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Author: S. Shirali
Publisher: Universities Press
ISBN: 9788173714139
Category : Mathematics
Languages : en
Pages : 334
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Book Description
Author: S. Shirali
Publisher: Universities Press
ISBN: 9788173714139
Category : Mathematics
Languages : en
Pages : 334
Get Book Here
Book Description
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: 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: 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: 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: Sanjoy Mahajan
Publisher: MIT Press
ISBN: 0262265591
Category : Education
Languages : en
Pages : 152
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Book Description
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.
Author: J. Michael Steele
Publisher: Cambridge University Press
ISBN: 9780521546775
Category : Mathematics
Languages : en
Pages : 320
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Book Description
This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence of fascinating problems whose solutions are presented as they might have been discovered - either by one of history's famous mathematicians or by the reader. The problems emphasize beauty and surprise, but along the way readers will find systematic coverage of the geometry of squares, convexity, the ladder of power means, majorization, Schur convexity, exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.
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: 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.
