"One inexperienced in higher mathematics may very well question the necessity of irrational numbers since all numbers used in computation are rational. For example, one computes the area of a circle by using the formula A = [pi]r² and substituting 22/7 or some other approximate value for [pi]. Furthermore, the rational numbers are dense on the straight line, and so physical means can be used to determine whether a given length or ratio is rational. However, in theoretical mathematics there is a need for a real number system to give all limiting values. Calculus, as we know it, could not exist without the irrational numbers. The purpose of this paper is to make a careful study of the real number system, to develop some criteria for the irrationality of certain numbers, and to analyze the proofs of the irrationality of a few simple irrational numbers"--Preface. / "January 1959." / Typescript. / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Paul J. McCarthy, Professor Directing Paper. / Includes bibliographical references (leaf 36).

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This study is meant to replicate research by O’Toole (1997), investigating the effectiveness of Rational Emotive Behavioural Therapy (REBT), and REBT combined with REST, in reducing and treating social anxiety disorder (SAD). The present study used a counselling programme grounded in REBT and/or REST to re-examine the effects of REBT and/or REST on treating SAD in college students in a Saudi Arabian university. An experimental pre-test, post-test, control group design was utilised, and quantitative and content analysis data were collected and analysed using O’Toole’s measures after being ‘Arabicised’ and standardised. Social anxiety was measured using the Interaction Anxiousness Scale and the Shyness Scale. Seventy-five volunteers, who were undergraduate students at King Abdul Aziz University, participated in the study. The measures were used in placing the clients in their respective groups in the empirical study and for comparing pre-testing data with post-testing and follow-up results. Findings indicated that both treatments of REBT-only and REST plus REBT proved effective in the reduction of prior irrational beliefs, considering their reduced irrational thinking scores at the advanced stages of the study. That notwithstanding, follow-up post-comparison analyses confirmed that REST plus REBT therapy is more effective than REBT only. Content analysis data derived from the reflections and cognitions of the participants yielded findings that support and integrate with the results obtained from the quantitative study, which involved the use of numerical scales. The findings were later compared and contrasted with the basal study findings and in congruence with prior research reviewed. Finally, the present study recommended that REBT should be supported by REST to gain more effective psychotherapeutic results with SAD patients by efficaciously reducing their irrational beliefs. The study also recommended conducting future research to tap into the relationship between religiosity and REBT, harnessing REBT/REST counselling programmes.

The number self-identified non-theists is on the rise in the United States. With a recent influx of religious skepticism in various forms of media, the existence of this ideological minority is becoming more salient. This growing population remains understudied in the social sciences. The present survey research attempts to improve this deficit by examining prejudice toward atheists among college students and exploring possible correlates and predictors, including irrational beliefs, self-esteem, and religiosity. More than 80% of respondents exhibited some form of bias against atheists, with religiosity emerging as a viable predictor. This study found a significant correlation between prejudice scores and irrational beliefs. This significance does not hold true, however, for all demographic groups.

This report examines the theory of continued fractions and how their use enhances the secondary mathematics curriculum. The use of continued fractions to calculate best approximants of real numbers is justified geometrically, and famous irrational numbers are described as continued fractions. Periodic continued fractions and other applications of continued fractions are also discussed. / text

