MMI bakalaureusetööd – Bachelor's theses. Kuni 2015

Selle kollektsiooni püsiv URIhttps://hdl.handle.net/10062/30415

Sirvi

Nüüd näidatakse 1 - 20 56

Применение принципа равномерной органиченности к теории суммируемости
(Tartu Ülikool, 1999) Удальцова, Елена; Soomer, Virge, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Optimaalsete veomarsruutide leidmine kahe lao korral
(Tartu Ülikool, 2002) Kuresson, Aire; Kangro, Raul, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Hüpoteeside kontrollimine ja võimsuse arvutamine Analyst Application abil
(Tartu Ülikool, 2002) Bileva, Anna; Parring, Anne-Mai, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Autonoomsete diferentsiaalvõrrandite süsteemide perioodilised lahendid
(Tartu Ülikool, 2002) Korobova, Evelin; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Hulkade ja funktsioonide r-kumerus
(Tartu Ülikool, 2005) Kivi, Karin; Soomer, Virge, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Asümmeetria ja järsakuse karakteristikud
(Tartu Ülikool, 2005) Kilgi, Helle; Kollo, Tõnu, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Rajaülesande lahendamine ratsionaalsplainidega kollokatsioonimeetodil
(Tartu Ülikool, 2006) Mehide, Inga; Fischer, Malle, juhendaja; Oja, Peeter, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Riccati diferentsiaalvõrrand finantsmatemaatikas
(Tartu Ülikool, 2007) Kuld, Anu; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Rajaülesande lahendamine ratsionaalsplainidega kollokatsioonimeetodil
(Tartu Ülikool, 2007) Nurk, Anni; Fischer, Malle, juhendaja; Oja, Peeter, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
B-splainid ja nende rakendused
(Tartu Ülikool, 2007) Kuljus, Elina; Fischer, Malle, juhendaja; Oja, Peeter, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Ruutsplainidega interpoleerimine ühtlasel võrgul
(Tartu Ülikool, 2008) Frolova, Svetlana; Pedas, Arvet, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Ajaskaalal määratud funktsioonide diferentseerimine ja integreerimine
(Tartu Ülikool, 2009) Karm, Märten; Leiger, Toivo, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Otsese ja kaudse meetodi võrdlemine aktsiahinna kasvamise tõenäosuse leidmisel päevasisese kauplemise tingimustes
(Tartu Ülikool, 2009) Olvik, Ander; Kangro, Raul, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Otsesuunatud tehisnärvivõrgud paketis R
(Tartu Ülikool, 2013) Liivoja, Merili; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Human brain is a complex and powerful system that is able to solve a wide variety of tasks. The aim of many scientists is to develop a computer simulation that mimics the brain functions and solves problems the way our brains do. Very simplified models of biological neural networks are artificial neural networks. There are two different types of artificial neural networks – feed forward neural networks and recurrent neural networks. This thesis gives an overview of feed-forward neural networks and their working principles. The thesis is divided into two main parts. The first part is the theory of feed-forward neural networks and the second part is a practical example of neural network with software R. The first part gives an overview of the artificial neuron and its history. Also different types of artificial neurons are introduced. The first part includes instructions of how feed-forward neural networks are composed and explains how they calculate the results. Separate chapter is devoted to training artificial neural networks. The chapter gives an overview of two main training algorithms – perceptron training algorithm and back-propagation algorithm. The first is designed to train perceptrons and the second is often used in training multi-layer feed-forward neural networks. The last topic explains how to construct feed-forward neural networks with software R. It includes a tutorial of how to build a neural network that calculates the square root. The tutorial will produce a neural network which takes a single input and produces a single output. Input is the number that we want square rooting and the output is the square root of the input.
Matemaatika võimalikest rakendustest muusikas
(Tartu Ülikool, 2013) Simson, Mai; Abel, Mati, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
The aim of this bachelor’s thesis is to give an overview of some mathematical applications which can be used in music. The thesis is mainly based on three books: “Simple Gamma” by Georgi Evgenevitš Šilov, “Occidents’ History of Music” by Igor Garšnek and “Music: A Mathematical Offering” by Dave Benson. The thesis consists of four chapters. In the first chapter we give definitions to different terms that are used in the thesis. The second chapter briefly describes the common history in music and mathematics. The aim of the third chapter is to explain the construction of the musical scale using logarithms and chain fractures. The final chapter focuses on different mathematical applications used in music. We will discuss Iannis Xenakis’s theory about the algebraic qualities of the intervals, the theory that Pierre Boulez used to compose his “Structures I”, Urmas Sisask using mathematics and astronomy to compose his choir piece “Gloria Patri” and also some mathematical methods that could be used to describe music.
Osakeste parvega optimeerimise rakendamine elektribörsil
(Tartu Ülikool, 2013) Rakaselg, Gerda; Miidla, Peep, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
