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115 Trigonometry Problems from the AwesomeMath Summer Program

Author : Titu Andreescu

Publisher :

Page : 200 pages

File Size : 27,20 MB

Release : 2017-11

Category : Trigonometry

ISBN : 9780999342800

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Book Description

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.



114 Exponent and Logarithm Problems from the AwesomeMath Summer Program

Author : Titu Andreescu

Publisher :

Page : 150 pages

File Size : 24,22 MB

Release : 2016-12-05

Category :

ISBN : 9780996874564

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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.



108 Algebra Problems from the AwesomeMath Year-round Program

Author : Titu Andreescu

Publisher :

Page : 0 pages

File Size : 32,36 MB

Release : 2014

Category : Algebra

ISBN : 9780988562271

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Book Description

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.



103 Trigonometry Problems

Author : Titu Andreescu

Publisher : Springer Science & Business Media

Page : 222 pages

File Size : 25,81 MB

Release : 2006-03-04

Category : Mathematics

ISBN : 0817644326

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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



102 Combinatorial Problems

Author : Titu Andreescu

Publisher : Springer Science & Business Media

Page : 125 pages

File Size : 18,42 MB

Release : 2013-11-27

Category : Mathematics

ISBN : 0817682228

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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.



Number Theory

Author : Titu Andreescu

Publisher :

Page : 686 pages

File Size : 45,6 MB

Release : 2017-07-15

Category : Number theory

ISBN : 9780988562202

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Book Description

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.



Math Leads for Mathletes

Author : Titu Andreescu

Publisher :

Page : 0 pages

File Size : 37,19 MB

Release : 2014

Category : Mathematics

ISBN : 9780988562264

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Book Description

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.



109 Inequalities from the AwesomeMath Summer Program

Author : Titu Andreescu

Publisher :

Page : 0 pages

File Size : 45,71 MB

Release : 2015

Category : Inequalities (Mathematics)

ISBN : 9780988562288

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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.



Complex Numbers from A to ...Z

Author : Titu Andreescu

Publisher : Springer Science & Business Media

Page : 336 pages

File Size : 17,25 MB

Release : 2007-10-08

Category : Mathematics

ISBN : 0817644490

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Book Description

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory



Introduction to Number Theory

Author : Mathew Crawford

Publisher : Ingram

Page : 0 pages

File Size : 12,29 MB

Release : 2008

Category : Number theory

ISBN : 9781934124123

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Book Description

"Learn the fundamentals of number theory from former MATHCOUNTS, AHSME, and AIME perfect scorer Mathew Crawford. Topics covered in the book include primes & composites, multiples & divisors, prime factorization and its uses, base numbers, modular arithmetic, divisibility rules, linear congruences, how to develop number sense, and much more. The text is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes motivated solutions to these problems, through which concepts and curriculum of number theory are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. In addition to the instructional material, the book contains hundreds of problems ... This book is ideal for students who have mastered basic algebra, such as solving linear equations. Middle school students preparing for MATHCOUNTS, high school students preparing for the AMC, and other students seeking to master the fundamentals of number theory will find this book an instrumental part of their mathematics libraries."--Publisher's website