115 Trigonometry Problems From The Awesomemath Summer Program

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115 Trigonometry Problems from the AwesomeMath Summer Program

Titu Andreescu,Vlad Crisan
115 Trigonometry Problems from the AwesomeMath Summer Program Book PDF

Author : Titu Andreescu,Vlad Crisan
Publisher : Unknown
Page : 200 pages
File Size : 50,6 Mb
Release : 2017-11
Category : Trigonometry
ISBN : 0999342800

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115 Trigonometry Problems from the AwesomeMath Summer Program by Titu Andreescu,Vlad Crisan Pdf

Focusing on Trigonometry reveals a wealth of alternate approaches to solving intricate geometry problems while providing foundational support in other areas of mathematics such as Fourier Analysis and Differential Equations. It is time for Trigonometry to receive the attention it deserves in this stand-alone book where the theory chapter is an invaluable pedagogical resource with lots of examples and guided exercises and the subsequent chapters offer a collection of carefully selected introductory through advanced problems and solutions intended to enhance the problem-solving skills of the reader. This book is not only for those studying for mathematics Olympiads but all individuals who want a better understanding of Trigonometry so they will be more successful in different settings such as a calculus course. This book offers a comprehensive overview of the trigonometric functions and contains a collection of 115 carefully selected introductory and advanced problems in Trigonometry from world-wide renowned Olympiads and mathematical magazines, as well as original problems designed by the authors. Together with the beautiful examples and the creative solutions, the present text is a valuable resource and teaching material for anybody who wants to explore the beauty of Trigonometry.

106 Geometry Problems from the AwesomeMath Summer Program

Titu Andreescu,Michal Rolínek,Josef Tkadlec
106 Geometry Problems from the AwesomeMath Summer Program Book PDF

Author : Titu Andreescu,Michal Rolínek,Josef Tkadlec
Publisher : Unknown
Page : 0 pages
File Size : 40,6 Mb
Release : 2013
Category : Geometry
ISBN : 0979926947

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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.

108 Algebra Problems from the AwesomeMath Year-round Program

Titu Andreescu,Adithya Ganesh
108 Algebra Problems from the AwesomeMath Year round Program Book PDF

Author : Titu Andreescu,Adithya Ganesh
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 2014
Category : Algebra
ISBN : 0988562278

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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.

Problems from the Book

Titu Andreescu,Gabriel Dospinescu
Problems from the Book Book PDF

Author : Titu Andreescu,Gabriel Dospinescu
Publisher : Xyz Press
Page : 0 pages
File Size : 55,5 Mb
Release : 2010
Category : Mathematics
ISBN : 0979926904

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Problems from the Book by Titu Andreescu,Gabriel Dospinescu Pdf

In this volume they present innumerable beautiful results, intriguing problems, and ingenious solutions. The problems range from elementary gems to deep truths.

105 Algebra Problems from the AwesomeMath Summer Program

Titu Andreescu
105 Algebra Problems from the AwesomeMath Summer Program Book PDF

Author : Titu Andreescu
Publisher : Unknown
Page : 0 pages
File Size : 51,6 Mb
Release : 2013
Category : Algebra
ISBN : 0979926955

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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.

103 Trigonometry Problems

Titu Andreescu,Zuming Feng
103 Trigonometry Problems Book PDF

Author : Titu Andreescu,Zuming Feng
Publisher : Springer Science & Business Media
Page : 214 pages
File Size : 46,6 Mb
Release : 2006-03-06
Category : Mathematics
ISBN : 9780817644321

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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

109 Inequalities from the AwesomeMath Summer Program

Titu Andreescu,Adithya Ganesh
109 Inequalities from the AwesomeMath Summer Program Book PDF

Author : Titu Andreescu,Adithya Ganesh
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 2015
Category : Inequalities (Mathematics)
ISBN : 0988562286

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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.

Straight from the Book

Titu Andreescu,Gabriel Dospinescu
Straight from the Book Book PDF

Author : Titu Andreescu,Gabriel Dospinescu
Publisher : Unknown
Page : 0 pages
File Size : 46,5 Mb
Release : 2012
Category : Mathematics
ISBN : 0979926939

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Straight from the Book by Titu Andreescu,Gabriel Dospinescu Pdf

This book is a compilation of many suggestions, much advice, and even more hard work. Its main objective is to provide solutions to the problems which were originally proposed in the first 12 chapters of Problems from the Book. The volume is far more than a collection of solutions. The solutions are used as motivation for the introduction of some very clear mathematical expositions. This is absolutely state-of-the-art material. Everyone who loves mathematics and mathematical thinking should acquire this book.

102 Combinatorial Problems

Titu Andreescu,Zuming Feng
102 Combinatorial Problems Book PDF

Author : Titu Andreescu,Zuming Feng
Publisher : Springer Science & Business Media
Page : 125 pages
File Size : 52,9 Mb
Release : 2013-11-27
Category : Mathematics
ISBN : 9780817682224

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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.

