In Mathematical Olympiad and Competitions

Author: Gangsong Leng

Publisher: World Scientific Publishing Company

ISBN: 9814696501

Category: Mathematics

Page: 144

View: 7671

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.
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Insights and Strategies

Author: Kim Hoo Hang,Haibin Wang

Publisher: World Scientific Publishing Company

ISBN: 9814583766

Category:

Page: 356

View: 4286

This new volume of the Mathematical Olympiad Series focuses on the topic of geometry. Basic and advanced theorems commonly seen in Mathematical Olympiad are introduced and illustrated with plenty of examples. Special techniques in solving various types of geometrical problems are also introduced, while the authors elaborate extensively on how to acquire an insight and develop strategies in tackling difficult geometrical problems. This book is suitable for any reader with elementary geometrical knowledge at the lower secondary level. Each chapter includes sufficient scaffolding and is comprehensive enough for the purpose of self-study. Readers who complete the chapters on the basic theorems and techniques would acquire a good foundation in geometry and may attempt to solve many geometrical problems in various mathematical competitions. Meanwhile, experienced contestants in Mathematical Olympiad competitions will find a large collection of problems pitched at competitions at the international level, with opportunities to practise and sharpen their problem-solving skills in geometry. Request Inspection Copy
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In Mathematical Olympiad and Competitions

Author: Yuefeng Feng

Publisher: World Scientific Publishing Company

ISBN: 9814723185

Category: Mathematics

Page: 232

View: 3235

In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on methods of discrete extremization, such as inequality control, repeated extremum, partial adjustment, exploiting symmetry, polishing transform, space estimates, etc.
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In Mathematical Olympiad and Competitions

Author: Zun Shan

Publisher: World Scientific Publishing Company

ISBN: 9813141514

Category: Mathematics

Page: 208

View: 1280

In China, lots of excellent students who are good at maths take an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they have won the first place almost every year. The author is one of the senior coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. This book will, in an interesting problem-solving way, explain what probability theory is: its concepts, methods and meanings; particularly, two important concepts — probability and mathematical expectation (briefly expectation) — are emphasized. It consists of 65 problems, appended by 107 exercises and their answers.
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Problems and Solutions

Author: Xiong Bin,Lee Peng Yee

Publisher: World Scientific

ISBN: 9813142952

Category: Mathematics

Page: 368

View: 2396

The International Mathematical Olympiad (IMO) is a very important competition for high school students. China has taken part in the IMO 31 times since 1985 and has won the top ranking for countries 19 times, with a multitude of gold medals for individual students. The six students China has sent every year were selected from 60 students among approximately 300 students who took part in the annual China Mathematical Competition during the winter months. This book includes the problems and solutions of the most important mathematical competitions from 2010 to 2014 in China, such as China Mathematical Competition, China Mathematical Olympiad, China Girls' Mathematical Olympiad. These problems are almost exclusively created by the experts who are engaged in mathematical competition teaching and researching. Some of the solutions are from national training team and national team members, their wonderful solutions being the feature of this book. This book is useful to mathematics fans, middle school students engaged in mathematical competition, coaches in mathematics teaching and teachers setting up math elective courses.
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For Senior SectionVolume 1

Author: Jiagu Xu

Publisher: World Scientific Publishing Company

ISBN: 9813100591

Category: Mathematics

Page: 556

View: 3863

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 beyond the usual syllabus, but introduces a variety of concepts and methods in modern mathematics as well. In each lecture, the concepts, theories and methods are taken as the core. The examples serve to explain and enrich their intentions and to indicate their applications. Besides, appropriate number of test questions is available for the readers' practice and testing purpose. Their detailed solutions are also conveniently provided. The examples are not very complicated so readers can easily understand. There are many real competition questions included which students can use to verify their abilities. These test questions originate from many countries all over the world. This book will serve as a useful textbook of mathematical Olympiad courses, a self-study lecture notes for students, or as a reference book for related teachers and researchers.
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from the Polish Mathematical Olympiads

Author: S. Straszewicz

Publisher: Elsevier

ISBN: 1483280314

Category: Mathematics

Page: 376

View: 1307

Popular Lectures in Mathematics, Volume 12: Mathematical Problems and Puzzles: From the Polish Mathematical Olympiads contains sample problems from various fields of mathematics, including arithmetic, algebra, geometry, and trigonometry. The contest for secondary school pupils known as the Mathematical Olympiad has been held in Poland every year since 1949/50. This book is composed of two main parts. Part I considers the problems and solutions about integers, polynomials, algebraic fractions and irrational experience. Part II focuses on the problems of geometry and trigonometric transformation, along with their solutions. The provided solutions aim to extend the student’s knowledge of mathematics and train them in mathematical thinking. This book will prove useful to secondary school mathematics teachers and students.
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vom Lösen mathematischer Probleme

Author: George Pólya

Publisher: N.A

ISBN: 9783772006081

Category:

Page: 266

View: 2596

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der elementaren Kombinatorik, Zahlentheorie und Geometrie

Author: Ross Honsberger

Publisher: Springer-Verlag

ISBN: 3322859304

Category: Mathematics

Page: 179

View: 1911

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Author: H.S. Coxeter

Publisher: Springer-Verlag

ISBN: 3034851510

Category: Juvenile Nonfiction

Page: 558

View: 8123

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Author: István Reiman

Publisher: Anthem Press

ISBN: 1843311976

Category: Education

Page: 217

View: 2542

The famed International Mathematical Olympiad has been challenging students worldwide for over 40 years. The first competition was held in Romania in 1959 with seven countries participating. It has since expanded to attract competitors from over 80 countries, representing all five continents. This first volume features every question set from 1959–75, along with comprehensive solutions and multiple answers where applicable. A fantastic selection of mathematical puzzles, this fully updated three volume series will be of interest to serious mathematicians and enthusiasts alike. István Reiman’s compilation of logic puzzles and questions will tease the intellect of all those with a mathematical mind.
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Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662577674

Category: Mathematics

Page: 360

View: 3388

Diese fünfte deutsche Auflage enthält ein ganz neues Kapitel über van der Waerdens Permanenten-Vermutung, sowie weitere neue, originelle und elegante Beweise in anderen Kapiteln. Aus den Rezensionen: “... es ist fast unmöglich, ein Mathematikbuch zu schreiben, das von jedermann gelesen und genossen werden kann, aber Aigner und Ziegler gelingt diese Meisterleistung in virtuosem Stil. [...] Dieses Buch erweist der Mathematik einen unschätzbaren Dienst, indem es Nicht-Mathematikern vorführt, was Mathematiker meinen, wenn sie über Schönheit sprechen.” Aus der Laudatio für den “Steele Prize for Mathematical Exposition” 2018 "Was hier vorliegt ist eine Sammlung von Beweisen, die in das von Paul Erdös immer wieder zitierte BUCH gehören, das vom lieben (?) Gott verwahrt wird und das die perfekten Beweise aller mathematischen Sätze enthält. Manchmal lässt der Herrgott auch einige von uns Sterblichen in das BUCH blicken, und die so resultierenden Geistesblitze erhellen den Mathematikeralltag mit eleganten Argumenten, überraschenden Zusammenhängen und unerwarteten Volten." www.mathematik.de, Mai 2002 "Eine einzigartige Sammlung eleganter mathematischer Beweise nach der Idee von Paul Erdös, verständlich geschrieben von exzellenten Mathematikern. Dieses Buch gibt anregende Lösungen mit Aha-Effekt, auch für Nicht-Mathematiker." www.vismath.de "Ein prächtiges, äußerst sorgfältig und liebevoll gestaltetes Buch! Erdös hatte die Idee DES BUCHES, in dem Gott die perfekten Beweise mathematischer Sätze eingeschrieben hat. Das hier gedruckte Buch will eine "very modest approximation" an dieses BUCH sein.... Das Buch von Aigner und Ziegler ist gelungen ..." Mathematische Semesterberichte, November 1999 "Wer (wie ich) bislang vergeblich versucht hat, einen Blick ins BUCH zu werfen, wird begierig in Aigners und Zieglers BUCH der Beweise schmökern." www.mathematik.de, Mai 2002
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From the Training of the USA IMO Team

Author: Titu Andreescu,Dorin Andrica,Zuming Feng

Publisher: Springer Science & Business Media

ISBN: 9780817645618

Category: Mathematics

Page: 204

View: 2268

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory.
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Author: Werner Ballmann

