Softcover ISBN:  9781735831558 
Product Code:  XYZ/46 
List Price:  $59.95 
AMS Member Price:  $47.96 
Softcover ISBN:  9781735831558 
Product Code:  XYZ/46 
List Price:  $59.95 
AMS Member Price:  $47.96 

Book DetailsXYZ SeriesVolume: 46; 2022; 307 ppMSC: Primary 00; 97
This book contains ten frequently recurring themes in algebraic problems. Each chapter starts with a brief introduction that includes examples useful for the reader to grasp the main ideas needed to solve the proposed problems. The first chapter deals with quadratic functions and underscores the use of the discriminant and the relations involving the roots of a quadratic trinomial and its coefficients.
The second chapter emphasizes that every square of a real number is nonnegative. This simple property leads to numerous applications also encountered in subsequent chapters. Chapter 3 focuses on several inequalities, including the most famous inequality in the world of mathematical Olympiads: the CauchySchwarz Inequality. Chapter 4 is devoted to problems related to minima and maxima of algebraic expressions. These problems can also be approached using the techniques studied in the previous chapter.
The fifth chapter is about a beautiful identity involving the cubes of three numbers and the triple of their product and you will see that this identity has numerous interesting applications. Chapter 6 deals with complex numbers. Some definitions and useful results are given to assist the reader in solving the proposed problems. The seventh chapter features Lagrange's Identity, which has various unexpected applications, including those involving problems related to number theory. Chapter 8 focuses on the socalled Sophie Germain's Identity. Here, too, you will find problems in which the application of this identity will be anything but obvious. Chapter 9 looks at expressions of the form \(t + k/t\) and meaningful applications. Finally, the last chapter is about the fifthdegree polynomials \(x^5 + x \pm 1\) and assorted nonroutine problems. Solutions to all proposed problems are provided in the second part of the book: there is a corresponding solution chapter for each of the ten chapters in the first part.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
ReadershipThe intended audience is students who are training for the mathematical Olympiads who want to improve their skills in algebra and especially in the recurrent themes presented in this book. Teachers and professors who train the students for the competitions and organize mathematical circles can benefit from this book as well.

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This book contains ten frequently recurring themes in algebraic problems. Each chapter starts with a brief introduction that includes examples useful for the reader to grasp the main ideas needed to solve the proposed problems. The first chapter deals with quadratic functions and underscores the use of the discriminant and the relations involving the roots of a quadratic trinomial and its coefficients.
The second chapter emphasizes that every square of a real number is nonnegative. This simple property leads to numerous applications also encountered in subsequent chapters. Chapter 3 focuses on several inequalities, including the most famous inequality in the world of mathematical Olympiads: the CauchySchwarz Inequality. Chapter 4 is devoted to problems related to minima and maxima of algebraic expressions. These problems can also be approached using the techniques studied in the previous chapter.
The fifth chapter is about a beautiful identity involving the cubes of three numbers and the triple of their product and you will see that this identity has numerous interesting applications. Chapter 6 deals with complex numbers. Some definitions and useful results are given to assist the reader in solving the proposed problems. The seventh chapter features Lagrange's Identity, which has various unexpected applications, including those involving problems related to number theory. Chapter 8 focuses on the socalled Sophie Germain's Identity. Here, too, you will find problems in which the application of this identity will be anything but obvious. Chapter 9 looks at expressions of the form \(t + k/t\) and meaningful applications. Finally, the last chapter is about the fifthdegree polynomials \(x^5 + x \pm 1\) and assorted nonroutine problems. Solutions to all proposed problems are provided in the second part of the book: there is a corresponding solution chapter for each of the ten chapters in the first part.
A publication of XYZ Press. Distributed in North America by the American Mathematical Society.
The intended audience is students who are training for the mathematical Olympiads who want to improve their skills in algebra and especially in the recurrent themes presented in this book. Teachers and professors who train the students for the competitions and organize mathematical circles can benefit from this book as well.