Books by Titu Andreescu

A sequel to the 116 Algebraic Inequalities from the AwesomeMath Year-round Program and 118 Inequalities for Mathematics Competitions. The book delves into other elementary techniques but also powerful methods and generalizations for constrained optimization in the theory of inequalities.

Building bridges between classical results and contemporary nonstandard problems, this highly relevant work embraces important topics in analysis and algebra from a problem-solving perspective.

The ubiquity of polynomials and their ability to characterize complex patterns let us better understand generalizations, theorems, and elegant paths to solutions that they provide. We strive to showcase the true beauty of polynomials through a well-thought collection of problems from mathematics competitions and intuitive lectures.

Help your students to think critically and creatively through team-based problem solving instead of focusing on testing and outcomes.Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as outcomes rather than as individuals who require guidance on thinking critically and creatively. Awesome Math focuses on team-based problem solving to teach discrete mathematics, a subject essential for success in the STEM careers of the future. Built on the increasingly popular growth mindset, this timely book emphasizes a problem-solving approach for developing the skills necessary to think critically, creatively, and collaboratively.In its current form, math education is a series of exercises: straightforward problems with easily-obtained answers. Problem solving, however, involves multiple creative approaches to solving meaningful and interesting problems. The authors, co-founders of the multi-layered educational organization AwesomeMath, have developed an innovative approach to teaching mathematics that will enable educators to:* Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world* Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration* Encourage and reinforce curiosity, critical thinking, and creativity in their students* Get students into the growth mindset, coach math teams, and make math fun again* Create lesson plans built on problem based learning and identify and develop educational resources in their schoolsAwesome Math: Teaching Mathematics with Problem Based Learning is a must-have resource for general education teachers and math specialists in grades 6 to 12, and resource specialists, special education teachers, elementary educators, and other primary education professionals.

Includes problem-solving tactics and practical test-taking techniques that provide enrichment and preparation for various math competitions. This title provides comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry.

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.

Covers such topics as: 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.

Covers telescoping sums and products in algebra and trigonometry; the use of complex numbers and de Moivre's Formula; Abel's summation formula; mathematical induction; combinatorial identities; and multiplicative functions and the use of Mobius function. The theory is presented together with rich examples.

Trigonometry finally receives the attention it deserves in this stand-alone book. The theory chapter is an invaluable pedagogical resource with lots of examples and guided exercises. 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 reveiws the last two decades of computational techniques and progress in the classical theory of quadratic diophantine equations. Presents important quadratic diophantine equations and applications, and includes excellent examples and open problems.

Featuring a problem-solving approach to linear algebra, this work aims to develop the theoretical foundations of vector spaces, linear equations, matrix algebra, eigen vectors, and orthogonality. It also emphasizes applications and connections to fields such as biology, economics, computer graphics, cryptography, and political science.

This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not "linear".

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 this title is an instructive resource for students striving for success at national and international competitions.

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory.