Download or read book Topics in Geometric Inequalities written by Titu Andreescu and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a sequel to 113 Geometric Inequalities from the AwesomeMath Summer Program, this book extends the themes discussed in the former book and broadens a problem-solver's competitive arsenal. Strategies from multiple fields, such as Algebra, Calculus, and pure Geometry provide the reader with varied methods useful in mathematics competitions. Starting with the fundamentals such as the triangle inequality and ""broken lines'', the book progresses increasingly to more sophisticated machinery such as the Averaging Method, Quadratic Forms, Finite Fourier Transforms, Level Curves, the Erdös-Mordell and Brunn-Minkowski Inequalities, as well as the Isoperimetric Theorem, to name a few. Rich theory and generalizations accompany the aforementioned topics to supply the reader with a rigorous exploration of fields associated with geometric inequalities.
Download or read book Recent Advances in Geometric Inequalities written by Dragoslav S. Mitrinovic and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometric Inequalities written by Yurii D. Burago and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.
Download or read book Geometric Inequalities written by Hayk Sedrakyan and published by Springer. This book was released on 2017-05-27 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. 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 geometric inequalities.
Download or read book Geometric Inequalities written by Nicholas D. Kazarinoff and published by Mathematical Association of America (MAA). This book was released on 1961 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Anybody who liked their first geometry course (and some who did not) will enjoy the simply stated geometric problems about maximum and minimum lengths and areas in this book. Many of these already fascinated the Greeks, for example, the problem of enclosing the largest possible area by a fence of given length, and some were solved long ago; but others remain unsolved even today. Some of the solutions of the problems posed in this book, for example, the problem of inscribing a triangle of smallest perimeter into a given triangle, were supplied by world famous mathematicians, other by high school students.
Download or read book Inequalities in Geometry and Applications written by Gabriel-Eduard Vîlcu and published by MDPI. This book was released on 2021-03-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the recent developments in the field of geometric inequalities and their applications. The volume covers a vast range of topics, such as complex geometry, contact geometry, statistical manifolds, Riemannian submanifolds, optimization theory, topology of manifolds, log-concave functions, Obata differential equation, Chen invariants, Einstein spaces, warped products, solitons, isoperimetric problem, Erdös–Mordell inequality, Barrow’s inequality, Simpson inequality, Chen inequalities, and q-integral inequalities. By exposing new concepts, techniques and ideas, this book will certainly stimulate further research in the field.
Download or read book Isoperimetric Inequalities written by Isaac Chavel and published by Cambridge University Press. This book was released on 2001-07-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced introduction emphasizes the variety of ideas, techniques, and applications of the subject.
Download or read book Inequalities for Differential Forms written by Ravi P. Agarwal and published by Springer Science & Business Media. This book was released on 2009-09-19 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.
Download or read book 113 Geometric Inequalities from the AwesomeMath Summer Program written by Adrian Andreescu and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the curious reader looking to sharpen their arsenal of mathematical strategies on the Olympiad level, 113 Geometric Inequalities from the AwesomeMath Summer Program is a valuable addition. This problem-solving methodology prompts key ideas in other domains such as calculus or complex numbers as the solutions are usually nonstandard in a geometric sense. Nevertheless, trying your hand at these types of inequalities consolidates your mathematical reasoning while exposing you to a broad range of problems, all teeming with insightful inequality-type solutions.
Download or read book Inequalities written by Radmila Bulajich Manfrino and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Inequalities written by Yurii D. Burago and published by Springer. This book was released on 2012-12-22 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: A 1988 classic, covering Two-dimensional Surfaces; Domains on the Plane and on Surfaces; Brunn-Minkowski Inequality and Classical Isoperimetric Inequality; Isoperimetric Inequalities for Various Definitions of Area; and Inequalities Involving Mean Curvature.
Download or read book Titu Andreescu and Mark Saul written by Titu Andreescu and published by American Mathematical Soc.. This book was released on 2016-12-19 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not “linear”. The central topic of inequalities is linked to others in mathematics. Often these topics relate to much more than algebraic inequalities. There are also “secret” pathways through the book. Each chapter has a subtext, a theme which prepares the student for learning other mathematical topics, concepts, or habits of mind. For example, the early chapters on the arithmetic mean/geometric mean inequality show how very simple observations can be leveraged to yield useful and interesting results. Later chapters give examples of how one can generalize a mathematical statement. The chapter on the Cauchy-Schwarz inequality provides an introduction to vectors as mathematical objects. And there are many other secret pathways that the authors hope the reader will discover—and follow. 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.
Download or read book Selected Topics in Geometry with Classical Vs Computer Proving written by Pavel Pech and published by World Scientific. This book was released on 2007 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents various automatic techniques based on Grbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects ? which cannot be easily done with a ruler and compass.Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically ? without using computer where possible ? so that readers can compare the strengths and weaknesses of both approaches.
Download or read book Geometric Inequalities written by and published by . This book was released on 1969 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inequalities written by B.J. Venkatachala and published by Springer. This book was released on 2018-05-09 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Inequalities written by Zdravko Cvetkovski and published by Springer Science & Business Media. This book was released on 2012-01-06 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Analysis and Geometry of Hardy s Inequality written by Alexander A. Balinsky and published by Springer. This book was released on 2015-10-20 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz’ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy’s Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.
