Gottfried Wilhelm Leibniz English Version
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Libertarianism, Culture, and Personal Predispositions
Undergraduate Journal of Psychology 22 Libertarianism, Culture, and Personal Predispositions Ida Hepsø, Scarlet Hernandez, Shir Offsey, & Katherine White Kennesaw State University Abstract The United States has exhibited two potentially connected trends – increasing individualism and increasing interest in libertarian ideology. Previous research on libertarian ideology found higher levels of individualism among libertarians, and cross-cultural research has tied greater individualism to making dispositional attributions and lower altruistic tendencies. Given this, we expected to observe positive correlations between the following variables in the present research: individualism and endorsement of libertarianism, individualism and dispositional attributions, and endorsement of libertarianism and dispositional attributions. We also expected to observe negative correlations between libertarianism and altruism, dispositional attributions and altruism, and individualism and altruism. Survey results from 252 participants confirmed a positive correlation between individualism and libertarianism, a marginally significant positive correlation between libertarianism and dispositional attributions, and a negative correlation between individualism and altruism. These results confirm the connection between libertarianism and individualism observed in previous research and present several intriguing questions for future research on libertarian ideology. Key Words: Libertarianism, individualism, altruism, attributions individualistic, made apparent -
Learning/Teaching Philosophy in Sign Language As a Cultural Issue
DOI: 10.15503/jecs20131-9-19 Journal of Education Culture and Society No. 1_2013 9 Learning/teaching philosophy in sign language as a cultural issue Maria de Fátima Sá Correia [email protected] Orquídea Coelho [email protected] António Magalhães [email protected] Andrea Benvenuto [email protected] Abstract This paper is about the process of learning/teaching philosophy in a class of deaf stu- dents. It starts with a presentation of Portuguese Sign Language that, as with other sign lan- guages, is recognized as a language on equal terms with vocal languages. However, in spite of the recognition of that identity, sign languages have specifi city related to the quadrimodal way of their production, and iconicity is an exclusive quality. Next, it will be argued that according to linguistic relativism - even in its weak version - language is a mould of thought. The idea of Philosophy is then discussed as an area of knowledge in which the author and the language of its production are always present. Finally, it is argued that learning/teaching Philosophy in Sign Language in a class of deaf students is linked to deaf culture and it is not merely a way of overcoming diffi culties with the spoken language. Key words: Bilingual education, Deaf culture, Learning-teaching Philosophy, Portuguese Sign Language. According to Portuguese law (Decreto-Lei 3/2008 de 7 de Janeiro de 2008 e Law 21 de 12 de Maio de 2008), in the “escolas de referência para a educação bilingue de alunos surdos” (EREBAS) (reference schools for bilingual education of deaf stu- dents) deaf students have to attend classes in Portuguese Sign Language. -
EMMA GOLDMAN, ANARCHISM, and the “AMERICAN DREAM” by Christina Samons
AN AMERICA THAT COULD BE: EMMA GOLDMAN, ANARCHISM, AND THE “AMERICAN DREAM” By Christina Samons The so-called “Gilded Age,” 1865-1901, was a period in American his tory characterized by great progress, but also of great turmoil. The evolving social, political, and economic climate challenged the way of life that had existed in pre-Civil War America as European immigration rose alongside the appearance of the United States’ first big businesses and factories.1 One figure emerges from this era in American history as a forerunner of progressive thought: Emma Goldman. Responding, in part, to the transformations that occurred during the Gilded Age, Goldman gained notoriety as an outspoken advocate of anarchism in speeches throughout the United States and through published essays and pamphlets in anarchist newspapers. Years later, she would synthe size her ideas in collections of essays such as Anarchism and Other Essays, first published in 1917. The purpose of this paper is to contextualize Emma Goldman’s anarchist theory by placing it firmly within the economic, social, and 1 Alan M. Kraut, The Huddled Masses: The Immigrant in American Society, 1880 1921 (Wheeling, IL: Harlan Davidson, 2001), 14. 82 Christina Samons political reality of turn-of-the-twentieth-century America while dem onstrating that her theory is based in a critique of the concept of the “American Dream.” To Goldman, American society had drifted away from the ideal of the “American Dream” due to the institutionalization of exploitation within all aspects of social and political life—namely, economics, religion, and law. The first section of this paper will give a brief account of Emma Goldman’s position within American history at the turn of the twentieth century. -
