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History of PI
Bernátová, Eliška ; Kvasz, Ladislav (advisor) ; Pilous, Derek (referee)
My bachelor thesis "History of " aims to inform about the development of this constant. I tried to proceed chronologically from the beginnings in ancient Egypt through ancient Greece, the Middle Ages, the Renaissance to the Modern Era and the computer's world. In the chapters "The Mysterious Middle Ages" and " the Hunting of the Precise Numbers" are focused mainly on the most important personalities of the time. Of course, the problem of was dealt with a countless number of mathematicians, but to mention each any of them would take a lot of time and the thesis would have hundreds of pages. After due consideration I selected the most interesting personalities, those whose contribution to the development of deserved it most. In the next chapter, "Irrationality and Transcendence" I primarily focused on mathematical theorems and their proofs. This chapter is the most important in my opinion. Many circumstances related to the number are resolved there in. In the final chapter, which I called " in the Computer World" I mention only the most important computers until 1967 because of the very rapid development of technology after wards.
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Riemann zeta function
Čoupek, Petr ; Rokyta, Mirko (advisor) ; Zahradník, Miloš (referee)
Riemann zeta function represents an important tool in analytical number theory with various applications in quantum mechanics, probability theory and statistics. First introduced by Bernhard Riemann in 1859, zeta function is a central object of many outstanding problems. From previous results follows the importance of zeta function for further development in the field of number theory. This thesis provides basic properties of the Riemann zeta function. In particular, we prove theorems concerning the distribution of its roots outside and inside the critical strip which leads to the formulation of the Riemann hypothesis and theorems concerning the irrationality of selected values of the Riemann zeta function including the proof of the irrationality of ζ(3). 1
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Irrationality in the perception of money
Juhásová, Zuzana ; Chytilová, Julie (advisor) ; Želinský, Tomáš (referee)
Irrationality is a phenomenon that can be seen in every aspect of human life. In many cases people do not behave rationally in terms of economic theory and they often do not even realise it. This thesis aims at problem of irrationality in the perception of money and describes anomalies in rational decision-making. First, it introduces the topics that behavioural economics is concerned with and its place among other sciences. It brings the overview of history of behavioural economics and the most influential people that are responsible for its evolution. Next, it briefly summarizes the most common research methods used. After that, the concept of rationality is described, both from classical economics and behavioural points of view. The core of the thesis is the experiment that is an example of irrationality in the perception of money. Studies that examined this problem are presented. Finally, a conducted survey is presented, which detects the presence of irrational behaviour.
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Irrational Behaviour
Vlach, Tomáš ; Koubek, Ivo (advisor) ; Kvaček, Jan (referee)
This thesis questions the notion of rationally behaving individuals as an as- sumption of microeconomic and macroeconomic models. Its goal is to show that foundations on which the modern economics is built are not so much solid. Selected topics are discussed theoretically and subsequently confirmed empir- ically by existing research studies. Afterwards, they are extended by related findings and potential implications for human behaviour. The thesis contains examples of irrational behaviour in which it is possible to behave rationally as well as examples in which it is very difficult to do so. The results imply that irrationality is present in many different domains. Because the assumption of rationality is repeatedly violated, economic models are not able to properly describe and predict human behaviour. Keywords Irrationality; opportunity costs; loss aversion; self-control; procrastination; cognitive illusions Author's e-mail tvlach92@seznam.cz Supervisor's e-mail koubek@fsv.cuni.cz
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Situation of the Surrealist Subject
Svěrák, Šimon ; Zuska, Vlastimil (advisor) ; Dadejík, Ondřej (referee)
Univerzita Karlova v Praze Filosofická fakulta katedra estetiky Diploma thesis Šimon Svěrák Situation of the Surrealist Subject (abstract) 2012 thesis supervisor: prof. PhDr. Vlastimil Zuska, CSc. Abstract This thesis focuses on the situation of a substantial subject in the historical development of the surrealist experience and confronts it with our original postmodern interpretation of thoughts of early Marx. The surrealist consciousness is based on a dialectical opposition between rational and irrational elements of cognitive processes. André Breton apprehends this dialectics under the perspective of love life and relates it to values of love, freedom and poetry. Nevertheless, this conception changes in the immanent development of the surrealist consciousness from Breton over the work and thoughts Salvador Dalí and Mikuláš Medek to Vratislav Effenberger. Effenberger removes positive values from surrealism and puts emphasis on the critical functions of the irrational. On the psychological field, all these ideas are based on the conception of the unconscious which means there is the substantial approach in them. Our critical interpretation of Marx shows, that the surrealist concept of subject is in the contradiction with its substantial determination. The subject has to be perceived as the essential...