Publisher: Springer-Verlag

ISBN: 3034809018

Category: Mathematics

Page: 162

View: 1470

Das Buch bietet eine Einführung in die Topologie, Differentialtopologie und Differentialgeometrie. Es basiert auf Manuskripten, die in verschiedenen Vorlesungszyklen erprobt wurden. Im ersten Kapitel werden grundlegende Begriffe und Resultate aus der mengentheoretischen Topologie bereitgestellt. Eine Ausnahme hiervon bildet der Jordansche Kurvensatz, der für Polygonzüge bewiesen wird und eine erste Idee davon vermitteln soll, welcher Art tiefere topologische Probleme sind. Im zweiten Kapitel werden Mannigfaltigkeiten und Liesche Gruppen eingeführt und an einer Reihe von Beispielen veranschaulicht. Diskutiert werden auch Tangential- und Vektorraumbündel, Differentiale, Vektorfelder und Liesche Klammern von Vektorfeldern. Weiter vertieft wird diese Diskussion im dritten Kapitel, in dem die de Rhamsche Kohomologie und das orientierte Integral eingeführt und der Brouwersche Fixpunktsatz, der Jordan-Brouwersche Zerlegungssatz und die Integralformel von Stokes bewiesen werden. Das abschließende vierte Kapitel ist den Grundlagen der Differentialgeometrie gewidmet. Entlang der Entwicklungslinien, die die Geometrie der Kurven und Untermannigfaltigkeiten in Euklidischen Räumen durchlaufen hat, werden Zusammenhänge und Krümmung, die zentralen Konzepte der Differentialgeometrie, diskutiert. Den Höhepunkt bilden die Gaussgleichungen, die Version des theorema egregium von Gauss für Untermannigfaltigkeiten beliebiger Dimension und Kodimension. Das Buch richtet sich in erster Linie an Mathematik- und Physikstudenten im zweiten und dritten Studienjahr und ist als Vorlage für ein- oder zweisemestrige Vorlesungen geeignet.
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Author: Richard Courant,Herbert Robbins

Publisher: Springer-Verlag

ISBN: 3662000539

Category: Mathematics

Page: N.A

View: 2617

47 brauchen nur den Nenner n so groß zu wählen, daß das Intervall [0, IJn] kleiner wird als das fragliche Intervall [A, B], dann muß mindestens einer der Brüche m/n innerhalb des Intervalls liegen. Also kann es kein noch so kleines Intervall auf der Achse geben, das von rationalen Punkten frei wäre. Es folgt weiterhin, daß es in jedem Intervall unendlich viele rationale Punkte geben muß; denn wenn es nur eine endliche Anzahl gäbe, so könnte das Intervall zwischen zwei beliebigen benachbarten Punkten keine rationalen Punkte enthalten, was, wie wir eben sahen, unmöglich ist. § 2. Inkommensurable Strecken, irrationale Zahlen und der Grenzwertbegriff 1. Einleitung Vergleicht man zwei Strecken a und b hinsichtlich ihrer Größe, so kann es vor kommen, daß a in b genau r-mal enthalten ist, wobei r eine ganze Zahl darstellt. In diesem Fall können wir das Maß der Strecke b durch das von a ausdrücken, indem wir sagen, daß die Länge von b das r-fache der Länge von a ist.
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American high school mathematics examinations and American invitational mathematics examinations 1983-1988

Author: George Berzsenyi,Stephen B. Maurer

Publisher: N.A

ISBN: 9780883856406

Category: Mathematics

Page: 286

View: 2238

Over the years perhaps the most popular of the MAA problem books have been the high school contest books, covering the yearly American High School Mathematics Examinations (AHSME) that began in 1950, co-sponsored from the start by the MAA. Book V also includes the first six years of the American Invitational Mathematics Examination (AIME) which was developed as an intermediate step between the AHSME & the USA Mathematical Olympiad (USAMO). The AIME has a unique answer format - all answers are integers between 0 & 999. New material, not included in premenu contents books is: * a comprehensive guide to other problem materials world wide, * additional solutions, * dropped problems, * statistical information, * information on test development & history. This volume is a must for avid fans of elementary problems. Contest Books I-IV appear as NML volumes 5, 17, 25, & 29. See below.
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auf den Spuren des größten Rätsels der Mathematik