Notes on Calculus II Integral Calculus Miguel A. Lerma
Notes on Calculus II Integral Calculus Miguel A. Lerma November 22, 2002 Contents Introduction 5 Chapter 1. Integrals 6 1.1. Areas and Distances. The Definite Integral 6 1.2. The Evaluation Theorem 11 1.3. The Fundamental Theorem of Calculus 14 1.4. The Substitution Rule 16 1.5. Integration by Parts 21 1.6. Trigonometric Integrals and Trigonometric Substitutions 26 1.7. Partial Fractions 32 1.8. Integration using Tables and CAS 39 1.9. Numerical Integration 41 1.10. Improper Integrals 46 Chapter 2. Applications of Integration 50 2.1. More about Areas 50 2.2. Volumes 52 2.3. Arc Length, Parametric Curves 57 2.4. Average Value of a Function (Mean Value Theorem) 61 2.5. Applications to Physics and Engineering 63 2.6. Probability 69 Chapter 3. Differential Equations 74 3.1. Differential Equations and Separable Equations 74 3.2. Directional Fields and Euler’s Method 78 3.3. Exponential Growth and Decay 80 Chapter 4. Infinite Sequences and Series 83 4.1. Sequences 83 4.2. Series 88 4.3. The Integral and Comparison Tests 92 4.4. Other Convergence Tests 96 4.5. Power Series 98 4.6. Representation of Functions as Power Series 100 4.7. Taylor and MacLaurin Series 103 3 CONTENTS 4 4.8. Applications of Taylor Polynomials 109 Appendix A. Hyperbolic Functions 113 A.1. Hyperbolic Functions 113 Appendix B. Various Formulas 118 B.1. Summation Formulas 118 Appendix C. Table of Integrals 119 Introduction These notes are intended to be a summary of the main ideas in course MATH 214-2: Integral Calculus. -
Analysis of Functions of a Single Variable a Detailed Development
ANALYSIS OF FUNCTIONS OF A SINGLE VARIABLE A DETAILED DEVELOPMENT LAWRENCE W. BAGGETT University of Colorado OCTOBER 29, 2006 2 For Christy My Light i PREFACE I have written this book primarily for serious and talented mathematics scholars , seniors or first-year graduate students, who by the time they finish their schooling should have had the opportunity to study in some detail the great discoveries of our subject. What did we know and how and when did we know it? I hope this book is useful toward that goal, especially when it comes to the great achievements of that part of mathematics known as analysis. I have tried to write a complete and thorough account of the elementary theories of functions of a single real variable and functions of a single complex variable. Separating these two subjects does not at all jive with their development historically, and to me it seems unnecessary and potentially confusing to do so. On the other hand, functions of several variables seems to me to be a very different kettle of fish, so I have decided to limit this book by concentrating on one variable at a time. Everyone is taught (told) in school that the area of a circle is given by the formula A = πr2: We are also told that the product of two negatives is a positive, that you cant trisect an angle, and that the square root of 2 is irrational. Students of natural sciences learn that eiπ = 1 and that sin2 + cos2 = 1: More sophisticated students are taught the Fundamental− Theorem of calculus and the Fundamental Theorem of Algebra. -
Variables in Mathematics Education
Variables in Mathematics Education Susanna S. Epp DePaul University, Department of Mathematical Sciences, Chicago, IL 60614, USA http://www.springer.com/lncs Abstract. This paper suggests that consistently referring to variables as placeholders is an effective countermeasure for addressing a number of the difficulties students’ encounter in learning mathematics. The sug- gestion is supported by examples discussing ways in which variables are used to express unknown quantities, define functions and express other universal statements, and serve as generic elements in mathematical dis- course. In addition, making greater use of the term “dummy variable” and phrasing statements both with and without variables may help stu- dents avoid mistakes that result from misinterpreting the scope of a bound variable. Keywords: variable, bound variable, mathematics education, placeholder. 1 Introduction Variables are of critical importance in mathematics. For instance, Felix Klein wrote in 1908 that “one may well declare that real mathematics begins with operations with letters,”[3] and Alfred Tarski wrote in 1941 that “the invention of variables constitutes a turning point in the history of mathematics.”[5] In 1911, A. N. Whitehead expressly linked the concepts of variables and quantification to their expressions in informal English when he wrote: “The ideas of ‘any’ and ‘some’ are introduced to algebra by the use of letters. it was not till within the last few years that it has been realized how fundamental any and some are to the very nature of mathematics.”[6] There is a question, however, about how to describe the use of variables in mathematics instruction and even what word to use for them. -
BY PLATO• ARISTOTLE • .AND AQUINAS I
