Download and read online Mathematical Olympiad in China 2009 2010 in PDF and EPUB The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in the IMO 21 times since 1985 and has won the top ranking for countries 14 times, with a multitude of golds for individual students. The six students China has sent every year were selected from 20 to 30 students among approximately 130 students who took part in the annual China Mathematical Competition during the winter months. This volume of comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2009 to 2010. Mathematical Olympiad problems with solutions for the years 2002–2008 appear in an earlier volume, Mathematical Olympiad in China. Contents:2008–2009 China Mathematical Competition2008–2009 China Mathematical Competition (Complementary Test)2009–2010 China Mathematical Olympiad2009–2010 China National Team Selection Test2008–2009 China Girls' Mathematical Olympiad2008–2009 China Western Mathematical Olympiad2009–2010 China Southeastern Mathematical Olympiad2009–2010 International Mathematical Olympiad Readership: Mathematics students, school teachers, college lecturers, university professors; mathematics enthusiasts. Keywords:Mathematics;International Mathematical Olympiad;China;Mathematics ProblemsReviews: “The book's organization where solutions immediately follow problems, should prove a convenience for inspiring math teachers with limited Olympiad experience. ” Mathematical Association of America
Download and read online Mathematical Olympiad in China in PDF and EPUB The International Mathematical Olympiad (IMO) is a competition for high school students. China has taken part in IMO twenty times since 1985 and has won the top ranking for countries thirteen times, with a multitude of golds for individual students. The 6 students China sent every year were selected from 20 to 30 students among approximately 130 students who take part in the China Mathematical Competition during the winter months. This volume comprises a collection of original problems with solutions that China used to train their Olympiad team in the years from 2003 to 2006.
Download and read online Lecture Notes on Mathematical Olympiad Courses in PDF and EPUB Olympiad mathematics is not a collection of techniques of solving mathematical problems but a system for advancing mathematical education. This book is based on the lecture notes of the mathematical Olympiad training courses conducted by the author in Singapore. Its scope and depth not only covers and exceeds the usual syllabus, but introduces a variety concepts and methods in modern mathematics. In each lecture, the concepts, theories and methods are taken as the core. The examples are served to explain and enrich their intension and to indicate their applications. Besides, appropriate number of test questions is available for reader''s practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so that readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions are from many countries, e.g. China, Russia, USA, Singapore, etc. In particular, the reader can find many questions from China, if he is interested in understanding mathematical Olympiad in China. This book serves as a useful textbook of mathematical Olympiad courses, or as a reference book for related teachers and researchers. Errata(s). Errata. Sample Chapter(s). Lecture 16: Quadratic Surd Expressions and Their Operations (183k). Request Inspection Copy. Contents.: Volume 2: Congruence of Integers; Decimal Representation of Integers; Pigeonhole Principle; Linear Inequality and System of Linear Inequalities; Inequalities with Absolute Values; Geometric Inequalities; Solutions to Testing Questions; and other chapters. Readership: Mathematics students, school teachers, college lecturers, university professors; mathematics enthusiasts.
Download and read online The Art of Problem Solving Volume 1 in PDF and EPUB "...offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover
Download and read online A First Step to Mathematical Olympiad Problems in PDF and EPUB See also A SECOND STEP TO MATHEMATICAL OLYMPIAD PROBLEMS The International Mathematical Olympiad (IMO) is an annual international mathematics competition held for pre-collegiate students. It is also the oldest of the international science olympiads, and competition for places is particularly fierce. This book is an amalgamation of the first 8 of 15 booklets originally produced to guide students intending to contend for placement on their country's IMO team. The material contained in this book provides an introduction to the main mathematical topics covered in the IMO, which are: Combinatorics, Geometry and Number Theory. In addition, there is a special emphasis on how to approach unseen questions in Mathematics, and model the writing of proofs. Full answers are given to all questions. Though A First Step to Mathematical Olympiad Problems is written from the perspective of a mathematician, it is written in a way that makes it easily comprehensible to adolescents. This book is also a must-read for coaches and instructors of mathematical competitions.
