...Syllabus Cambridge International A Level Further Mathematics Syllabus code 9231 For examination in June and November 2013 Contents Cambridge A Level Further Mathematics Syllabus code 9231 1. Introduction ..................................................................................... 2 1.1 1.2 1.3 1.4 Why choose Cambridge? Why choose Cambridge International A Level Further Mathematics? Cambridge Advanced International Certificate of Education (AICE) How can I find out more? 2. Assessment at a glance .................................................................. 5 3. Syllabus aims and objectives ........................................................... 7 4. Curriculum content .......................................................................... 8 4.1 Paper 1 4.2 Paper 2 5. Mathematical notation................................................................... 17 6. Resource list .................................................................................. 22 7 Additional information.................................................................... 26 . 7 .1 7 .2 7 .3 7 .4 7 .5 7 .6 Guided learning hours Recommended prior learning Progression Component codes Grading and reporting Resources Cambridge A Level Further Mathematics 9231. Examination in June and November 2013. © UCLES 2010 1. Introduction 1.1 Why choose Cambridge? University of Cambridge International Examinations (CIE) is the world’s largest provider of international...
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...Unit 5 Lecture notes: Microeconomic Theory Econ 629 Department of Economics, Texas A&M University Rodrigo A. Velez∗ b Department of Economics, Texas A&M University, College Station, TX 77843 USA September 9, 2014 Contents 1 Consumer’s Revealed Preference 1.1 Preference maximization . . . . . . . . 1.2 Utility maximization . . . . . . . . . . 1.3 Properties of demand correspondence . 1.4 Continuity of choice . . . . . . . . . . 1.5 Problems . . . . . . . . . . . . . . . . 1.6 Expenditure minimization problem . . 1.7 Problems . . . . . . . . . . . . . . . . 2 Homework assignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 2 2 3 3 5 9 10 1 Consumer’s Revealed Preference What are the testable implications of consumers’ preference maximization? For simplicity, we assume throughout this section that prices are strictly positive. We denote the set of Walrasian budget sets with strictly positive W prices B++ . We assume throughout that X ≡ RL . + ∗ All errors are my own. rvelezca@econmail.tamu.edu 1 1.1 Preference maximization Let be a preference relation on X. Recall from our abstract study of choice that the choices of the agent represented by in a budget set B(p, w) ∈ B W are given by: C (p, w) ≡ {x ∈ B(p, w) : for each y ∈ B(p, w), x y}. 1.2 Utility maximization Suppose that preference is represented...
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...Educational Standards A. G. Com/172 Educational Standards Education is a vital good, like fresh food or medical treatment, and this has been proven since the 1800s. Although it is a responsibility of the individual States, the United States (U.S.) Government assumes the responsibility of deciding what constitutes “education” for school-age children in America (American History Journal, 2010). The American Government holds the sentiment that change to public schools’ curriculum is critical to advancement. This paper will discuss whether or not raising the U.S. Educational standard will give American students an advantage professionally. The History of the United States Education Department The American Educational Department was created in 1867 to gather information on schools and teaching. This information was used to help the United States produce effective schools. For over 130 years the department of education continues to provide information on what works in education to teachers and policy makers. In 1946, The United States Department of Education (ED) began vocational training in high schools. These training programs consisted of agriculture, industrial arts, and home economics, and were focused on better preparing students for future careers. In 1957, the U.S. voiced concerns...
