The USSR olympiad problem book : selected problems and theorems of elementary mathematics = Izbrannye zadachi i teoremy elementarnoi matematiki, ch. 1. English

Titu Andreescu, Oleg Mushkarov, Luchezar Stoyanov, Titu Andreescu

Questions Of Maxima And Minima Have Great Practical Significance, With Applications To Physics, Engineering, And Economics; They Have Also Given Rise To Theoretical Advances, Notably In Calculus And Optimization. Indeed, While Most Texts View The Study Of Extrema Within The Context Of Calculus, This Carefully Constructed Problem Book Takes A Uniquely Intuitive Approach To The Subject: It Presents Hundreds Of Extreme-value Problems, Examples, And Solutions Primarily Through Euclidean Geometry. Key Features And Topics: * Comprehensive Selection Of Problems, Including Greek Geometry And Optics, Newtonian Mechanics, Isoperimetric Problems, And Recently Solved Problems Such As Malfatti’s Problem * Unified Approach To The Subject, With Emphasis On Geometric, Algebraic, Analytic, And Combinatorial Reasoning * Presentation And Application Of Classical Inequalities, Including Cauchy--schwarz And Minkowski’s Inequality; Basic Results In Calculus, Such As The Intermediate Value Theorem; And Emphasis On Simple But Useful Geometric Concepts, Including Transformations, Convexity, And Symmetry * Clear Solutions To The Problems, Often Accompanied By Figures * Hundreds Of Exercises Of Varying Difficulty, From Straightforward To Olympiad-caliber Written By A Team Of Established Mathematicians And Professors, This Work Draws On The Authors’ Experience In The Classroom And As Olympiad Coaches. By Exposing Readers To A Wealth Of Creative Problem-solving Approaches, The Text Communicates Not... Leer más…

Heinrich Dörrie

"The collection, drawn from arithmetic, algebra, pure and algebraic geometry and astronomy, is extraordinarily interesting and attractive." — __Mathematical Gazette__ This uncommonly interesting volume covers 100 of the most famous historical problems of elementary mathematics. Not only does the book bear witness to the extraordinary ingenuity of some of the greatest mathematical minds of history — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others — but it provides rare insight and inspiration to any reader, from high school math student to professional mathematician. This is indeed an unusual and uniquely valuable book. The one hundred problems are presented in six categories: 26 arithmetical problems, 15 planimetric problems, 25 classic problems concerning conic sections and cycloids, 10 stereometric problems, 12 nautical and astronomical problems, and 12 maxima and minima problems. In addition to defining the problems and giving full solutions and proofs, the author recounts their origins and history and discusses personalities associated with them. Often he gives not the original solution, but one or two simpler or more interesting demonstrations. In only two or three instances does the solution assume anything more than a knowledge of theorems of elementary mathematics; hence, this is a book with an extremely wide appeal. Some of the most celebrated and intriguing items are:... Leer más…

Compiled And With Solutions By Samuel L. Greitzer

The International Olympiad has been held annually since 1959; the U.S. began participating in 1974, when the Sixteenth International Olympiad was held in Erfurt, G.D.R. In 1974 and 1975, the National Science Foundation funded a three week summer training session with Samuel L. Greitzer of Rutgers University and Murray Klamkin of the University of Alberta as the U.S. teams' coaches. Summer training sessions in 1976, 1977 were funded by grants from the Army Research Office and Office of Naval Research. To date the U.S. teams have consistently placed among the top three national scores: second in 1974(the USSR was first), third in 1975 (behind Hungary and the G.D.R) and 1976 (behind the USSR and Great Britain) and first in 1977. Members of U.S. team are selected from the 100 top scorers on the Annual High School Examinations (see NML vols. 5, 17, 25) by subsequent competition in the U.S. Mathematical Olympiad. In this volume the demonstrably effective coach and prime mover in planning the participation of the U.S.A. in the I.M.O., Samuel L. Greitzer, has compiled all the IMO problems from the First through the Nineteenth (1977) IMO and their solutions, some based on the contestants' papers. The problems ae solvable by methods accessible to secondary school students in most nations, but insight and ingenuity are often required. A chronological examination of the questions throws some light on the changes and trends in secondary school mathematics curricula. Leer más…

A M Yaglom; Basil Gordon; I M Yaglom

Over 170 challenging problems ranging from the relatively simple to the extremely difficult. Volume 1 contains 100 problems on probability theory and combinatorial analysis. Leer más…

A M Yaglom; Basil Gordon; I M Yaglom

Over 170 challenging problems ranging from the relatively simple to the extremely difficult. Volume 2 contains 74 problems on points and lines, topology, convex polygons, nondecimal counting and other topics. Includes solutions. Leer más…

Edited By Titu Andreescu And Zuming Feng

This volume contains a large range of problems, with and without solutions, taken from 25 national and regional mathematics olympiads from around the world, and the problems are drawn from several years' contests. In many cases, more than one solution is given to a single problem in order to highlight different problem-solving strategies. The collection is intended as practice for students preparing for these competitions. Teachers and general readers looking for interesting problems will find also it very useful. Leer más…