Même si le surréalisme au 21ème siècle est généralement jugé comme un mouvement dépassé dont les années les plus actives ont eu lieu dans l'entre-deux-guerres, c'est-à-dire de 1918 à 1939, il y a encore des échos et des rémanences du surréalisme aujourd'hui, longtemps après la fin apparente du mouvement. Le présent travail explore les oeuvres de Louis-René des Forêts, à savoir Le Bavard et La Chambre des enfants, par rapport aux oeuvres surréalistes, à savoir Nadja, le "Manifeste du surréalisme," et L'Amour fou, afin de déterminer dans quelle mesure les composantes du surréalisme telles que le hasard objectif, les attributs de l'esprit conscient et inconscient, l'irrationalité, et le jeu de la fiction et de la réalité font encore écho et restent présentes dans les oeuvres littéraires à présent. Les résultats de cette analyse indiquent que les oeuvres littéraires fictives d'aujourd'hui sont largement imprégnées de nombreuses composantes surréalistes dans certains cas directement et dans d'autres cas indirectement. / Master of Arts / Although Surrealism in the 21st century is generally considered to be an outdated movement whose most active years took place in the interwar period from 1918 to 1939, there are still echoes and afterglow of Surrealism today, long after the movement's apparent end. The present work explores the works of Louis-René des Forêts, Le Bavard and La Chambre des enfants, in relation to the Surrealist works, Nadja, le "Manifeste du surréalisme," and L'Amour fou, in order to determine the extent to which components of Surrealism such as objective chance, attributes of the conscious and unconscious mind, irrationality, and the interplay of fiction and reality still echo and remain present in fictional literary works today. The results of this analysis indicate that today's fictional literary works are largely infused with many Surrealist components, in some cases directly and in other cases indirectly.

The scope and purpose of this thesis is an evaluation of Camus' literary and philosophical works and their implication to the concept of political revolt. His examination of the origins and effects of modern political revolutions provided insight to the nature of the twentieth century totalitarianism. His ideas also helped to explain the modern emergence of "irrational" terror and political oppression.

Although everyone knows that rational thinking is so important, people still always make some decisions by irrational emotion. Previous studies of making decisions suggest that decision makers mainly maximize their own profit based on economical principle and also with the ability to assess every decision selection¡¦s benefit and cost. They also indicate that most management level decision makers may use analytical, rational and logical ways to analyze every problem they encounter and when it refers to decision making. In our daily life, what do we exactly conform to the suggestion of rational decision making theories? Is irrational decision making with emotional involvement consistent with our daily choice and important decision? People make all kinds of decisions no matter they are important or easy decision for himself /herself or for the others. In other word, decisions build up and make up our life, so it is important to understand what kind of factors affects our step of decision making. Through reviewing of the essays and theses, induction of the interview information, we realize rational and irrational factors intervene into the process of decision making. In terms to decision making, we choose ¡§marriage¡¨ as our research scope, discuss rational and irrational factor affect decision makers¡¦ thinking through the four step of decision making: information collection, development of programs, selection of program and implementation of program. In the step of information collection, individual will search for rational consideration and irrational element. Decision maker will make the decision and influence by irrational factors which include affection, emotion and feeling. When it comes to implementation, some ideas emerge in their mind.

Advances in information technology have amplified issues related to privacy and the disclosure of personal information. New technologies have enabled an explosion in the amount and variety of information created, stored, and potentially shared about people, and there has been a corresponding explosion in privacy-related concerns and conversations in academic and non-academic forums. This dissertation contributes to one such conversation, adding to our understanding of the mechanisms that shape individuals' privacy concerns in the context of disclosure of personal information. Individuals must overcome their information privacy concerns in order for personal information disclosure to take place, but the mechanisms surrounding this process are highly dependent on the context of disclosure. Accordingly, this research seeks to build understanding around the ways in which privacy concerns are mitigated or counterbalanced in three different disclosure contexts. Essay 1, positioned in the e-commerce context, contributes uniquely to an emerging stream of disclosure research that considers irrationality within the privacy disclosure decision process. Essay 2 is focused on a less frequently examined disclosure context - online social networks - and examines the tension between individuals' privacy concerns and their desire for social benefits and personal expression, focusing especially on the social network technology's ability to support impression management behavior. Finally, Essay 3 examines the mitigation of privacy concerns in the context of involuntary disclosure - increasingly common in the modern online environment - wherein the primary goal is to reduce concerns or anxiety regarding the information already disclosed. In comparing disclosure processes across these contexts, this research provides insights regarding consistencies and distinctions among the different domains. Insights gained, both within and across these contexts, are valuable to both privacy researchers and professional stakeholders.

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