Methods And Techniques For Proving Inequalities

Author : Yong Su,Bin Xiong
Publisher : World Scientific Publishing Company
Page : 228 pages
File Size : 44,8 Mb
Release : 2015-10-06
Category : Mathematics
ISBN : 9789814696470

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Methods and Techniques for Proving Inequalities by Yong Su,Bin Xiong Pdf

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The authors are coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book explains many basic techniques for proving inequalities such as direct comparison, method of magnifying and reducing, substitution method, construction method, and so on.

Author : Yong Su
Publisher : Unknown
Page : 229 pages
File Size : 51,6 Mb
Release : 2015
Category : Electronic
ISBN : 9814696463

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Methods And Techniques For Proving Inequalities by Yong Su Pdf

Author : Zdravko Cvetkovski
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 46,6 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9783642237928

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Inequalities by Zdravko Cvetkovski Pdf

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 : Michael T. Todinov
Publisher : CRC Press
Page : 142 pages
File Size : 53,9 Mb
Release : 2020-06-02
Category : Technology & Engineering
ISBN : 9781000076448

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Risk and Uncertainty Reduction by Using Algebraic Inequalities by Michael T. Todinov Pdf

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction. It equips readers with powerful domain-independent methods for reducing risk based on algebraic inequalities and demonstrates the significant benefits derived from the application for risk and uncertainty reduction. Algebraic inequalities: • Provide a powerful reliability improvement, risk and uncertainty reduction method that transcends engineering and can be applied in various domains of human activity • Present an effective tool for dealing with deep uncertainty related to key reliability-critical parameters of systems and processes • Permit meaningful interpretations which link abstract inequalities with the real world • Offer a tool for determining tight bounds for the variation of risk-critical parameters and complying the design with these bounds to avoid failure • Allow optimising designs and processes by minimising the deviation of critical output parameters from their specified values and maximising their performance This book is primarily for engineering professionals and academic researchers in virtually all existing engineering disciplines.

Author : Samin Riasat
Publisher : Unknown
Page : 63 pages
File Size : 44,9 Mb
Release : 2019-07-20
Category : Electronic
ISBN : 108132970X

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Basics of Olympiad Inequalities by Samin Riasat Pdf

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 : Radmila Bulajich Manfrino,José Antonio Gómez Ortega,Rogelio Valdez Delgado
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 47,7 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9783034600507

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Inequalities by Radmila Bulajich Manfrino,José Antonio Gómez Ortega,Rogelio Valdez Delgado Pdf

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 : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 55,5 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243

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How to Prove It by Daniel J. Velleman Pdf

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Author : Shi-xiong Liu
Publisher : World Scientific
Page : 607 pages
File Size : 53,5 Mb
Release : 2022-04-08
Category : Mathematics
ISBN : 9789811229909

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Problems And Solutions In Mathematical Olympiad (High School 2) by Shi-xiong Liu Pdf

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 : Hayk Sedrakyan,Nairi Sedrakyan
Publisher : Springer
Page : 243 pages
File Size : 46,7 Mb
Release : 2018-07-05
Category : Mathematics
ISBN : 9783319778365

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Algebraic Inequalities by Hayk Sedrakyan,Nairi Sedrakyan Pdf

This unique collection of new and classical problems provides full coverage of algebraic inequalities. Many of the exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. Algebraic Inequalities can be considered a continuation of the book Geometric Inequalities: Methods of Proving by the authors. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving algebraic inequalities.

Author : Gangsong Leng
Publisher : World Scientific Publishing Company
Page : 144 pages
File Size : 55,5 Mb
Release : 2015-10-21
Category : Mathematics
ISBN : 9789814696500

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Geometric Inequalities by Gangsong Leng Pdf

In China, lots of excellent maths students take an active interest in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad. In the past ten years China's IMO Team has achieved outstanding results — they won the first place almost every year. The author is one of the coaches of China's IMO National Team, whose students have won many gold medals many times in IMO. This book is part of the Mathematical Olympiad Series which discusses several aspects related to maths contests, such as algebra, number theory, combinatorics, graph theory and geometry. The book elaborates on Geometric Inequality problems such as inequality for the inscribed quadrilateral, the area inequality for special polygons, linear geometric inequalities, etc.

Author : Michael T. Todinov
Publisher : CRC Press
Page : 208 pages
File Size : 41,7 Mb
Release : 2020-06-02
Category : Mathematics
ISBN : 9781000076400

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Risk and Uncertainty Reduction by Using Algebraic Inequalities by Michael T. Todinov Pdf

This book covers the application of algebraic inequalities for reliability improvement and for uncertainty and risk reduction. It equips readers with powerful domain-independent methods for reducing risk based on algebraic inequalities and demonstrates the significant benefits derived from the application for risk and uncertainty reduction. Algebraic inequalities: • Provide a powerful reliability improvement, risk and uncertainty reduction method that transcends engineering and can be applied in various domains of human activity • Present an effective tool for dealing with deep uncertainty related to key reliability-critical parameters of systems and processes • Permit meaningful interpretations which link abstract inequalities with the real world • Offer a tool for determining tight bounds for the variation of risk-critical parameters and complying the design with these bounds to avoid failure • Allow optimising designs and processes by minimising the deviation of critical output parameters from their specified values and maximising their performance This book is primarily for engineering professionals and academic researchers in virtually all existing engineering disciplines.

Author : Peter Baumgartner,Reiner Ha hnle,Joachim Posegga
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 40,8 Mb
Release : 1995-04-26
Category : Computers
ISBN : 3540593381

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Theorem Proving with Analytic Tableaux and Related Methods by Peter Baumgartner,Reiner Ha hnle,Joachim Posegga Pdf

This volume constitutes the proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods, TABLEAU '95, held at Schloß Rheinfels, St. Goar, Germany in May 1995. Originally tableau calculi and their relatives were favored primarily as a pedagogical device because of their advantages at the presentation level. The 23 full revised papers in this book bear witness that these methods have now gained fundamental importance in theorem proving, particularly as competitors for resolution methods. The book is organized in sections on extensions, modal logic, intuitionistic logic, the connection method and model elimination, non-clausal proof procedures, linear logic, higher-order logic, and applications

Author : Pascal Schreck,Julien Narboux,Jürgen Richter-Gebert
Publisher : Springer
Page : 259 pages
File Size : 53,8 Mb
Release : 2011-11-10
Category : Computers
ISBN : 9783642250705

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Automated Deduction in Geometry by Pascal Schreck,Julien Narboux,Jürgen Richter-Gebert Pdf

This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on Automated Deduction in Geometry, ADG 2010, held in Munich, Germany in July 2010. The 13 revised full papers presented were carefully selected during two rounds of reviewing and improvement from the lectures given at the workshop. Topics addressed by the papers are incidence geometry using some kind of combinatoric argument; computer algebra; software implementation; as well as logic and proof assistants.

Author : Kim Hoo Hang,Haibin Wang
Publisher : World Scientific Publishing Company
Page : 356 pages
File Size : 46,6 Mb
Release : 2017-05-19
Category : Electronic
ISBN : 9789814583763

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Solving Problems in Geometry by Kim Hoo Hang,Haibin Wang Pdf

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. Request Inspection Copy

Author : Jiri Herman,Radan Kucera,Jaromir Simsa
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461212706

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Equations and Inequalities by Jiri Herman,Radan Kucera,Jaromir Simsa Pdf

A look at solving problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises.