Author: Adrian Andreescu
Publisher:
ISBN: 9780979926983
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Titu Andreescu
Publisher:
ISBN: 9780999342831
Category : Geometry, Algebraic
Languages : en
Pages : 0
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Book Description
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.
Author: Titu Andreescu
Publisher:
ISBN: 9780988562288
Category : Inequalities (Mathematics)
Languages : en
Pages : 0
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Book Description
This book explores the theory and techniques involved in proving algebraic inequalities. To expand the reader's mathematical toolkit, the authors present problems from journals and contests from around the world. Inequalities are an essential topic in Olympiad problem solving, and 109 Inequalities will serve as an instructive resource for students striving for success at national and international competitions. Inequalities are also of great theoretical interest and pave the way towards advanced topics such as analysis, probability theory, and measure theory. Most of all, the authors hope that the reader finds inspiration in both the struggle and beauty of proving algebraic inequalities.
Author: Titu Andreescu
Publisher:
ISBN: 9780979926952
Category : Algebra
Languages : en
Pages : 0
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Book Description
The main purpose of this book is to provide an introduction to central topics in elementary algebra from a problem-solving point of view. While working with students who were preparing for various mathematics competitions or exams, the author observed that fundamental algebraic techniques were not part of their mathematical repertoire. Since algebraic skills are not only critical to algebra itself but also to numerous other mathematical fields, a lack of such knowledge can drastically hinder a student's performance. Taking the above observations into account, the author has put together this introductory book using both simple and challenging examples which shed light upon essential algebraic strategies and techniques, as well as their application in diverse meaningful problems. This work is the first volume in a series of such books. The featured topics from elementary and classical algebra include factorizations, algebraic identities, inequalities, algebraic equations and systems of equations. More advanced concepts such as complex numbers, exponents and logarithms, as well as other topics, are generally avoided.Nevertheless, some problems are constructed using properties of complex numbers which challenge and expose the reader to a broader spectrum of mathematics. Each chapter focuses on specific methods or strategies and provides an ample collection of accompanying problems that graduate in difficulty and complexity. In order to assist the reader with verifying mastery of the theoretical component, 105 problems are included in the last sections of the book, of which 52 are introductory and 53 are advanced. All problems come together with solutions, many employing several approaches and providing the motivation behind the solutions offered.
Author: Vlad Matei
Publisher:
ISBN: 9780996874526
Category : Combinatorial analysis
Languages : en
Pages : 0
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Book Description
This book aims to give students a chance to begin exploring some introductory to intermediate topics in combinatorics, a fascinating and accessible branch of mathematics centered around (among other things) counting various objects and sets. We include chapters featuring tools for solving counting problems, proof techniques, and more to give students a broad foundation to build on. The only prerequisites are a solid background in arithmetic, some basic algebra, and a love for learning math.
Author: Titu Andreescu
Publisher:
ISBN: 9780996874564
Category :
Languages : en
Pages : 150
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Book Description
This book covers the theoretical background of exponents and logarithms, as well as some of their important applications. Starting from the basics, the reader will gain familiarity with how the exponential and logarithmic functions work, and will then learn how to solve different problems with them. The authors give the readers the opportunity to test their understanding of the topics discussed by exposing them to 114 carefully chosen problems, whose full solutions can be found at the end of the book.
Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 0817682228
Category : Mathematics
Languages : en
Pages : 125
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Book Description
"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.
Author: Titu Andreescu
Publisher: Springer Science & Business Media
ISBN: 0817644326
Category : Mathematics
Languages : en
Pages : 222
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Book Description
* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training
Author: Robert Bosch
Publisher:
ISBN: 9780996874540
Category :
Languages : en
Pages : 200
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Book Description
Author: Titu Andreescu
Publisher:
ISBN: 9780999342862
Category :
Languages : en
Pages : 552
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Book Description
