109 Inequalities From The Awesomemath Summer Program

Author : Titu Andreescu,Adithya Ganesh
Publisher : Unknown
Page : 0 pages
File Size : 52,6 Mb
Release : 2015
Category : Inequalities (Mathematics)
ISBN : 0988562286

Get Book

109 Inequalities from the AwesomeMath Summer Program by Titu Andreescu,Adithya Ganesh Pdf

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 : Adrian Andreescu,Titu Andreescu,Oleg Mushkarov
Publisher : Unknown
Page : 0 pages
File Size : 47,5 Mb
Release : 2017
Category : Electronic
ISBN : 097992698X

Get Book

113 Geometric Inequalities from the AwesomeMath Summer Program by Adrian Andreescu,Titu Andreescu,Oleg Mushkarov Pdf

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,Adithya Ganesh
Publisher : Unknown
Page : 0 pages
File Size : 51,7 Mb
Release : 2014
Category : Algebra
ISBN : 0988562278

Get Book

108 Algebra Problems from the AwesomeMath Year-round Program by Titu Andreescu,Adithya Ganesh Pdf

The book covers many classical topics in elementary algebra, including factoring, quadratic functions, irrational expressions, Vieta's relations, equations and systems of equations, inequalities, sums and products, and polynomials. Expanding upon the previous work in the series, 105 Problems in Algebra from the AwesomeMath Summer Program, this book features additional more advanced topics, including exponents and logarithms, complex numbers, and trigonometry. The special section on trigonometric substitutions and more explores seemingly algebraic problems with natural geometric and trigonometric interpretations. To give the reader practice with the strategies and techniques discussed in each of the chapters, the authors have included 108 diverse problems, of which 54 are introductory and 54 are advanced. Solutions to all of these problems are provided, in which different approaches are compared.

Author : Titu Andreescu,Marius Stănean
Publisher : Unknown
Page : 0 pages
File Size : 43,7 Mb
Release : 2018
Category : Algebra
ISBN : 0996874585

Get Book

116 Algebraic Inequalities from the AwesomeMath Year-Round Program by Titu Andreescu,Marius Stănean Pdf

This book would certainly help Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various competitive levels. The inequalities from each section are ordered increasingly by the number of variables: one, two, three, four, and multi-variables. Each problem has at least one complete solution and many problems have multiple solutions, useful in developing the necessary array of mathematical machinery for competitions.

Author : Vlad Matei,Elizabeth Reiland
Publisher : Unknown
Page : 0 pages
File Size : 53,6 Mb
Release : 2016
Category : Combinatorial analysis
ISBN : 0996874526

Get Book

112 Combinatorial Problems from the AwesomeMath Summer Program by Vlad Matei,Elizabeth Reiland Pdf

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 : Unknown
Page : 0 pages
File Size : 43,7 Mb
Release : 2013
Category : Algebra
ISBN : 0979926955

Get Book

105 Algebra Problems from the AwesomeMath Summer Program by Titu Andreescu Pdf

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 : Titu Andreescu,Michal Rolínek,Josef Tkadlec
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 2013
Category : Geometry
ISBN : 0979926947

Get Book

106 Geometry Problems from the AwesomeMath Summer Program by Titu Andreescu,Michal Rolínek,Josef Tkadlec Pdf

This book contains 106 geometry problems used in the AwesomeMath Summer Program to train and test top middle and high-school students from the U.S. and around the world. Just as the camp offers both introductory and advanced courses, this book also builds up the material gradually. The authors begin with a theoretical chapter where they familiarize the reader with basic facts and problem-solving techniques. Then they proceed to the main part of the work, the problem sections. The problems are a carefully selected and balanced mix which offers a vast variety of flavors and difficulties, ranging from AMC and AIME levels to high-end IMO problems. Out of thousands of Olympiad problems from around the globe, the authors chose those which best illustrate the featured techniques and their applications. The problems meet the authors' demanding taste and fully exhibit the enchanting beauty of classical geometry. For every problem, they provide a detailed solution and strive to pass on the intuition and motivation behind it. Many problems have multiple solutions.Directly experiencing Olympiad geometry both as contestants and instructors, the authors are convinced that a neat diagram is essential to efficiently solve a geometry problem. Their diagrams do not contain anything superfluous, yet emphasize the key elements and benefit from a good choice of orientation. Many of the proofs should be legible only from looking at the diagrams.

