Polynomials form the cornerstone of modern mathematics and other discrete fields, and this book will showcase the true beauty of polynomials through a discerning collection of problems from mathematics competitions and intuitive lectures. Through the problems, lecture, and theory, readers will gain the knowledge, strategies, and tricks to fully appreciate, solve, and enjoy solving polynomials.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

Cross discipline discoveries with multiple solutions provided makes Topics in Geometric Inequalities a must have for dedicated problem solvers that will strengthen readers' abilities to analyze, dissect, and invent creative methods—all skills that are necessary to succeed in mathematics competitions. Readers will also learn innovative and powerful techniques in geometric arguments.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

Mathematical Reflections: Two Wonderful Years is a compilation and revision of the 2016 and 2017 volumes from the online journal of the same name. This book is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a fire for mathematics. Passionate readers submitted many of the problems, solutions, and articles and all require creativity, experience, and comprehensive mathematical knowledge.

This book is a great resource for students training for advanced national and international mathematics competitions such as USAMO and IMO.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

Math Leads for Mathletes Book 2 is part of the Math Leads for Mathletes series, providing more challenging units for young math problem solvers and many others! The book draws on the authors' experience working with young mathletes and on the collective wisdom of mathematics educators around the world to help parents and mentors challenge and teach their aspiring math problem solvers. The topics contained in this book are best suited for middle schoolers, although students who discovered competitive mathematics in later grades will also benefit from the material. This book will help students advance in several directions important in competitive mathematics: algebra, combinatorics, geometry, and number theory. It presents a variety of problem solving strategies and challenges readers to explain their solutions, write proofs, and explore connections with other problems.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

The main areas covered are: (1) telescoping sums and products in algebra and trigonometry; (2) the use of complex numbers and de Moivre's formula; (3) Abel's summation formula; (4) mathematical induction; (5) combinatorial identities; and (6) multiplicative functions and the use of Möbius function.

The theory is presented together with rich examples. At the end, readers are invited to solve problems from a list of 125 questions divided into three levels.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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 multivariables. 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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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 tool for anybody who wants to explore the beauty of trigonometry.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This books stems from the desire to publish Cuban National Mathematical Olympiad problems with elegant solutions and illustrations. It encompasses all problems from the 2001 to 2016 Olympiads, except for 2002, with thorough, in-depth solutions. This work is much more than a compilation of problems; it is a meticulous exposition with complete solutions to every problem, allowing readers to grasp the problem-solving techniques discussed.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book is an English translation of a text written by Constantin Mihalescu, a retired artillery colonel and enthusiastic amateur mathematician. It contains a comprehensive collection of the most important properties of points, lines, and circles related to triangles and quadrilaterals, as they were known by the mid-1950s, and a rich assortment of problems to entice and inspire readers of all levels. Topics covered include the nine-point circle, the Simson line, the orthopolar triangles, the orthopole, the Gergonne and Nagel points, the Miquel point and circle, the Carnot circle, the Brocard points, the Lemoine point and circles, the Newton-Gauss line, and much more.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

For curious readers 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, the book encourages readers to try their hand at these types of inequalities. The goal is to consolidate mathematical reasoning while providing exposure to a broad range of problems, all teeming with insightful inequality-type solutions.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

The book includes 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 mathematics.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book takes familiar ideas and extends them to a rich variety of problems. The intended audience is the ambitious high school or college student. The topics covered span algebra, geometry, number theory, and even a few elements of mathematical analysis. Each chapter explores specific themes and ideas that underlie the aforementioned subject areas. The “landscapes” presented provide a “view” into areas that are not typically encountered in great depth in standard coursework but nonetheless have profound implications.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book, a compilation and revision of the 2014 and 2015 volumes from the online journal of the same name, is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a fire for mathematics. Passionate readers submitted many of the problems, solutions, and articles and all require creativity, experience, and comprehensive mathematical knowledge.

This book is a great resource for students training for advanced national and international mathematics competitions such as USAMO and IMO.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

Algebra plays a fundamental role in math and science and provides a uniform language with which we can express mathematical concepts. The field of number theory also relies heavily on algebraic machinery. This book provides the strong foundation in algebra and number theory necessary to master other mathematical disciplines. The authors cover the fundamentals of their own areas of mathematics and discuss important techniques and strategies that frequently arise in junior-level Olympiad problems.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book showcases the synthetic problem-solving methods which frequently appear in modern-day Olympiad geometry and makes them accessible even to readers with little familiarity in the subject. Each chapter is presented as a short story of its own and includes numerous solved exercises with detailed explanations and related insights to assist the reader on this journey.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book is a compilation and revision of the 2012 and 2013 volumes from the online journal of the same name. This book is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a fire for mathematics. Passionate readers submitted many of the problems, solutions, and articles and all require creativity, experience, and comprehensive mathematical knowledge. This book is a great resource for students training for advanced national and international mathematics competitions such as USAMO and IMO.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book is a compilation and revision of the 2010 and 2011 volumes from the online journal of the same name. This book is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a fire for mathematics. Many of the problems, solutions, and articles were submitted by passionate readers and all require creativity, experience, and comprehensive mathematical knowledge. This book is a great resource for students training for advanced national and international mathematics competitions such as USAMO and IMO.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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 enrichment material by teachers, parents, math coaches, or in math clubs and circles.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

The authors, who have attended the BMO several times as leaders and/or deputy leaders, present a complete description of the evolution of the BMO from its creation until the present. All problems are presented with complete solutions. Many problems have alternative solutions or extensions. A preparatory addendum, containing additional concepts and useful classical results, has been incorporated at the end of the book.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

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.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book is a compilation and revision of the 2008 and 2009 volumes from the online journal of the same name. This book is aimed at high school students, participants in math competitions, undergraduates, and anyone who has a fire for mathematics. Many of the problems, solutions, and articles were submitted by passionate readers and all require creativity, experience, and comprehensive mathematical knowledge. This book is a great resource for students training for advanced national and international mathematics competitions such as USAMO and IMO.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

This book is a systematic and comprehensive approach to functional equations as a whole. Unlike in other branches of competitive mathematics, there is very little theory; instead, the methods and techniques utilized in solving these equations play the most important part. For this reason the book takes a highly practical path and includes lots of problems designed to teach students how to familiarize themselves with every strategy employed, as well as how to experiment in combining and manipulating different techniques.

This work contains all the important functional equations given at contests in recent years, classified by the way the equations are solved. It explains the reasoning behind each method and offers advice on how to invent meaningful solutions.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.

The authors provide a combination of enthusiasm and experience, which will delight any reader. In this volume, they present innumerable beautiful results, intriguing problems, and ingenious solutions. The problems range from elementary gems to deep truths. A truly delightful and highly instructive book, this will prepare the engaged reader not only for any mathematics competition they may enter but also for a lifetime of mathematical enjoyment. This book is a must for the bookshelves of both aspiring and seasoned mathematicians.

A publication of XYZ Press. Distributed in North America by the American Mathematical Society.