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...Discrete Applied Mathematics 158 (2010) 1644–1649 Contents lists available at ScienceDirect Discrete Applied Mathematics journal homepage: www.elsevier.com/locate/dam The k-in-a-tree problem for graphs of girth at least k W. Liu a , N. Trotignon b,∗ a Université Grenoble 1, Joseph Fourier, France b CNRS, LIAFA, Université Paris 7, Paris Diderot, France article info Article history: Received 10 July 2009 Received in revised form 28 May 2010 Accepted 3 June 2010 Available online 1 July 2010 Keywords: Tree Algorithm Three-in-a-tree k-in-a-tree Girth Induced subgraph abstract For all integers k ≥ 3, we give an O(n4 )-time algorithm for the problem whose instance is a graph G of girth at least k together with k vertices and whose question is ‘‘Does G contains an induced subgraph containing the k vertices and isomorphic to a tree?’’. This directly follows for k = 3 from the three-in-a-tree algorithm of Chudnovsky and Seymour and for k = 4 from a result of Derhy, Picouleau and Trotignon. Here we solve the problem for k ≥ 5. Our algorithm relies on a structural description of graphs of girth at least k that do not contain an induced tree covering k given vertices (k ≥ 5). © 2010 Elsevier B.V. All rights reserved. 1. Introduction Many interesting classes of graphs are defined by forbidding induced subgraphs; see [1] for a survey. This is why the detection of several kinds of induced subgraph is interesting; see [5], where many such...
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...This is page i Printer: Opaque this A Mathematical Introduction to Fluid Mechanics Alexandre Chorin Department of Mathematics University of California, Berkeley Berkeley, California 94720-3840, USA Jerrold E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, California 91125, USA ii iii A Mathematical Introduction to Fluid Mechanics iv Library of Congress Cataloging in Publication Data Chorin, Alexandre A Mathematical Introduction to Fluid Mechanics, Third Edition (Texts in Applied Mathematics) Bibliography: in frontmatter Includes. 1. Fluid dynamics (Mathematics) 2. Dynamics (Mathematics) I. Marsden, Jerrold E. II. Title. III. Series. ISBN 0-387 97300-1 American Mathematics Society (MOS) Subject Classification (1980): 76-01, 76C05, 76D05, 76N05, 76N15 Copyright 1992 by Springer-Verlag Publishing Company, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer-Verlag Publishing Company, Inc., 175 Fifth Avenue, New York, N.Y. 10010. Typesetting and illustrations prepared by June Meyermann, Gregory Kubota, and Wendy McKay The cover illustration shows a computer simulation of a shock diffraction by a pair of cylinders, by John Bell, Phillip Colella, William Crutchfield, Richard Pember, and Michael Welcome...
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...A LINEAR-TIME ALGORITHM FOR EVALUATING SERIES OF SCHUR FUNCTIONS CY CHAN, VESSELIN DRENSKY, ALAN EDELMAN, AND PLAMEN KOEV Abstract. We present a new algorithm for computing all Schur functions sλ(x1, x2, . . . , xn) for all partitions λ of integers not exceeding N in time O(n2K ), where K ≡ #{λ| |λ| ≤ N} N N is the number of those partitions. In particular, this algorithm has optimal complexity for evaluating truncated series of Schur functions such as the hypergeometric function of a matrix argument. 1. Introduction We present a new highly efficient algorithm for computing the finite truncation (for k ≤ N) of the hypergeometric function of a matrix argument X in the complex case: X XN 1 (a1)κ · · · (ap)κ (1) pFq(a , . . . , a1 p; b , . . . , b1 q; X) ≡ · · sκ(x , x , . . . , x1 2 n), Hκ (b1)κ · · · (bq)κ k=0 κ`k where Y (2) (a)κ ≡ (a − i + j) (i,j)∈κ ...
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...Natural Computing Series Series Editors: G. Rozenberg Th. Bäck A.E. Eiben J.N. Kok H.P. Spaink Leiden Center for Natural Computing Advisory Board: S. Amari G. Brassard K.A. De Jong C.C.A.M. Gielen T. Head L. Kari L. Landweber T. Martinetz Z. Michalewicz M.C. Mozer E. Oja G. P˘ un J. Reif H. Rubin A. Salomaa M. Schoenauer H.-P. Schwefel C. Torras a D. Whitley E. Winfree J.M. Zurada For further volumes: www.springer.com/series/4190 Franz Rothlauf Design of Modern Heuristics Principles and Application Prof. Dr. Franz Rothlauf Chair of Information Systems and Business Administration Johannes Gutenberg Universität Mainz Gutenberg School of Management and Economics Jakob-Welder-Weg 9 55099 Mainz Germany rothlauf@uni-mainz.de Series Editors G. Rozenberg (Managing Editor) rozenber@liacs.nl Th. Bäck, J.N. Kok, H.P. Spaink Leiden Center for Natural Computing Leiden University Niels Bohrweg 1 2333 CA Leiden, The Netherlands A.E. Eiben Vrije Universiteit Amsterdam The Netherlands ISSN 1619-7127 Natural Computing Series ISBN 978-3-540-72961-7 e-ISBN 978-3-540-72962-4 DOI 10.1007/978-3-540-72962-4 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011934137 ACM Computing Classification (1998): I.2.8, G.1.6, H.4.2 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations...