This bachelor thesis consists of giving an overview of the electircity market in Estonia, introducing the method of particle swarm optimization (PSO) and implementing PSO on a problem associated with electricity market. Electricity market was opened only in the beginning of year 2013 in Estonia. Thus this subject is topical at the moment. We concentrate on power producers in the day-ahead market, specifically on submitting an offer curve to the day-ahead market. In order to maximize profit, power companies need appropriate bidding strategies. In this thesis one strategy is described and a method for calculating necessary prices and quantities for electricity is introduced. Particle swarm optimization is a computation technique, which is inspired by swarm behaviour such as fish schooling or bird flocking. PSO is initialized with a population of random particles and it searches for solution by updating generations. The particles fly through the n-dimensional problem space moving towards both current individual and current global optimum position. In last chapter of this thesis a theoretical example of finding an offer curve for two electricity generators is solved implementing particle swarm optimization. It is modelled using MATLAB.
Minkowski aegruumi geomeetriast
(Tartu Ülikool, 2013) Lätt, Priit; Abramov, Viktor, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
We consider a four-dimensional real vector space in which three coordinates describe the space, and the fourth coordinate describes time. Such a vector space, equipped with Minkowski metric, is said to be a Minkowski spacetime, denotedM and sometimes referred just as Minkowski space. In the beginning of 20th century it emerged from the works of Hermann Minkowski and Henry Poincar e that this mathematical tool can be really useful in areas like the theory of special relativity. The rst objective of this thesis is to introduce the classical properties of Minkowski spacetime in a way that doesn't get into the details about the physical meaning of the topic. The main focus is on the elements of the spacetime and the orthogonal maps that describe the transformations of these elements. As this topic, the Minkowski spacetime, has many applications in physics, most of the literature on it originates from physics, rather than mathematics. In the books that are written by physicists, strict proofs are not given properly or they are avoided entirely. Sometimes physical discussion is considered as a proof, but as shown in proposition 3.1 for example, things are not so obvious after all in a mathematical point of view. In contrary, the aim of this thesis is to ll this gap by giving rigorous proof to all the statements that are made. The last part of the thesis takes a new course and tries to introduce tools from branch of mathematics called di erential geometry. Apparatus described there can be useful not just describing the structure of Minkowski spacetime, but also wide areas of theoretical physics. At last, we generalize classical spacetime and present the Minkowski superspace { a space with anticommuting coordinates that has become a useful tool in the eld theory. This is all done in a bit less formal way. This thesis consists of four sections. In the rst section we recall such topics that are not strictly connected to the thesis but have great impact on further understanding of the paper. For example Gram{Schmidt orthogonalization process is reminded and we prove one of the fundamental results related to dot product, the Cauchy{Schwartz{Bunjakowski inequality. We also describe the rules of the multipication of block matrices as 42 well as nding the inverse of block matrix. Map called matrix exponential is introduced as it plays a key role in the nal part of the thesis. Considered the geometrical meaning of the paper we nd ourselves stopping for a bit longer to study the idea of topological manifold. Second section sets an objective to describe the elements or events of the Minkowski spacetime. For that we give a strict de nition of dot product and move on to the concept of pseudoeucleidic space. After that we describe the dot product in Minkowski spacetime, which gives us the metric. It appears that by the metric we can factorize the elements of spacetime into three distinct classes, these are spacelike, timelike and nullvectors. The last subsection is there to describe the orthogonal transformations of Minkowski space, referred as Lorentz transformations. We show how these transformations can be represented in both coordinates and matrix form and what is the connection between the transformations and the metric of M. Finally we prove that the set of all Lorentz transformatioins has a very natural group structure, the Lorentz group. In the third section we continue with the observation of Lorentz transformations. In the rts subsection we take a closer look at the properties of such transformations and concentrate on the most important of them. As a result we nd a rotation subgroup of Lorentz group. We proceed with noting that Lorentz transformations remain the distances invariant. That encourages us to look for other such transformations that share the same property. As it happens translations are of this kind and by observing translations with Lorentz transformations together, we get the symmetry group of Minkowski spacetime, the Poincar e group. The fourth section takes another course. In this section the objective is to introduce, via more popular approach, the connections between Minkowski spacetime and di erential geometry, and to uncover the term superspace with the surrounding mathematics. In the part of di erential geometry we de ne Lie algebra with its representation and give examples to clear the topic. As expected we then nd ourselves de ning Lie group which we later connect with Lie algebra by giving an informal description. The section, as well as the paper is then nished with the introduction of Minkowski superspace. For that we de ne terms such as superalgebra and give a well known example, the Grassmann algebra. By avoiding strict mathematical formalism, we show what are functions on superspace and how to nd integral or derivative of such functions.
