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| Author | : Todev |
| Publisher | : |
| Total Pages | : 604 |
| Release | : 2010-07 |
| Genre | : Juvenile Nonfiction |
| ISBN | : 9780982771327 |
This is a great collection of geometry problems from Mathematical Olympiads and competitions around the world.
| Author | : Evan Chen |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 311 |
| Release | : 2021-08-23 |
| Genre | : Education |
| ISBN | : 1470466201 |
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 a 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.
| Author | : Shi-xiong Liu |
| Publisher | : World Scientific |
| Total Pages | : 607 |
| Release | : 2022-04-08 |
| Genre | : Mathematics |
| ISBN | : 9811229902 |
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
| Author | : Răzvan Gelca |
| Publisher | : Springer |
| Total Pages | : 857 |
| Release | : 2017-09-19 |
| Genre | : Mathematics |
| ISBN | : 3319589881 |
This book takes the reader on a journey through the world of college mathematics, focusing on some of the most important concepts and results in the theories of polynomials, linear algebra, real analysis, differential equations, coordinate geometry, trigonometry, elementary number theory, combinatorics, and probability. Preliminary material provides an overview of common methods of proof: argument by contradiction, mathematical induction, pigeonhole principle, ordered sets, and invariants. Each chapter systematically presents a single subject within which problems are clustered in each section according to the specific topic. The exposition is driven by nearly 1300 problems and examples chosen from numerous sources from around the world; many original contributions come from the authors. The source, author, and historical background are cited whenever possible. Complete solutions to all problems are given at the end of the book. This second edition includes new sections on quad ratic polynomials, curves in the plane, quadratic fields, combinatorics of numbers, and graph theory, and added problems or theoretical expansion of sections on polynomials, matrices, abstract algebra, limits of sequences and functions, derivatives and their applications, Stokes' theorem, analytical geometry, combinatorial geometry, and counting strategies. Using the W.L. Putnam Mathematical Competition for undergraduates as an inspiring symbol to build an appropriate math background for graduate studies in pure or applied mathematics, the reader is eased into transitioning from problem-solving at the high school level to the university and beyond, that is, to mathematical research. This work may be used as a study guide for the Putnam exam, as a text for many different problem-solving courses, and as a source of problems for standard courses in undergraduate mathematics. Putnam and Beyond is organized for independent study by undergraduate and gradu ate students, as well as teachers and researchers in the physical sciences who wish to expand their mathematical horizons.
| Author | : Kim Hoo Hang |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 250 |
| Release | : 2017 |
| Genre | : Mathematics |
| ISBN | : 9789814583749 |
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.
| Author | : Sotirios E. Louridas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 238 |
| Release | : 2014-07-08 |
| Genre | : Mathematics |
| ISBN | : 1461472733 |
"Problem-Solving and Selected Topics in Euclidean Geometry: in the Spirit of the Mathematical Olympiads" contains theorems which are of particular value for the solution of geometrical problems. Emphasis is given in the discussion of a variety of methods, which play a significant role for the solution of problems in Euclidean Geometry. Before the complete solution of every problem, a key idea is presented so that the reader will be able to provide the solution. Applications of the basic geometrical methods which include analysis, synthesis, construction and proof are given. Selected problems which have been given in mathematical olympiads or proposed in short lists in IMO's are discussed. In addition, a number of problems proposed by leading mathematicians in the subject are included here. The book also contains new problems with their solutions. The scope of the publication of the present book is to teach mathematical thinking through Geometry and to provide inspiration for both students and teachers to formulate "positive" conjectures and provide solutions.
| Author | : H. S. M. Coxeter |
| Publisher | : American Mathematical Society |
| Total Pages | : 193 |
| Release | : 2021-12-30 |
| Genre | : Mathematics |
| ISBN | : 1470466414 |
Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.
| Author | : Bin Xiong |
| Publisher | : World Scientific |
| Total Pages | : 580 |
| Release | : 2022-04-07 |
| Genre | : Mathematics |
| ISBN | : 9811229872 |
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
| Author | : Titu Andreescu |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2014 |
| Genre | : Geometry |
| ISBN | : 9780988562226 |
This book represents a collection of carefully selected geometry problems designed for passionate geometers and students preparing for the IMO. Assuming the theory and the techniques presented in the first two geometry books published by XYZ Press, 106 Geometry Problems from the AwesomeMath Summer Program and 107 Problems from the AwesomeMath Year-Round Program, this book presents a multitude of beautiful synthetic solutions that are meant to give a sense of how one should think about difficult geometry problems. On average, each problem comes with at least two such solutions and with additional remarks about the underlying configuration.
| Author | : Titu Andreescu |
| Publisher | : Cambridge University Press |
| Total Pages | : 340 |
| Release | : 2002-05-16 |
| Genre | : Mathematics |
| ISBN | : 9780883858059 |
Challenging problems in maths plus solutions to those featured in the earlier Olympiad book.