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...How to Succeed in Physics (and reduce your workload) Kyle Thomas, Lead Author Luke Bruneaux, Supporting Author Veritas Tutors, LLC How To Succeed in Physics | 2 About the Authors Kyle Thomas Kyle is currently a PhD candidate in the Psychology Department at Harvard University where he studies evolutionary social psychology and serves as a teaching fellow for graduate and undergraduate courses. Kyle has primarily tutored and taught Physics and Organic Chemistry through the UC Santa Cruz peer tutoring program where he became a program administrator. About Veritas Tutors Founded by two Harvard graduates in 2005, Veritas Tutors (www. veritutors.com) is the premiere provider of educational services and products in the Boston area. Offering subject tutoring, standardized test preparation, and admissions consulting, Veritas Tutors is dedicated to providing the best possible instruction to each of its students. Working with educators and consultants from Harvard, Yale, Columbia, MIT, and other elite academic institutions, our students all receive personalized guidance to achieve their goals in and out of the classroom. If you Luke Bruneaux have any questions, comments, or concerns, please contact us at info@ Luke holds a BA Summa Cum Laude from the University of Pennsylvania, veritutors.com or 1-877-265-6582. an MS from the University of Chicago and is working towards a PhD in physics at Harvard University. Luke was awarded a 2011 Derek Bok ...
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...The Web Resource Space Model Web Information Systems Engineering and Internet Technologies Book Series Series Editor: Yanchun Zhang, Victoria University, Australia Editorial Board: Robin Chen, AT&T Umeshwar Dayal, HP Arun Iyengar, IBM Keith Jeffery, Rutherford Appleton Lab Xiaohua Jia, City University of Hong Kong Yahiko Kambayashi† Kyoto University Masaru Kitsuregawa, Tokyo University Qing Li, City University of Hong Kong Philip Yu, IBM Hongjun Lu, HKUST John Mylopoulos, University of Toronto Erich Neuhold, IPSI Tamer Ozsu, Waterloo University Maria Orlowska, DSTC Gultekin Ozsoyoglu, Case Western Reserve University Michael Papazoglou, Tilburg University Marek Rusinkiewicz, Telcordia Technology Stefano Spaccapietra, EPFL Vijay Varadharajan, Macquarie University Marianne Winslett, University of Illinois at Urbana-Champaign Xiaofang Zhou, University of Queensland Other Books in the Series: Semistructured Database Design by Tok Wang Ling, Mong Li Lee, Gillian Dobbie ISBN 0-378-23567-1 Web Content Delivery edited by Xueyan Tang, Jianliang Xu and Samuel T. Chanson ISBN 978-0-387-24356-6 Web Information Extraction and Integration by Marek Kowalkiewicz, Maria E. Orlowska, Tomasz Kaczmarek and Witold Abramowicz ISBN 978-0-387-72769-1 FORTHCOMING The Web Resource Space Model Hai Zhuge Chinese Academy of Sciences Hai Zhuge Key Lab of Intelligent Information Processing Institute of Computing Technology Chinese Academy of Sciences P.O. Box 2704-28 No. 6 Science South...
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...Notes on Probability Peter J. Cameron ii Preface Here are the course lecture notes for the course MAS108, Probability I, at Queen Mary, University of London, taken by most Mathematics students and some others in the first semester. The description of the course is as follows: This course introduces the basic notions of probability theory and develops them to the stage where one can begin to use probabilistic ideas in statistical inference and modelling, and the study of stochastic processes. Probability axioms. Conditional probability and independence. Discrete random variables and their distributions. Continuous distributions. Joint distributions. Independence. Expectations. Mean, variance, covariance, correlation. Limiting distributions. The syllabus is as follows: 1. Basic notions of probability. Sample spaces, events, relative frequency, probability axioms. 2. Finite sample spaces. Methods of enumeration. Combinatorial probability. 3. Conditional probability. Theorem of total probability. Bayes theorem. 4. Independence of two events. Mutual independence of n events. Sampling with and without replacement. 5. Random variables. Univariate distributions - discrete, continuous, mixed. Standard distributions - hypergeometric, binomial, geometric, Poisson, uniform, normal, exponential. Probability mass function, density function, distribution function. Probabilities of events in terms of random variables. 6. Transformations of a single random variable. Mean, variance, median,...
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...logistic model in the late previous century is reminded. We conclude by referring to some generalizations of the logistic model, which were used to describe growth and diffusion processes in the context of technological innovation, and for which the author studied the chaotic behaviour by means of a series of computer experiments, performed in the eighties of last century by means of the then emerging “micro-computer” technology. 1 P.-F. Verhulst and the Royal Military Academy in Brussels In the year 1844, at the age of 40, when Pierre-Fran¸ois Verhulst on November c 30 presented his contribution to the “M´moires de l’Acad´mie” of the young e e Belgian nation, a paper which was published the next year in “tome XVIII” with the title: “Recherches math´matiques sur la loi d’accroissement de la e population” (mathematical investigations of the law of population growth), he did certainly not know that his work would be the starting point for further research by Raymond Pearl and Lowell J. Reed [10, 11], by the famous A.-J. Lotka [8] and independently by Volterra [16] and later by V.A. Kostitzin [5], in the fields of mathematical biology, biometry, and demography. It was in these M´moires that he introduced a growth model for a...
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...MULTIMEDIA LEARNING MATERIALS FROM THE EXPERTS PRODUCT CATALOGUE JANUARY 2012–JUNE 2012 BPP Learning Media has been producing high quality study materials for more than 30 years. We are the publisher of choice for students, tuition providers, companies and professional bodies in more than 150 countries worldwide. Using the expertise of our specialist authors and tutors, we have developed a range of innovative study aids in a variety of formats including web delivery, audio-visual products, CD-ROMs and books. Our products are designed to support a variety of different learning styles, ensuring all students make the most of their study time and successfully achieve their learning outcomes. This catalogue is your comprehensive guide to the qualifications we publish for and the learning materials we offer in support of those qualifications, together with our UK and overseas stockists directory. CONNECT WITH US bpp.com/learningmedia twitter.com/bpplm LinkedIn: BPP Learning Media Clients contents 04 ABoUt Us WhaT’s neW aT 12 BPP LeaRning MeDia 14 insTiTUTe OF LeaDeRshiP anD ManageMenT (iLM) 15 MeDiCaL seRies assOCiaTiOn OF BUsiness exeCUTives (aBe) 16 a BRanD neW 17 aPPROaCh a neW iDenTiTY 17 a neW PROPOsiTiOn 18 inFORMaTiOn FOR BOOKseLLeRs 20 WhOLesaLe ORDeRs 23 BeCOMe a sTOCKisT TUiTiOn PROviDeRs 24 TeRMs anD COnDiTiOns OF saLe RegiOnaL saLes ManageRs 24 CUsTOMeR seRviCes PRinTeD 25 PRODUCTs 26 sTUDY TexTs PRaCTiCe & RevisiOn KiTs 27 PassCaRDs 28 eLeCTROniC PRODUCTs...
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...A FIRST COURSE IN PROBABILITY This page intentionally left blank A FIRST COURSE IN PROBABILITY Eighth Edition Sheldon Ross University of Southern California Upper Saddle River, New Jersey 07458 Library of Congress Cataloging-in-Publication Data Ross, Sheldon M. A first course in probability / Sheldon Ross. — 8th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-13-603313-4 ISBN-10: 0-13-603313-X 1. Probabilities—Textbooks. I. Title. QA273.R83 2010 519.2—dc22 2008033720 Editor in Chief, Mathematics and Statistics: Deirdre Lynch Senior Project Editor: Rachel S. Reeve Assistant Editor: Christina Lepre Editorial Assistant: Dana Jones Project Manager: Robert S. Merenoff Associate Managing Editor: Bayani Mendoza de Leon Senior Managing Editor: Linda Mihatov Behrens Senior Operations Supervisor: Diane Peirano Marketing Assistant: Kathleen DeChavez Creative Director: Jayne Conte Art Director/Designer: Bruce Kenselaar AV Project Manager: Thomas Benfatti Compositor: Integra Software Services Pvt. Ltd, Pondicherry, India Cover Image Credit: Getty Images, Inc. © 2010, 2006, 2002, 1998, 1994, 1988, 1984, 1976 by Pearson Education, Inc., Pearson Prentice Hall Pearson Education, Inc. Upper Saddle River, NJ 07458 All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Pearson Prentice Hall™ is a trademark of Pearson Education, Inc...
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...А.Н. АНДРЕЕВА МАРКЕТИНГОВЫЕ КОММУНИКАЦИИ ПРОГРАММА КУРСА АННОТАЦИЯ КУРСА Курс «Маркетинговые коммуникации» рассматривает и анализирует различные коммуникационные инструменты современного маркетинга и их комбинации (рекламу, PR, стимулирование сбыта, рекламу на местах продажи и т.д.) в контексте маркетинговой ориентации деятельности компании. Основной акцент курса сделан на понимание и создание эффективного плана маркетинговых коммуникаций, с ясными и последовательными целями и задачами, а также критериями оценки коммуникационных программ в маркетинге. Курс является авторским и предполагает глубокое вовлечение студентов, специализирующихся в маркетинге, в процесс выбора инструментов маркетинговых коммуникаций в зависимости от целей и задач маркетинга организации. Цель курса • Формирование у студентов целостного представления о системе маркетинговых коммуникаций входящих в состав комплекса маркетинга (маркетинг-микса). Задачи курса • Изучение и анализ основных инструментов маркетинговых коммуникаций: реклама, связи с общественностью, стимулирование сбыта, прямой маркетинг, мерчендайзинг и POS-материалы, маркетинг событий, продакт плейсмент и т.д. • Анализ и создание базы для принятия решений в сфере бюджетирования коммуникационных маркетинговых программ. • Формирование у студентов знаний и навыков планирования, управления и оценки коммуникационных программ (кампаний) в сфере маркетинга, направленных на эффективное продвижение продуктов (услуг) организации...
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...Some Problems in Symmetric and Asymmetric Cryptography A thesis submitted for the partial fulfillment of the degree of Doctor of Philosophy in Mathematics By SANTOSH KUMAR YADAV Under the supervision of Prof. Sunder Lal and Prof. S. C. Arora DEPARTMENT OF MATHEMATICS DR. B. R. AMBEDKAR UNIVERSITY, AGRA (FORMERLY AGRA UNIVERSITY) 2010 *Sanskrit verse dating back to the pre-Christian era Dedicated to my Teachers, Friends, Students and Family Members DECLARATION I do hereby declare that the present research work has been carried out by me under the supervision of Prof. Sunder Lal and Prof. S. C. Arora. This work has not been submitted elsewhere for any other degree, diploma, fellowship or any other similar title. Santosh Kumar Yadav Research Scholar CERTIFICATE This is to certify that the thesis entitled “Some Problems in Symmetric and Asymmetric Cryptography” submitted to Dr. B.R.Ambedkar University, Agra for the degree of Doctor of Philosophy by Mr. Santosh Kumar Yadav, is a bonafide record of research work done by him under our supervision. To the best of our knowledge, this thesis has not previously formed the basis for the award to any candidate of any degree, diploma, fellowship or any other similar title and the work has not been submitted to any university or institution, for the award of any other degree. S. C. ARORA SUNDER LAL (Co-supervisor) (Supervisor) Professor Professor of Mathematics, and Department of Mathematics Pro-Vice Chancellor ...
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