Aasia optsioonide hindamine
(Tartu Ülikool, 2013) Kask, Rain; Raus, Toomas, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Determining the correct value of an option is the main problem in option theory. There are several factors which determine the price of an option. In addition to these factors, Asian options also depend on the history of the underlying asset which complicates the correct pricing of an Asian option. Although the structure of an Asian option is more complex than for example European option's, many of the typical numerical methods can still be used to nd the price of an Asian option when modi ed correctly. In the rst part of this thesis some of these typical numerical methods are introduced. The basic idea of lattice method, di erential method and Monte-Carlo method are described by showing how to nd a value of a usual European option step by step. The last and main part of this thesis is dedicated to Asian options and lattice method. It is shown how to modify the lattice method so that it could be used for pricing an Asian option. The modi ed lattice method for pricing an Asian option is called forward shooting grid method (FSG) and was rst used in 1993 by Hull and White for nding the value of Asian and lookback options. The method is described thoroughly and 2 di erent approaches (Barraquand-Pudet method and modi ed Hull-White method) for choosing the average price of an underlying asset are introduced. To ensure that the FSG method can truly be used for pricing an Asian option, some results obtained by using the FSG method with di erent parameters N, and are brought out in the last section of the thesis. The prices found by Barraquand and Pudet method and modi ed Hull and White method are compared with a price of an unrealistic Asian option, which analytical value can be found. For one more realistical case of an Asian option the prices found by FSG method are compared with a price found by Monte-Carlo method. Source codes (written in Python) for FSG method and Monte-Carlo method are brought out in Appendixes (Lisad).
Dünaamiliste süsteemide ja geneetika mudelid
(Tartu Ülikool, 2013) Lillo, Karin; Puman, Ella, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
Dynamic systems are systems, which develop or change in time. With every model in this thesis there is given a story about the origin of given system or equation and necessary information. In addition to models there are also different charts to simplify the understanding of the models. Systems in this thesis are based on differential equations, because differential equations describe dynamic systems, which are continuous in time. Attention is paid to systems, in which the differential equations are nonlinear, because these could lead to chaotic solutions. All the models are given with initial conditions and some models also have charts, which show the change of the solution if a parameter has been changed a little. It is clear, that all systems may not lead to chaos with every value, but if the parameters are changed and solutions are analysed, it is seen that even a slightest change may lead to a chaos. With models it is easy to experiment with the real world. Without such models we were often left to manipulate real systems in order to understand the relationships of cause and effect. Models help to realize the consequences of the actions of mankind without harming the nature or the real world. In this thesis, two basic genetic problems were discussed, the mating of two alleles and natural selection and mutation. These models are quite simple, yet they provide enough infor-mation to understand the base of these problems in the real world. It is also possible to make these models more precise, which will lead to more accurate results and more precise predictions to real life cause and effect situations. In conclusion, models just make a lot of things easier to understand.
Elastsete plaatide painde ülesanded
(Tartu Ülikool, 2013) Kasepuu, Kaile; Lellep, Jaan, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
The aim of this work is to introduce the Basic equations of the Kirchhoff’s bending theory. The current study consists on two parts. In the first part we derive the governing differential equation for the deflection for thin plate bending. In the second part we study the bending of thin rectangular plates subjected to the transverse pressure. We find the middle surface of the plate in the case of cylindrical bending. It appears that in this case the differential equation of equilibrium can be solved by direct integration. Also we present Navier’s method for rectangular plates with simply supported boundary conditions on all four edges. We look for the solution of the equilibrium equation in the form of double seires. Each term of this series is a product of trigonometrical functions which meet the boundary conditions spontaneously.

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Sirvi MMI bakalaureusetööd – Bachelor's theses. Kuni 2015 Kuupäev järgi