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The number π and continued fractions
Švejdová, Aneta ; Halas, Zdeněk (advisor) ; Slavík, Antonín (referee)
This bachelor thesis deals with one of the well-known mathematical constants, the number π. The form is understandable to higher-year students of secondary schools interested in mathematics. At first, it presents the best known ways people in history tried to approximate the number π. It includes the methods of Egyptians, the people of ancient Mesopotamia and the method of Archimedes. It also presents expressing π in the form of infinite product according to F. Viète and J. Wallis. The second part of the thesis focuses on expressing the number π by continued fractions, which are at first generally defined. We introduce essential relations among them. Then the thesis presents expressing the number π in the form of continued fractions according to J. H. Lambert, L. Euler and W. Brouncker. Finally, proofs of the irrationality of π using continued fractions are presented together with a simple proof of its transcendence. The aim of the thesis is to extend information about π stated in popular books, to explain and clarify basic ideas leading to these claims.
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Irrationality of consumer choice and the effect of nudging decision-making: A field experiment on tipping
Alferovičová, Marija ; Korbel, Václav (advisor) ; Gregor, Martin (referee)
Ekonomy i psychology po celém světě vždy zajímala otázka procesu lidského rozhodování. Eko- nomové zd·razňují význam teorie úžitku během rozhodování, kdežto psychologové se zaměřují na r·zné vnitřní a vnější stimuly ovlivňující naše rozhodnutí. Oba tyto přístupy m·žeme najít v be- haviorální ekonomií, kde oba koncepty mezi sebou těsně spolupracují. Znalost r·zných ekonomic- kých i psychologických faktor·, které ovlivňují náš výběr m·že být mimo jiné přínosná například ve výzkumu spropitného. Abychom našli r·zné d·vody pro placení spropitného, vytvořili jsme experiment ohledně výše spropitného u českých zákazník·. Procentuální výše spropitného byla zkoumána v závislosti na pohlaví obsluhy, velikosti skupiny, která navštívila restauraci, velikosti účtu na jednu osobu a také byl zkoumán vliv tří na sobě nezávislých intervencí. Tyto intervence byly zaměřeny na altruistické chování, reciprocitu a dobrou náladu zp·sobenou personalizací. Výsledky experimentu jsou překvapující a neshodují se s výsledky z předchozích experiment·. Bylo zjištěno, že intervence spojené s altruismem a reciprocitou mají negativní vliv na výši spro- pitného, avšak intervence spojená s personalizací nemá žádný vliv na spropitné. Ve výsledku se také poukazuje na klíčový vliv země, ve které je experiment proveden. 1
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Irrational Behaviour
Vlach, Tomáš ; Koubek, Ivo (advisor) ; Kvaček, Jan (referee)
This thesis questions the notion of rationally behaving individuals as an as- sumption of microeconomic and macroeconomic models. Its goal is to show that foundations on which the modern economics is built are not so much solid. Selected topics are discussed theoretically and subsequently confirmed empir- ically by existing research studies. Afterwards, they are extended by related findings and potential implications for human behaviour. The thesis contains examples of irrational behaviour in which it is possible to behave rationally as well as examples in which it is very difficult to do so. The results imply that irrationality is present in many different domains. Because the assumption of rationality is repeatedly violated, economic models are not able to properly describe and predict human behaviour. Keywords Irrationality; opportunity costs; loss aversion; self-control; procrastination; cognitive illusions Author's e-mail tvlach92@seznam.cz Supervisor's e-mail koubek@fsv.cuni.cz
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