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Author: Radmila Bulajich Manfrino
Publisher: Springer Science & Business Media
ISBN: 303460050X
Category : Mathematics
Languages : en
Pages : 214
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Book Description
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
Author: Radmila Bulajich Manfrino
Publisher: Springer Science & Business Media
ISBN: 303460050X
Category : Mathematics
Languages : en
Pages : 214
Get Book Here
Book Description
This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
Author: Yongcheng Chen
Publisher:
ISBN: 9781470130350
Category :
Languages : en
Pages : 222
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Book Description
Math Competition Books Series - The rearrangement inequality is a powerful problem-solving tool. For example, many fundamental inequalities, such as the AM-GM inequality, the Cauchy inequality, and the Chebyshev's inequality, can be generated from the rearrangement inequality.This book shows how you can use the rearrangement inequality to solve a variety of problems.The book can be used by students preparing for math competitions such as Mathcounts, AMC 10/12, AIME (American Invitational Mathematics Examination), and USAJMO/USAMO.
Author: Arthur Engel
Publisher: Springer Science & Business Media
ISBN: 0387226419
Category : Mathematics
Languages : en
Pages : 404
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Book Description
A unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. Written for trainers and participants of contests of all levels up to the highest level, this will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week", thus bringing a creative atmosphere into the classrooms. Equally, this is a must-have for individuals interested in solving difficult and challenging problems. Each chapter starts with typical examples illustrating the central concepts and is followed by a number of carefully selected problems and their solutions. Most of the solutions are complete, but some merely point to the road leading to the final solution. In addition to being a valuable resource of mathematical problems and solution strategies, this is the most complete training book on the market.
Author: Samin Riasat
Publisher:
ISBN: 9781081329709
Category :
Languages : en
Pages : 63
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Book Description
More than a decade ago I published some notes on inequalities on the WWW with the same title as this book aimed for mathematical olympiad preparation. I do not have specific data on how widespread it became. However, search results on the WWW, publication data on ResearchGate and occasional emails from teachers and students gave me evidence that it had indeed spread worldwide. While I was greatly overwhelmed and humbled that so many people across the world read my notes and presumably found them useful, I also felt it necessary to write a more detailed and improved version. This culminated in the publication of this book. While the main topics from the original notes have not changed, this book does contain more details and explanations. I therefore hope that it will be even more useful to everyone.
Author: Zdravko Cvetkovski
Publisher: Springer Science & Business Media
ISBN: 3642237924
Category : Mathematics
Languages : en
Pages : 439
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Book Description
This work is about inequalities which play an important role in mathematical Olympiads. It contains 175 solved problems in the form of exercises and, in addition, 310 solved problems. The book also covers the theoretical background of the most important theorems and techniques required for solving inequalities. It is written for all middle and high-school students, as well as for graduate and undergraduate students. School teachers and trainers for mathematical competitions will also gain benefit from this book.
Author: Thomas Bartz-Beielstein
Publisher: Springer
ISBN: 3319107623
Category : Computers
Languages : en
Pages : 977
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Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Parallel Problem Solving from Nature, PPSN 2013, held in Ljubljana, Slovenia, in September 2014. The total of 90 revised full papers were carefully reviewed and selected from 217 submissions. The meeting began with 7 workshops which offered an ideal opportunity to explore specific topics in evolutionary computation, bio-inspired computing and metaheuristics. PPSN XIII also included 9 tutorials. The papers are organized in topical sections on adaption, self-adaption and parameter tuning; classifier system, differential evolution and swarm intelligence; coevolution and artificial immune systems; constraint handling; dynamic and uncertain environments; estimation of distribution algorithms and metamodelling; genetic programming; multi-objective optimisation; parallel algorithms and hardware implementations; real world applications; and theory.
Author: B.J. Venkatachala
Publisher: Springer
ISBN: 9811087326
Category : Mathematics
Languages : en
Pages : 527
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Book Description
This book discusses about the basic topics on inequalities and their applications. These include the arithmetic mean–geometric mean inequality, Cauchy–Schwarz inequality, Chebyshev inequality, rearrangement inequality, convex and concave functions and Muirhead's theorem. The book contains over 400 problems with their solutions. A chapter on geometric inequalities is a special feature of this book. Most of these problems are from International Mathematical Olympiads and from many national mathematical Olympiads. The book is intended to help students who are preparing for various mathematical competitions. It is also a good source book for graduate students who are consolidating their knowledge of inequalities and their applications.
Author: Yongcheng Chen
Publisher: Createspace Independent Publishing Platform
ISBN: 9781544675176
Category :
Languages : en
Pages : 146
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Book Description
Math Competition Books Series -- The AM-GM inequality is a powerful problem-solving tool. This book shows how you can use the AM-GM Inequality to solve a variety of problems, such as geometry, equations, inequalities, and finding the maximum/minimum value. The book can be used by students preparing for math competitions such as Mathcounts, AMC 8/10/12, and AIME (American Invitational Mathematics Examination). Each chapter consists of (1) basic skill and knowledge section with examples, (2) exercise problems, and (3) detailed solutions to all problems. 9th book: Problem Solving Using Auxiliary Lines https: //www.amazon.com/dp/1975681754 10th book: https: //www.amazon.com/Problem-Solving-Using-Vietas-Theorem/dp/1542800056
Author: Costas Efthimiou
Publisher: American Mathematical Soc.
ISBN: 0821853147
Category : Mathematics
Languages : en
Pages : 381
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Book Description
Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity. The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material. The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
Author: David Alexander Brannan
Publisher: Cambridge University Press
ISBN: 1139458957
Category : Mathematics
Languages : en
Pages : 103
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Book Description
Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.