Download and read online Investigating the Pedagogy of Mathematics in PDF and EPUB This book responds to the growing interest in the scholarship of mathematics teaching; over the last 20 years the importance of teachers' knowledge for effective teaching has been internationally recognised. For many mathematics teachers, the critical link between practice and knowledge is implied rather than explicitly understood or expressed. This means it can be difficult to assess and thus develop teachers' professional knowledge. The present book is based on two studies investigating exactly how teachers developed their pedagogical knowledge in mathematics from different sources. It describes: how teachers' own teaching experience and reflection, and their daily exchanges with colleagues, are the most important sources of knowledge,how important in-service training and organized professional activities are,how teachers' previous experiences as students, their pre-service training and their reading of professional literature have less influence on their professional knowledge. The findings in this book have significant implications for teachers, teacher educators, school administrators and educational researchers, as well as policy-makers and school practitioners worldwide. Contents:The Chicago Study:IntroductionReview of the LiteratureA Conceptual Framework of the StudyResearch Design and ProceduresFindings of the Chicago Study (I): Pedagogical Curricular KnowledgeFindings of the Chicago Study (II): Pedagogical Content KnowledgeFindings of the Chicago Study (III): Pedagogical Instructional KnowledgeFindings of the Chicago Study (IV): Some Other IssuesConclusions, Implications, and RecommendationsThe Singapore Study:The Singapore StudyComparison and Conclusion Readership: Teachers, teacher educators, school administrators, educational policy-makers and non-experts interested in education issues. Key Features:Focus on key issues of education: The book presents research in one of the most important issues in contemporary educational reform and development — how teachers develop their professional knowledgeRigorous and distinctive research methodology: The research presented in the book has three major distinctions from other published work in the concerned area. 1. More specific: it directly addresses the question of how teachers develop their knowledge in the domain of pedagogy; 2. More systematic: it takes into account the whole life of teachers, including their pre-service and in-service experiences, not just a special period of teachers' life or a special source of teachers' knowledge; 3. More representative: the research subjects consist of a substantial number of teachers with a wide range of experiences, and the selection of the sample is random in main stagesSignificance value: The research presented in the book has significance in both theory and practice concerning teacher professional knowledge. In addition, as the main body of the book is based on the authors' PhD study, the book is also valuable for doctoral students in relevant areas in their graduate study in terms of both content and methodKeywords:Mathematics Education;Mathematics Teachers;Teacher Education;Teacher Professional Development;Pedagogy of Mathematics;Pedagogical Content KnowledgeReviews: “Given the reforms in mathematics education, the issue of how teachers develop their knowledge has become a big challenge for practitioners as well as for researchers. While many people believe that teachers teach as they were taught, Prof Fan shows that the phenomenon is much more complex. This book is an important source for students, teachers, teacher educators, school administrators, and policy-makers.” Prof. Zemira Mevarech Dean of Faculty of Social Sciences, Bar-Ilan University and Former Chief Scientist of the Ministry of Education, Israel
Download and read online Selected Problems of the Vietnamese Mathematical Olympiad 1962 2009 in PDF and EPUB Vietnam has actively organized the National Competition in Mathematics and since 1962, the Vietnamese Mathematical Olympiad (VMO). On the global stage, Vietnam has also competed in the International Mathematical Olympiad (IMO) since 1974 and constantly emerged as one of the top ten. To inspire and further challenge readers, we have gathered in this book selected problems of the VMO from 1962 to 2008. A number of Selection Test problems are also included to aid in the formation and training of a national team for IMO. The book is highly useful for high school students and teachers, coaches and instructors preparing for mathematical olympiads, as well as non-experts simply interested in having the edge over their opponents in mathematical competitions.
Download and read online Euclidean Geometry in Mathematical Olympiads in PDF and EPUB This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.
Download and read online Problems of Number Theory in Mathematical Competitions in PDF and EPUB Number theory is an important research field of mathematics. In mathematical competitions, problems of elementary number theory occur frequently. These problems use little knowledge and have many variations. They are flexible and diverse. In this book, the author introduces some basic concepts and methods in elementary number theory via problems in mathematical competitions. Readers are encouraged to try to solve the problems by themselves before they read the given solutions of examples. Only in this way can they truly appreciate the tricks of problem-solving.
Download and read online Discover Probability in PDF and EPUB This is a unique book which explains the concept of probability and its applications with almost no mathematics. As the title states, the reader will discover the concept of probability, learn how to use it, and be made aware of some misuses of, and sometimes even abuse of, probability. The reader will come to know that a basic knowledge of probability is useful in life. It is a novel, self-teaching book that is easy to read, oftentimes entertaining and full of useful information on both probability and information theory. The style is reader-friendly. It will appeal to anyone who is interested in the "laws" that govern our daily lives. The detailed examples in the book are taken from daily life which anyone can identify with. The last section introduces the Shannon measure of information and its relationship to probabilities.
Download and read online The IMO Compendium in PDF and EPUB "The IMO Compendium" is the ultimate collection of challenging high-school-level mathematics problems and is an invaluable resource not only for high-school students preparing for mathematics competitions, but for anyone who loves and appreciates mathematics. The International Mathematical Olympiad (IMO), nearing its 50th anniversary, has become the most popular and prestigious competition for high-school students interested in mathematics. Only six students from each participating country are given the honor of participating in this competition every year. The IMO represents not only a great opportunity to tackle interesting and challenging mathematics problems, it also offers a way for high school students to measure up with students from the rest of the world. Until the first edition of this book appearing in 2006, it has been almost impossible to obtain a complete collection of the problems proposed at the IMO in book form. "The IMO Compendium" is the result of a collaboration between four former IMO participants from Yugoslavia, now Serbia and Montenegro, to rescue these problems from old and scattered manuscripts, and produce the ultimate source of IMO practice problems. This book attempts to gather all the problems and solutions appearing on the IMO through 2009. This second edition contains 143 new problems, picking up where the 1959-2004 edition has left off.
Download and read online Inequalities in PDF and EPUB This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
Download and read online Mathematical Thinking in PDF and EPUB Developing mathematical thinking is one of major aims of mathematics education. In mathematics education research, there are a number of researches which describe what it is and how we can observe in experimental research. However, teachers have difficulties developing it in the classrooms. This book is the result of lesson studies over the past 50 years. It describes three perspectives of mathematical thinking: Mathematical Attitude (Minds set), Mathematical Methods in General and Mathematical Ideas with Content and explains how to develop them in the classroom with illuminating examples.
Download and read online Count Down in PDF and EPUB Follows six American high school students on the quest for glory in the Olympics of math competitions--The International Mathematical Olympiad.
Download and read online Proof and Proving in Mathematics Education in PDF and EPUB One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.