Titu Andreescu; Zuming Feng; Mathematical Association Of America

Contained here are solutions to challenging problems from algebra, geometry, combinatorics and number theory featured in the earlier book, together with selected questions (without solutions) from national and regional Olympiads given during the year 2000. Intended for the serious student/problem solver, these books can help to improve performance in the Mathematical Olympiad competition. However, for those not entering the competition, there is much to challenge any mathematician, even those with advanced degrees. Different nations have different mathematical cultures, so you will find that some of the questions are extremely difficult and some rather easy. There are a wide variety of problems especially from those countries that have often done well in the IMO. Anyone interested in mathematical problem solving will encounter some beautiful mathematics in the pages of this book. If you are up to a real challenge, take some of these problems on! Leer más…

Titu Andreescu, Zuming Feng, George Lee Jr, Po-Ru Loh

This volume is a continuation of Mathematical Olympiads 1999-2000: Problems and Solutions From Around the World, republishing hundreds of mathematics problems and solutions from that book as well as selected problems (without solutions) from national and regional contests in 2001. The collection provides practice material for serious high-school level mathematicians who wish to prepare for the USA Math Olympiad (USAMO) and Team Selection Test (TST). The newly added 2001 problems were contributed by dozens of countries including Korea, Belarus, China, Poland, and Romania Leer más…

Shklarsky D. O., Yaglom I. M.; N. N. Chentzov

Over 300 challenging problems in algebra, arithmetic, elementary number theory and trigonometry. Complete solutions. 1962 edition. Leer más…

Titu Andreescu, Zuming Feng

102 Combinatorial Problems Consists Of Carefully Selected Problems That Have Been Used In The Training And Testing Of The Usa International Mathematical Olympiad (imo) Team. Key Features: * Provides In-depth Enrichment In The Important Areas Of Combinatorics By Reorganizing And Enhancing Problem-solving Tactics And Strategies * Topics Include: Combinatorial Arguments And Identities, Generating Functions, Graph Theory, Recursive Relations, Sums And Products, Probability, Number Theory, Polynomials, Theory Of Equations, Complex Numbers In Geometry, Algorithmic Proofs, Combinatorial And Advanced Geometry, Functional Equations And Classical Inequalities The Book Is Systematically Organized, Gradually Building Combinatorial Skills And Techniques And Broadening The Student's View Of Mathematics. Aside From Its Practical Use In Training Teachers And Students Engaged In Mathematical Competitions, It Is A Source Of Enrichment That Is Bound To Stimulate Interest In A Variety Of Mathematical Areas That Are Tangential To Combinatorics. By Titu Andreescu, Zuming Feng. Leer más…

Kuczma Marcin E., Windischbacher Erich, Australian Mathematics Trust

This is a rich collection of problems from the national Olympiads of Austria and Poland, which both have exceptionally strong traditions. The particular interest in the problems selected is that all have at least two independent solutions, highlighting one of the beauties of mathematics. Leer más…

D. Branzei 'et Alii'

lgli/M_Mathematics/MSch_School-level/Branzei D., et al. Junior Balkan mathematical olympiads (Plus, 2003)(ISBN 9738526509)(K)(T)(152s)_MSch_.djvu Leer más…

Alfred S. Posamentier, Charles T. Salkind

I liked this book very much. I solved every single problem in the book with two students that I tutor for International Math Olympiads and carefully read the hints and solutions proposed at the end of the book. They really teach how to "attack" geometry problems using simple stuff like angle chasing, drawing parallel lines etc. I cannot recommend this book more to the readers with some mathematical sophistication. I even have a suggestion for parents that have some sort of mathematical background (engineers, bankers, doctors, etc.): If you want to spend quality time with your children, get this book and enjoy solving the problems together. I cannot imagine a more amusing pastime. I am looking forward to seeing new titles from the authors. Leer más…

Tutorials in Algebra, Number Theory, Combinatorics and Geometry Leer más…

Titu Andreescu; Zuming Feng; Mathematical Association Of America

The Mathematical Olympiad examinations, covering the USA Mathematical Olympiad (USAMO) and the International Mathematical Olympiad (IMO), have been published annually since 1976 by the MAA American Mathematics Competitions. This is the fourth volume in that series published by the MAA in its Problem Book series. The IMO is a world mathematics competition for high school students that takes place each year in a different country. Students from all over the world participate in this competition. The USAMO and the Team Selection Test are the last two stages of the process that lead to the selection of the team representing the USA in the IMO. Problems and solutions from both of these competitions for the year 2003 are included in this volume. These Olympiad style exams consist of several challenging essay-type problems. Although a correct and complete solution to an Olympiad problem often requires deep analysis and careful argument, the problems require no more than a solid background in high school mathematics coupled with a dose of mathematical ingenuity. There are helpful hints provided for each of the problems. These hints often help lead the student to a solution of the problem. Complete solutions to each of the problems is also included, and many of the problems are presented together with a collection of remarkable solutions developed by the examination committees, contestants and experts, during or after the contest. For each problem with... Leer más…

Xu, Jiagu

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. Operations on Rational Numbers Linear Equations of Single Variable Multiplication Formulae Absolute Value and Its Applications Congruence of Triangles Similarity of Triangles Divisions of... Leer más…

George Polya And Jeremy Kilpatrick

This volume features a complete set of problems, hints, and solutions based on Stanford University's well-known competitive examination in mathematics. It offers students at both high school and college levels an excellent mathematics workbook. Filled with rigorous problems, it assists students in developing and cultivating their logic and probability skills. 1974 edition. Leer más…