104 Number Theory Problems From The Training Of The Usa Imo Team
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| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 214 |
| Release | : 2007-04-05 |
| Genre | : Mathematics |
| ISBN | : 0817645616 |
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.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 125 |
| Release | : 2013-11-27 |
| Genre | : Mathematics |
| ISBN | : 0817682228 |
"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.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 383 |
| Release | : 2009-06-12 |
| Genre | : Mathematics |
| ISBN | : 0817646450 |
This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving. Starting with the essentials, the text covers divisibility, unique factorization, modular arithmetic and the Chinese Remainder Theorem, Diophantine equations, binomial coefficients, Fermat and Mersenne primes and other special numbers, and special sequences. Included are sections on mathematical induction and the pigeonhole principle, as well as a discussion of other number systems. By emphasizing examples and applications the authors motivate and engage readers.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 296 |
| Release | : 2000-04-26 |
| Genre | : Mathematics |
| ISBN | : 9780817641900 |
A collection of problems put together by coaches of the U.S. International Mathematical Olympiad Team.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 222 |
| Release | : 2006-03-04 |
| Genre | : Mathematics |
| ISBN | : 0817644326 |
* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training
| Author | : Svetoslav Savchev |
| Publisher | : MAA |
| Total Pages | : 244 |
| Release | : 2003-02-27 |
| Genre | : Education |
| ISBN | : 9780883856451 |
Rather than simply a collection of problems, this book can be thought of as both a tool chest of mathematical techniques and an anthology of mathematical verse. The authors have grouped problems so as to illustrate and highlight a number of important techniques and have provided enlightening solutions in all cases. As well as this there are essays on topics that are not only beautiful but also useful. The essays are diverse and enlivened by fresh, non-standard ideas. This book not only teaches techniques but gives a flavour of their past, present and possible future implications. It is a collection of miniature mathematical works in the fullest sense.
| Author | : Titu Andreescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 256 |
| Release | : 2011-09-21 |
| Genre | : Mathematics |
| ISBN | : 0817682538 |
Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics. The book contains a stimulating collection of problems in the subjects of algebra, geometry, trigonometry, number theory and combinatorics. While it may be considered a sequel to "Mathematical Olympiad Challenges," the focus is on engaging a wider audience to apply techniques and strategies to real-world problems. Throughout the book students are encouraged to express their ideas, conjectures, and conclusions in writing. The goal is to help readers develop a host of new mathematical tools that will be useful beyond the classroom and in a number of disciplines.
| Author | : Titu Andreescu |
| Publisher | : |
| Total Pages | : 686 |
| Release | : 2017-07-15 |
| Genre | : Number theory |
| ISBN | : 9780988562202 |
Challenge your problem-solving aptitude in number theory with powerful problems that have concrete examples which reflect the potential and impact of theoretical results. Each chapter focuses on a fundamental concept or result, reinforced by each of the subsections, with scores of challenging problems that allow you to comprehend number theory like never before. All students and coaches wishing to excel in math competitions will benefit from this book as will mathematicians and adults who enjoy interesting mathematics.
| Author | : Dušan Djukić |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 819 |
| Release | : 2011-05-05 |
| Genre | : Mathematics |
| ISBN | : 1441998543 |
"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.
| Author | : Hans-Dietrich Gronau |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 298 |
| Release | : 2011-01-03 |
| Genre | : Mathematics |
| ISBN | : 3642145655 |
In July 2009 Germany hosted the 50th International Mathematical Olympiad (IMO). For the very first time the number of participating countries exceeded 100, with 104 countries from all continents. Celebrating the 50th anniversary of the IMO provides an ideal opportunity to look back over the past five decades and to review its development to become a worldwide event. This book is a report about the 50th IMO as well as the IMO history. A lot of data about all the 50 IMOs are included. We list the most successful contestants, the results of the 50 Olympiads and the 112 countries that have ever taken part. It is impressive to see that many of the world’s leading research mathematicians were among the most successful IMO participants in their youth. Six of them gave presentations at a special celebration: Bollobás, Gowers, Lovász, Smirnov, Tao and Yoccoz. This book is aimed at students in the IMO age group and all those who have interest in this worldwide leading competition for highschool students.
