this purpose. For this reason students are given the opportunity to gain stance to university mathematics knowledge that should be known from high school. In addition, his work allows him to enlarge knowledge of those topics and learn heavier and unusual examples.
|
|
|
Defining the exponential function and logarithm
Franc, Tomáš ; Bárta, Tomáš (advisor) ; Veselý, Jiří (referee)
In this diploma thesis we will introduce six de nitions of the natural exponential function and ve de nitions of the natural logarithmic function. We will prove the de nitions' correctness, derive basic properties of both funcions and show the equivalence of all de nitions for each function. We will see how these funcions are de ned in some textbooks for universities and in textbooks for grammar schools. We will discuss the bene ts and drawbacks of all de nitions and will use the criteria such as required theory and difficulty or length of proofs. At the end of the thesis we will make some recommendations regarding de ning these functions at high schools and universities and we will give several suggestions for an additional research.
|
|
|
Implementation of Statistical Functions Using HLS
Šinaľ, Peter ; Martínek, Tomáš (referee) ; Dvořák, Milan (advisor)
The aim of this thesis was to design and implement selected statistical functions used in technical analysis. I focused on moving averages, Black-Schles model for calculating option prices and Indicator Delta. These functions are through HLS transformed into an appropriate description for programmable FPGA. During the transformation process, emphasis is on low latency and resource consumption. Created solutions demonstrate the potential of HLS. They show complexity of the technical analysis and hardware requirements. Achieved results show high accuracy in the simulations. Deviation from the reference value is approximately 6,615*10e-3. The results also indicate thet that reducing latency does not necessarily cause an increase in the consumption of resources on the chip.
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