Suchergebnisse

"This book is a study of the mathematical ideas and techniques that are important to the two main arms of the area of Financial Mathematics: portfolio optimization and derivative valuation. The text is authored for courses taken by advanced undergraduates, MBA, or other students in quantitative finance programs"--

Intro -- Preface -- Introduction -- Contents -- Part I: The Continuous, the Discrete, and the Infinitesimal in the History of Thought -- Chapter 1: The Continuous and the Discrete in Ancient Greece, the Orient, and the European Middle Ages -- 1.1 Ancient Greece -- The Presocratics -- The Method of Exhaustion -- Plato -- Aristotle -- Epicurus -- The Stoics and Others -- 1.2 Oriental and Islamic Views -- China -- India -- Islamic Thought -- 1.3 The Philosophy of the Continuum in Medieval Europe -- Chapter 2: The Sixteenth and Seventeenth Centuries. The Founding of the Infinitesimal Calculus -- 2.1 The Sixteenth Century -- From Stevin to Kepler -- Galileo and Cavalieri -- 2.2 The 17th Century -- The Cartesian Philosophy -- Infinitesimals and Indivisibles -- Barrow and the Differential Triangle -- Newton -- Leibniz -- Supporters and Critics of Leibniz -- Bayle -- Chapter 3: The Eighteenth and Early Nineteenth Centuries: The Age of Continuity -- 3.1 The Mathematicians -- Euler -- 3.2 From D´Alembert to Carnot -- 3.3 The Philosophers -- Berkeley -- Hume -- Kant -- Hegel -- Chapter 4: The Reduction of the Continuous to the Discrete in the Nineteenth and Early Twentieth Centuries -- 4.1 Bolzano and Cauchy -- 4.2 Riemann -- 4.3 Weierstrass and Dedekind -- 4.4 Cantor -- 4.5 Russell -- 4.6 Hobson´s Choice -- Chapter 5: Dissenting Voices: Divergent Conceptions of the Continuum in the Nineteenth and Early Twentieth Centuries -- 5.1 Du Bois-Reymond -- 5.2 Veronese -- 5.3 Brentano -- 5.4 Peirce -- 5.5 Poincaré -- 5.6 Brouwer -- 5.7 Weyl -- Part II: Continuity and Infinitesimals in Today´s Mathematics -- Chapter 6: Topology -- 6.1 Topological Spaces -- 6.2 Manifolds -- Chapter 7: Category/Topos Theory -- 7.1 Categories and Functors -- 7.2 Pointless Topology -- 7.3 Sheaves and Toposes -- Chapter 8: Nonstandard Analysis.

It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K–8 or K–12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world–oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.

Citation: Gardiner, Mary Maud. Nature's mathematics. Senior thesis, Kansas State Agricultural College, 1893. ; Morse Department of Special Collections ; Introduction: We generally think of nature as being free from all mathematical exactness and regular arrangement – that nature never places herself in straight lines and exact angles. We feel that she is free from square and circles and of all things suggestive of mathematical government; that she is careless and easy and restricted to no such stiff ways as those of man, but picturesque in her irregularity, and purposeless in the promiscuous scattering of her elements over land and sea and sky. Such is the impression of the casual observer. But when we come to study nature more carefully, we find that it is not a miscellaneous collection of things without definite laws or regulations. We find these elements in circles, pentagons, ellipses and other geometrical forms.