i / REF1,l!;CTit.>NS ON ECONOMIC PROBLEMS / BY PLATO• ARISTOTLE • .AND AQUINAS ii ~FLECTIONS ON ECONO:MIC PROBLEMS 1 BY PLA'I'O, ARISTOTLE, JJJD AQUINAS, By EUGENE LAIDIBEL ,,SWEARINGEN Bachelor of Science Oklahoma Agricultural and Mechanical Collage Stillwater, Oklahoma 1941 Submitted to the Depertmeut of Economics Oklahoma Agricultural and Mechanical College In Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE 1948 iii f.. 'I. I ···· i·: ,\ H.: :. :· ··: ! • • ~ ' , ~ • • !·:.· : i_ ·, 1r 1i1. cr~~rJ3t L l: i{ ,\ I~ Y , '•T •)() 1 0 ,1 8 API-'HOV~D BY: .J ,.· 1.., J l.;"t .. ---- -··- - ·- ______.,.. I 7 -.. JI J ~ L / \ l v·~~ u ' ~) (;_,LA { 7 {- ' r ~ (\.7 __\ _. ...A'_ ..;f_ ../-_" ...._!)_.... ..." ___ ......._ ·;...;;; ··-----/ 1--.,i-----' ~-.._.._ :_..(__,,---- ....... Member of the Report Committee 1..j lj:,;7 (\ - . "'·- -· _ .,. ·--'--C. r, .~-}, .~- Q_ · -~ Q.- 1Head of the Department . · ~ Dean of the Graduate School 502 04 0 .~ -,. iv . r l Preface The purpose and plan of this report are set out in the Introduction. Here, I only wish to express my gratitude to Professor Russell H. Baugh who has helped me greatly in the preparation of this report by discussing the various subjects as they were in the process of being prepared. I am very much indebted to Dr. Harold D. Hantz for his commentaries on the report and for the inspiration which his classes in Philosophy have furnished me as I attempted to correlate some of the material found in these two fields, Ecor!.Omics and Philosophy. I should like also to acknowledge that I owe my first introduction into the relationships of Economics and Philosophy to Dean Raymond Thomas, and his com~ents on this report have been of great value. -
A Brief Tour of Vector Calculus
A BRIEF TOUR OF VECTOR CALCULUS A. HAVENS Contents 0 Prelude ii 1 Directional Derivatives, the Gradient and the Del Operator 1 1.1 Conceptual Review: Directional Derivatives and the Gradient........... 1 1.2 The Gradient as a Vector Field............................ 5 1.3 The Gradient Flow and Critical Points ....................... 10 1.4 The Del Operator and the Gradient in Other Coordinates*............ 17 1.5 Problems........................................ 21 2 Vector Fields in Low Dimensions 26 2 3 2.1 General Vector Fields in Domains of R and R . 26 2.2 Flows and Integral Curves .............................. 31 2.3 Conservative Vector Fields and Potentials...................... 32 2.4 Vector Fields from Frames*.............................. 37 2.5 Divergence, Curl, Jacobians, and the Laplacian................... 41 2.6 Parametrized Surfaces and Coordinate Vector Fields*............... 48 2.7 Tangent Vectors, Normal Vectors, and Orientations*................ 52 2.8 Problems........................................ 58 3 Line Integrals 66 3.1 Defining Scalar Line Integrals............................. 66 3.2 Line Integrals in Vector Fields ............................ 75 3.3 Work in a Force Field................................. 78 3.4 The Fundamental Theorem of Line Integrals .................... 79 3.5 Motion in Conservative Force Fields Conserves Energy .............. 81 3.6 Path Independence and Corollaries of the Fundamental Theorem......... 82 3.7 Green's Theorem.................................... 84 3.8 Problems........................................ 89 4 Surface Integrals, Flux, and Fundamental Theorems 93 4.1 Surface Integrals of Scalar Fields........................... 93 4.2 Flux........................................... 96 4.3 The Gradient, Divergence, and Curl Operators Via Limits* . 103 4.4 The Stokes-Kelvin Theorem..............................108 4.5 The Divergence Theorem ...............................112 4.6 Problems........................................114 List of Figures 117 i 11/14/19 Multivariate Calculus: Vector Calculus Havens 0. -
Philosophy of Science -----Paulk
PHILOSOPHY OF SCIENCE -----PAULK. FEYERABEND----- However, it has also a quite decisive role in building the new science and in defending new theories against their well-entrenched predecessors. For example, this philosophy plays a most important part in the arguments about the Copernican system, in the development of optics, and in the Philosophy ofScience: A Subject with construction of a new and non-Aristotelian dynamics. Almost every work of Galileo is a mixture of philosophical, mathematical, and physical prin~ a Great Past ciples which collaborate intimately without giving the impression of in coherence. This is the heroic time of the scientific philosophy. The new philosophy is not content just to mirror a science that develops independ ently of it; nor is it so distant as to deal just with alternative philosophies. It plays an essential role in building up the new science that was to replace 1. While it should be possible, in a free society, to introduce, to ex the earlier doctrines.1 pound, to make propaganda for any subject, however absurd and however 3. Now it is interesting to see how this active and critical philosophy is immoral, to publish books and articles, to give lectures on any topic, it gradually replaced by a more conservative creed, how the new creed gener must also be possible to examine what is being expounded by reference, ates technical problems of its own which are in no way related to specific not to the internal standards of the subject (which may be but the method scientific problems (Hurne), and how there arises a special subject that according to which a particular madness is being pursued), but to stan codifies science without acting back on it (Kant). -