Author: Marcus Du Sautoy

Publisher: C.H.Beck

ISBN: 9783406523205

Category: Primzahl

Page: 398

View: 3800

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Author: Serge Tabachnikov

Publisher: Springer-Verlag

ISBN: 3642319254

Category: Mathematics

Page: 165

View: 6950

Wie bewegt sich ein Massenpunkt in einem Gebiet, an dessen Rand er elastisch zurückprallt? Welchen Weg nimmt ein Lichtstrahl in einem Gebiet mit ideal reflektierenden Rändern? Anhand dieser und ähnlicher Fragen stellt das vorliegende Buch Zusammenhänge zwischen Billard und Differentialgeometrie, klassischer Mechanik sowie geometrischer Optik her. Dabei beschäftigt sich das Buch unter anderem mit dem Variationsprinzip beim mathematischen Billard, der symplektischen Geometrie von Lichtstrahlen, der Existenz oder Nichtexistenz von Kaustiken, periodischen Billardtrajektorien und dem Mechanismus für Chaos bei der Billarddynamik. Ergänzend wartet dieses Buch mit einer beachtlichen Anzahl von Exkursen auf, die sich verwandten Themen widmen, darunter der Vierfarbensatz, die mathematisch-physikalische Beschreibung von Regenbögen, der poincaresche Wiederkehrsatz, Hilberts viertes Problem oder der Schließungssatz von Poncelet.​
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Author: Kevin Wang

Publisher: N.A

ISBN: 9781944863197

Category:

Page: 152

View: 846

The math challenge curriculum textbook series is designed to help students learn the fundamental mathematical concepts and practice their in-depth problem solving skills with selected exercise problems. Ideally, these textbooks are used together with Areteem Institute's corresponding courses, either taken as live classes or as self-paced classes. According to the experience levels of the students in mathematics, the following courses are offered: Fun Math Problem Solving for Elementary School (grades 3-5) Algebra Readiness (grade 5; preparing for middle school) Math Challenge I-A Series (grades 6-8; intro to problem solving) Math Challenge I-B Series (grades 6-8; intro to math contests e.g. AMC 8, ZIML Div M) Math Challenge I-C Series (grades 6-8; topics bridging middle and high schools) Math Challenge II-A Series (grades 9+ or younger students preparing for AMC 10) Math Challenge II-B Series (grades 9+ or younger students preparing for AMC 12) Math Challenge III Series (preparing for AIME, ZIML Varsity, or equivalent contests) Math Challenge IV Series (Math Olympiad level problem solving) These courses are designed and developed by educational experts and industry professionals to bring real world applications into the STEM education. These programs are ideal for students who wish to win in Math Competitions (AMC, AIME, USAMO, IMO, ARML, MathCounts, Math League, Math Olympiad, ZIML, etc.), Science Fairs (County Science Fairs, State Science Fairs, national programs like Intel Science and Engineering Fair, etc.) and Science Olympiad, or purely want to enrich their academic lives by taking more challenges and developing outstanding analytical, logical thinking and creative problem solving skills. In Math Challenge II-B, students learn and practice in areas such as algebra and geometry at the high school level, as well as advanced number theory and combinatorics. Topics include polynomials, inequalities, special algebraic techniques, trigonometry, triangles and polygons, collinearity and concurrency, vectors and coordinates, numbers and divisibility, modular arithmetic, residue classes, advanced counting strategies, binomial coefficients, and various other topics and problem solving techniques involved in math contests such as the American Mathematics Competition (AMC) 10 and 12, ARML, beginning AIME, and Zoom International Math League (ZIML) Junior Varsity and Varsity Divisions. The course is divided into four terms: Summer, covering Algebra Fall, covering Geometry Winter, covering Combinatorics Spring, covering Number Theory The book contains course materials for Math Challenge II-B: Geometry. We recommend that students take all four terms. Each of the individual terms is self-contained and does not depend on other terms, so they do not need to be taken in order, and students can take single terms if they want to focus on specific topics. Students can sign up for the course at https: //classes.areteem.org for the live online version or at https: //www.edurila.com for the self-paced version.
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