Bøger af Titu Andreescu

Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a uniquely intuitive approach to the subject: it presents hundreds of extreme-value problems, examples, and solutions primarily through Euclidean geometry.Key features and topics:* Comprehensive selection of problems, including Greek geometry and optics, Newtonian mechanics, isoperimetric problems, and recently solved problems such as Malfatti's problem * Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning* Presentation and application of classical inequalities, including Cauchy--Schwarz and Minkowski's Inequality; basic results in calculus, such as the Intermediate Value Theorem; and emphasis on simple but useful geometric concepts, including transformations, convexity, and symmetry * Clear solutions to the problems, often accompanied by figures * Hundreds of exercises of varying difficulty, from straightforward to Olympiad-caliberWritten by a team of established mathematicians and professors, this work draws on the authors' experience in the classroom and as Olympiad coaches. By exposing readers to a wealth of creative problem-solving approaches, the text communicates not only geometry but also algebra, calculus, and topology. Ideal for use at the junior and senior undergraduate level, as well as in enrichment programs and Olympiad training for advanced high school students, this book's breadth and depth will appeal to a wide audience, from secondary school teachers and pupils to graduate students, professional mathematicians, and puzzleenthusiasts.

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.

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.

This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions.

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.

Problems illustrating important mathematical techniques with solutions and accompanying essays.

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.

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".

Complex Numbers from A to ... Z

Mathematical Olympiad Treasures aims at building a bridge between ordinary high school exercises and more sophisticated, intricate and abstract concepts in undergraduate mathematics.

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.

Mathematical Olympiad Challenges offers a rich collection of problems assembled by coaches of the U.S. Olympiad Team. The book is ideal for problem-solving courses and teacher development, for self-study, and for competition training. The Second Edition features 400 additional problems and solutions.

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.

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.

This introductory textbook takes a problem-solving approach to number theory, situating each concept within the framework of an example or a problem for solving.