106 Geometry Problems From The Awesomemath Summer Program

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.

This book contains 107 geometry problems used in the AwesomeMath Year-Round Program. The problems offer additional challenges for those who have progressed through the 106 Geometry Problems from the AwesomeMath Summer Camp publication. The book begins with a theoretical chapter, where the authors review basic facts and familiarize the reader with some more advanced techniques. The authors then 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 the authors provide a detailed solution and strive to pass on the intuition and motivation behind it. Numerous 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.

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.

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.

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.

Collection of nearly 200 unusual problems dealing with congruence and parallelism, the Pythagorean theorem, circles, area relationships, Ptolemy and the cyclic quadrilateral, collinearity and concurrency and more. Arranged in order of difficulty. Detailed solutions.

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.

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.