There are many countries around the world that hold Mathematics Competitions. The Competitions are extremely interesting since many professors try to create new interesting problems. If you want to take part in these competitions, you have to solve many problems. That means you must master your problem-solving skills. Challenging Problems from Around the World Vol 1 is a selected problem book. This book has only two chapters. The first chapter of this book is a collection of problems. We select many good problems from different sources. Most of them used to appear in Mathematics Competitions. In this part, we want the readers try their best to solve the problems. Remember that only a few people can solve all problems in this book. So, do not be up set if you cannot solve some problems. Even we cannot solve problems, we still gain some techniques in solving problems. The readers should keep in mind that the only way in learning Mathematics is to do Mathematics. The second chapter of this book was written about the solution to each problem that listed in the first chapter. We try to solve the problems step by step. We believe that the solutions will help the readers to understand well. Reading through this part, we hope the readers will learn many problem-solving strategies. Let this book be your close friend when you learn about Mathematics. We hope the readers have a great journey in reading this book. Richard S.Hammond
A beautiful part in Maths is inequality. There are a lot of techniques and theorems related to inequality. This is the main reason that inequality problems appear in most Mathematics Competitions. Therefore, if you want to be a part of the competitions, mastering in inequality is one thing that you must do. Challenging Problems in Inequalities is a little book about inequalities. This book will provide you with the basics, techniques and theorems in inequalities. We will guide you through many interesting things in inequalities. This book was written in three main parts. The first part is about techniques and theorems in proving inequalities. The second part is about problems. And the last part of the book is about solutions. In the first part of the book, we try to dive readers into the basic inequalities. We lead readers to understand many well-known theorems such as QM-AM-GM-HM inequality, Cauchy-Schwarz inequality, rearrangement inequality, Jensen's inequality, Schur's inequality and etc. Moreover, in each chapter, we give many examples in order to make to make sure that readers understand well about the theorem. Readers should keep in mind that learning maths is not about memorizing but it is all about understanding. The more you understand about the lesson, the more you perform really well in solving problems. In the second part of the book, we listed many challenging problems from around the world. The aim of this part is to help readers to practice their understanding in the first part. Readers should try their best to solve the given problems before seeing the solutions. It is good to figure the answers out by yourself. However, do not worry if you cannot solve them since the last part of the book is about solutions. In this part, we provide readers very detailed solutions to each problems. All problems were solved step by step. This part will help readers to evolve a lot. We hope this book will help readers a lot in inequalities.
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.
Maths Challenge has been written to provide an enrichment programme for able students at lower secondary level.DT Challenges provide stimulating questions to help students think more deeply about basic mathematical ideasDT Comments and solutions explain the mathematical ideas and provide tips on how to approach later questionsDT A Glossary defines all the mathematical terms used in the books in a precise way, making the books self-containedDT Suitable for individual, group, or class work, in school, or at homeDT Fully trialled over the last ten years by a group of teachers and advisers led by Tony Gardiner
BETHANY MACDONALD HAS TRAINED SIX LONG YEARS FOR THIS MOMENT. SHE'LL TRY TO SOLVE FIVE QUESTIONS IN THREE HOURS, FOR ONE IMPROBABLE DREAM. THE DREAM OF REPRESENTING HER COUNTRY, AND BECOMING A MATH OLYMPIAN. As a small-town girl in Nova Scotia bullied for liking numbers more than boys, and lacking the encouragement of her unsupportive single mother who frowns at her daughter's unrealistic ambition, Bethany's road to the International Math Olympiad has been marked by numerous challenges. Through persistence, perseverance, and the support of innovative mentors who inspire her with a love of learning, Bethany confronts these challenges and develops the creativity and confidence to reach her potential. In training to become a world-champion "mathlete", Bethany discovers the heart of mathematics - a subject that's not about memorizing formulas, but rather about problem-solving and detecting patterns to uncover truth, as well as learning how to apply the deep and unexpected connections of mathematics to every aspect of her life, including athletics, spirituality, and environmental sustainability. As Bethany reflects on her long journey and envisions her exciting future, she realizes that she has shattered the misguided stereotype that only boys can excel in math, and discovers a sense of purpose that through mathematics, she can and she will make an extraordinary contribution to society....