Number Theory

Titu Andreescu,Gabriel Dospinescu,Oleg Mushkarov
Number Theory Book PDF

Author : Titu Andreescu,Gabriel Dospinescu,Oleg Mushkarov
Publisher : Unknown
Page : 686 pages
File Size : 41,9 Mb
Release : 2017-07-15
Category : Number theory
ISBN : 0988562200

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Number Theory by Titu Andreescu,Gabriel Dospinescu,Oleg Mushkarov Pdf

Challenge your problem-solving aptitude in number theory with powerful problems that have concrete examples which reflect the potential and impact of theoretical results. Each chapter focuses on a fundamental concept or result, reinforced by each of the subsections, with scores of challenging problems that allow you to comprehend number theory like never before. All students and coaches wishing to excel in math competitions will benefit from this book as will mathematicians and adults who enjoy interesting mathematics.

Mathematical Induction

Titu Andreescu,Vlad Crisan
Mathematical Induction Book PDF

Author : Titu Andreescu,Vlad Crisan
Publisher : Unknown
Page : 432 pages
File Size : 52,7 Mb
Release : 2017-03-15
Category : Induction (Mathematics)
ISBN : 0996874593

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Mathematical Induction by Titu Andreescu,Vlad Crisan Pdf

This book serves as a very good resource and teaching material for anyone who wants to discover the beauty of Induction and its applications, from novice mathematicians to Olympiad-driven students and professors teaching undergraduate courses. The authors explore 10 different areas of mathematics, including topics that are not usually discussed in an Olympiad-oriented book on the subject. Induction is one of the most important techniques used in competitions and its applications permeate almost every area of mathematics.

Math Leads for Mathletes

Titu Andreescu,Brabislav Kisačanin
Math Leads for Mathletes Book PDF

Author : Titu Andreescu,Brabislav Kisačanin
Publisher : Unknown
Page : 0 pages
File Size : 47,9 Mb
Release : 2014
Category : Mathematics
ISBN : 098856226X

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Math Leads for Mathletes by Titu Andreescu,Brabislav Kisačanin Pdf

The topics contained in this book are best suited for advanced fourth and fifth graders as well as for extremely talented third graders or for anyone preparing for AMC 8 or similar mathematics contests. The concepts and problems presented could be used as an enrichment material by teachers, parents, math coaches, or in math clubs and circles.

An Introduction to Diophantine Equations

Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
An Introduction to Diophantine Equations Book PDF

Author : Titu Andreescu,Dorin Andrica,Ion Cucurezeanu
Publisher : Springer Science & Business Media
Page : 350 pages
File Size : 44,6 Mb
Release : 2010-09-02
Category : Mathematics
ISBN : 9780817645496

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An Introduction to Diophantine Equations by Titu Andreescu,Dorin Andrica,Ion Cucurezeanu Pdf

This problem-solving book is an introduction to the study of Diophantine equations, a class of equations in which only integer solutions are allowed. The presentation features some classical Diophantine equations, including linear, Pythagorean, and some higher degree equations, as well as exponential Diophantine equations. Many of the selected exercises and problems are original or are presented with original solutions. An Introduction to Diophantine Equations: A Problem-Based Approach is intended for undergraduates, advanced high school students and teachers, mathematical contest participants — including Olympiad and Putnam competitors — as well as readers interested in essential mathematics. The work uniquely presents unconventional and non-routine examples, ideas, and techniques.

Purple Comet! Math Meet

Titu Andreescu,Jonathan Kane
Purple Comet Math Meet Book PDF

Author : Titu Andreescu,Jonathan Kane
Publisher : Unknown
Page : 0 pages
File Size : 47,5 Mb
Release : 2013
Category : Mathematics
ISBN : 0979926912

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Purple Comet! Math Meet by Titu Andreescu,Jonathan Kane Pdf

This book is a comprehensive compilation of all the problems and solutions from the 2003 to 2012 Purple Comet Math Meet contests for middle and high school students. The problems featured not only employ an extensive range of mathematical concepts from algebra, geometry, number theory, and combinatorics but also encourage team collaboration. Any student interested in mathematics--whether looking to prepare for contests or, even more importantly, to sharpen math problem-solving skills--would cherish and enjoy this unique and pertinent collection of meaningful problems and solutions.

Lemmas in Olympiad Geometry

Titu Andreescu,Sam Korsky,Cosmin Pohoata
Lemmas in Olympiad Geometry Book PDF

Author : Titu Andreescu,Sam Korsky,Cosmin Pohoata
Publisher : Unknown
Page : 0 pages
File Size : 44,9 Mb
Release : 2016
Category : Geometry
ISBN : 0988562235

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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.