Edward B. Burger

Michael Starbird

The 5 Elements of Effective Thinking presents practical, lively, and inspiring ways for you to become more successful through better thinking. The idea is simple: You can learn how to think far better by adopting specific strategies. Brilliant people aren't a special breed--they just use their minds differently. By using the straightforward and thought-provoking techniques in The 5 Elements of Effective Thinking, you will regularly find imaginative solutions to difficult challenges, and you will discover new ways of looking at your world and yourself--revealing previously hidden opportunities. The book offers real-life stories, explicit action items, and concrete methods that allow you to attain a deeper understanding of any issue, exploit the power of failure as a step toward success, develop a habit of creating probing questions, see the world of ideas as an ever-flowing stream of thought, and embrace the uplifting reality that we are all capable of change. No matter who you are, the practical mind-sets introduced in the book will empower you to realize any goal in a more creative, intelligent, and effective manner. Filled with engaging examples that unlock truths about thinking in every walk of life, The 5 Elements of Effective Thinking is written for all who want to reach their fullest potential--including students, parents, teachers, businesspeople, professionals, athletes, artists, leaders, and lifelong learners. Whenever you are stuck, need a new idea, or want to learn and grow, The 5 Elements of Effective Thinking will inspire and guide you on your way. To share thinking stories, go to: http://5elementsofthinking.wordpress.com

The 5 Elements of Effective Thinking

Making Light of Weighty Ideas

Coincidences, Chaos, and All That Math Jazz

Los 5 elementos del pensamiento efectivo nos ofrece técnicas prácticas, entretenidas e inspiradoras para mejorar nuestra forma de pensar a partir de una idea simple: podemos aprender a pensar mejor adoptando estrategias específicas. La gente brillante no viene de otro mundo, simplemente usan su mente de forma diferente. Las técnicas propuestas en este libro nos enseñan a encontrar soluciones imaginativas a retos complicados, y a descubrir nuevas formas de ver el mundo y a nosotros mismos, encontrando nuevas oportunidades que nos habían pasado desapercibidas. Los 5 elementos que nos proponen los autores para pensar mejor son: 1 – Tierra: Fundamentar nuestro pensamiento; entender bien las cosas. 2 – Fuego: Aprender de los errores para enfocar las cosas de manera distinta y provechosa. 3 – Aire: Sé tu propio Sócrates: Plantearnos preguntas 4 – Agua: Seguir el flujo las ideas: mirar atrás, mirar hacia delante, crear nuevas ideas a partir de las viejas. 5 – elemento: Los cuatro elementos anteriores no sirven de nada si no se practican y no nos implicamos en el cambio. El libro también contiene ejemplos de historias reales y métodos concretos que nos permitirán desarrollar nuestra capacidad de razonar correctamente. Y, por último, descubriremos que todos somos capaces de cambiar.

Los 5 elementos del pensamiento efectivo

It is a rare mathematics book that can be called lucid, light-hearted, and profound, and yet these are the words that capture the spirit of The Heart of Mathematics. Using careful explanation, intriguing puzzles, and challenges, the authors invite readers to use open-ended thinking in discovering and constructing mathematical ideas. Throughout the book, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.

An Invitation to Effective Thinking

The Heart of Mathematics

Welcome to diophantine analysis--an area of number theory in which we attempt to discover hidden treasures and truths within the jungle of numbers by exploring rational numbers. Diophantine analysis comprises two different but interconnected domains--diophantine approximation and diophantine equations. This highly readable book brings to life the fundamental ideas and theorems from diophantine approximation, geometry of numbers, diophantine geometry and $p$-adic analysis. Through an engaging style, readers participate in a journey through these areas of number theory. Each mathematical theme is presented in a self-contained manner and is motivated by very basic notions. The reader becomes an active participant in the explorations, as each module includes a sequence of numbered questions to be answered and statements to be verified. Many hints and remarks are provided to be freely used and enjoyed. Each module then closes with a Big Picture Question that invites the reader to step back from all the technical details and take a panoramic view of how the ideas at hand fit into the larger mathematical landscape. This book enlists the reader to build intuition, develop ideas and prove results in a very user-friendly and enjoyable environment. Little background is required and a familiarity with number theory is not expected. All that is needed for most of the material is an understanding of calculus and basic linear algebra together with the desire and ability to prove theorems. The minimal background requirement combined with the author's fresh approach and engaging style make this book enjoyable and accessible to second-year undergraduates, and even advanced high school students. The author's refreshing new spin on more traditional discovery approaches makes this book appealing to any mathematician and/or fan of number theory.

A Journey Into Diophantine Analysis

Exploring the Number Jungle

Robert Tubbs

Professor Robert Tubbs

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.

An Intuitive Approach to Classical Transcendental Number Theory

Making Transcendence Transparent

Timothy D. Kanold

Juli K. Dixon

Houghton Mifflin Harcourt Publishing Company

Matthew R. Larson

Steve Leinwand

Martha E. Sandoval-Martinez

Advanced Mathematics 1

Florida Go Math

Michael P. Starbird

An irreverent and accessible explanation of challenging puzzles within the world of mathematics considers such topics as the link between a pineapple's spirals and the famous Fibonacci numbers, the shape of the universe as reflected by a twisted strip of paper, and the parallels between the Lincoln and Kennedy assassinations. 50,000 first printing.

Coincidences, Chaos, and All that Math Jazz

How you can become better at solving real-world problems by learning creative puzzle-solving skills We solve countless problems—big and small—every day. With so much practice, why do we often have trouble making simple decisions—much less arriving at optimal solutions to important questions? Are we doomed to this muddle—or is there a practical way to learn to think more effectively and creatively? In this enlightening, entertaining, and inspiring book, Edward Burger shows how we can become far better at solving real-world problems by learning creative puzzle-solving skills using simple, effective thinking techniques. Making Up Your Own Mind teaches these techniques—including how to ask good questions, fail and try again, and change your mind—and then helps you practice them with fun verbal and visual puzzles. The goal is not to quickly solve each challenge but to come up with as many different ways of thinking about it as possible. As you see the puzzles in ever-greater depth, your mind will change, helping you become a more imaginative and creative thinker in daily life. And learning how to be a better thinker pays off in incalculable ways for anyone—including students, businesspeople, professionals, athletes, artists, leaders, and lifelong learners. A book about changing your mind and creating an even better version of yourself through mental play, Making Up Your Own Mind will delight and reward anyone who wants to learn how to find better solutions to life’s innumerable puzzles. And the puzzles extend to the thought-provoking format of the book itself because one of the later short chapters is printed upside down while another is printed in mirror image, further challenging the reader to see the world through different perspectives and make new meaning.

Edward B. Burger

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