Differentiation Rules (Differential Calculus)
Differentiation Rules (Differential Calculus) 1. Notation The derivative of a function f with respect to one independent variable (usually x or t) is a function that will be denoted by D f . Note that f (x) and (D f )(x) are the values of these functions at x. 2. Alternate Notations for (D f )(x) d d f (x) d f 0 (1) For functions f in one variable, x, alternate notations are: Dx f (x), dx f (x), dx , dx (x), f (x), f (x). The “(x)” part might be dropped although technically this changes the meaning: f is the name of a function, dy 0 whereas f (x) is the value of it at x. If y = f (x), then Dxy, dx , y , etc. can be used. If the variable t represents time then Dt f can be written f˙. The differential, “d f ”, and the change in f ,“D f ”, are related to the derivative but have special meanings and are never used to indicate ordinary differentiation. dy 0 Historical note: Newton used y,˙ while Leibniz used dx . About a century later Lagrange introduced y and Arbogast introduced the operator notation D. 3. Domains The domain of D f is always a subset of the domain of f . The conventional domain of f , if f (x) is given by an algebraic expression, is all values of x for which the expression is defined and results in a real number. If f has the conventional domain, then D f usually, but not always, has conventional domain. Exceptions are noted below. -
Vol. 62, No. 3; September 1984 PUTNAM's PARADOX David Lewis Introduction. Hilary Putnam Has Devised a Bomb That Threatens To
Australasian Journal of Philosophy Vol. 62, No. 3; September 1984 PUTNAM'S PARADOX David Lewis Introduction. Hilary Putnam has devised a bomb that threatens to devastate the realist philosophy we know and love. 1 He explains how he has learned to stop worrying and love the bomb. He welcomes the new order that it would bring. (RT&H, Preface) But we who still live in the target area do not agree. The bomb must be banned. Putnam's thesis (the bomb) is that, in virtue of considerations from the theory of reference, it makes no sense to suppose that an empirically ideal theory, as verified as can be, might nevertheless be false because the world is not the way the theory says it is. The reason given is, roughly, that there is no semantic glue to stick our words onto their referents, and so reference is very much up for grabs; but there is one force constraining reference, and that is our intention to refer in such a way that we come out right; and there is no countervailing force; and the world, no matter what it is like (almost), will afford some scheme of reference that makes us come out right; so how can we fail to come out right? 2 Putnam's thesis is incredible. We are in the presence of paradox, as surely as when we meet the man who offers us a proof that there are no people, and in particular that he himself does not exist. 3 It is out of the question to follow the argument where it leads. -
Pioneers in Optics: Christiaan Huygens
Downloaded from Microscopy Pioneers https://www.cambridge.org/core Pioneers in Optics: Christiaan Huygens Eric Clark From the website Molecular Expressions created by the late Michael Davidson and now maintained by Eric Clark, National Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306 . IP address: [email protected] 170.106.33.22 Christiaan Huygens reliability and accuracy. The first watch using this principle (1629–1695) was finished in 1675, whereupon it was promptly presented , on Christiaan Huygens was a to his sponsor, King Louis XIV. 29 Sep 2021 at 16:11:10 brilliant Dutch mathematician, In 1681, Huygens returned to Holland where he began physicist, and astronomer who lived to construct optical lenses with extremely large focal lengths, during the seventeenth century, a which were eventually presented to the Royal Society of period sometimes referred to as the London, where they remain today. Continuing along this line Scientific Revolution. Huygens, a of work, Huygens perfected his skills in lens grinding and highly gifted theoretical and experi- subsequently invented the achromatic eyepiece that bears his , subject to the Cambridge Core terms of use, available at mental scientist, is best known name and is still in widespread use today. for his work on the theories of Huygens left Holland in 1689, and ventured to London centrifugal force, the wave theory of where he became acquainted with Sir Isaac Newton and began light, and the pendulum clock. to study Newton’s theories on classical physics. Although it At an early age, Huygens began seems Huygens was duly impressed with Newton’s work, he work in advanced mathematics was still very skeptical about any theory that did not explain by attempting to disprove several theories established by gravitation by mechanical means.