Author : Titu Andreescu,Alessandro Ventullo,Navid Safaei
Publisher : Unknown
Page : 234 pages
File Size : 45,9 Mb
Release : 2019-02-15
Category : Electronic
ISBN : 0999342843

Get Book

117 Polynomial Problems from the Awesomemath Summer Program by Titu Andreescu,Alessandro Ventullo,Navid Safaei Pdf

Author : M. Ram Murty,Jody (Indigo) Esmonde
Publisher : Springer Science & Business Media
Page : 354 pages
File Size : 49,7 Mb
Release : 2005-09-28
Category : Mathematics
ISBN : 9780387269986

Get Book

Problems in Algebraic Number Theory by M. Ram Murty,Jody (Indigo) Esmonde Pdf

The problems are systematically arranged to reveal the evolution of concepts and ideas of the subject Includes various levels of problems - some are easy and straightforward, while others are more challenging All problems are elegantly solved

Author : Titu Andreescu,Zuming Feng
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 42,5 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9780817682224

Get Book

102 Combinatorial Problems by Titu Andreescu,Zuming Feng Pdf

"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,Zuming Feng
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 52,9 Mb
Release : 2006-03-06
Category : Mathematics
ISBN : 9780817644321

Get Book

103 Trigonometry Problems by Titu Andreescu,Zuming Feng Pdf

* 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 : Titu Andreescu,Iurie Boreico,Nikolai Nikolov,Oleg Mushkarov
Publisher : Unknown
Page : 552 pages
File Size : 53,9 Mb
Release : 2020-01-15
Category : Electronic
ISBN : 099934286X

Get Book

Topics in Functional Equations by Titu Andreescu,Iurie Boreico,Nikolai Nikolov,Oleg Mushkarov Pdf

Author : Titu Andreescu,Cosmin Pohoata
Publisher : Unknown
Page : 0 pages
File Size : 51,5 Mb
Release : 2014
Category : Geometry
ISBN : 0988562227

Get Book

110 Geometry Problems for the International Mathematical Olympiad by Titu Andreescu,Cosmin Pohoata Pdf

This book represents a collection of carefully selected geometry problems designed for passionate geometers and students preparing for the IMO. Assuming the theory and the techniques presented in the first two geometry books published by XYZ Press, 106 Geometry Problems from the AwesomeMath Summer Program and 107 Problems from the AwesomeMath Year-Round Program, this book presents a multitude of beautiful synthetic solutions that are meant to give a sense of how one should think about difficult geometry problems. On average, each problem comes with at least two such solutions and with additional remarks about the underlying configuration.

Author : Titu Andreescu,Sam Korsky,Cosmin Pohoata
Publisher : Unknown
Page : 0 pages
File Size : 43,5 Mb
Release : 2016
Category : Geometry
ISBN : 0988562235

Get Book

Lemmas in Olympiad Geometry by Titu Andreescu,Sam Korsky,Cosmin Pohoata Pdf

This book showcases the synthetic problem-solving methods which frequently appear in modern day Olympiad geometry, in the way we believe they should be taught to someone with little familiarity in the subject. In some sense, the text also represents an unofficial sequel to the recent problem collection published by XYZ Press, 110 Geometry Problems for the International Mathematical Olympiad, written by the first and third authors, but the two books can be studied completely independently of each other. The work is designed as a medley of the important Lemmas in classical geometry in a relatively linear fashion: gradually starting from Power of a Point and common results to more sophisticated topics, where knowing a lot of techniques can prove to be tremendously useful. We treat each chapter as a short story of its own and include numerous solved exercises with detailed explanations and related insights that will hopefully make your journey very enjoyable.

Author : Radu Bumbacea
Publisher : Unknown
Page : 400 pages
File Size : 42,6 Mb
Release : 2020-03-30
Category : Electronic
ISBN : 0999342878

Get Book

Graph Theory by Radu Bumbacea Pdf