Edward B. Burger – författare

While the theory of transcendental numbers is a fundamental and important branch of number theory, most mathematicians know only its most elementary results. The aim of Making Transcendence Transparent is to provide the reader with an understanding of the basic principles and tools of transcendence theory and an intuitive framework within which the major results can be appreciated and their proofs can be understood. The book includes big picture overviews of the over-arching ideas, and general points of attack in particular arguments, so the reader will enjoy and appreciate the panoramic view of transcendence. It is designed to appeal to interested mathematicians, graduate students, and advanced undergraduates.

A book for the eternally curious, Coincidences fuses a professor’s understanding of the hidden mathematical skeleton of the universe with the sensibility of a stand-up comedian, making life’s big questions accessible and compelling. Each chapter opens with a surprising insight—not a mathematic formula, but a common observation. From there, the authors leapfrog over math and anecdote toward profound ideas about nature, art, and music. Coincidences is a book for lovers of puzzles and posers of outlandish questions, lapsed math aficionados and the formula-phobic alike.

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

How you can become better at solving real-world problems by learning creative puzzle-solving skillsWe 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.

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.

The Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen­ tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task. Thus transcendental numbers are an enigmatic species of number: We know they are all around us and yet it requires enormous effort to catch one. More often than not, they slip through our fingers and dissappear back into the dense jungle of numbers. Here we will venture to tame a few of these incredible creatures. In the pages ahead we offer an approach to transcendence that not only includes the intricate analysis but also the beautiful ideas behind the technical details. The phrase "classical transcendental number theory" in the title of this book refers to the most widely known results that were obtained in the nineteenth and early twentieth centuries. The reason for this focus is threefold. Firstly, this body of work requires only the mathematical techniques and tools familiar to advanced undergraduate mathematics students, and thus this area can be appreciated by a wide range of readers. Secondly, the ideas behind modem transcendence results are almost always an elaboration of the classical arguments we will explore here. And finally, and perhaps more importantly, this early work yields the transcendence of such admired and well-known numbers as e, rr, and even 2v'2.

The Journey Ahead At the heart of transcendental number theory lies an intriguing paradox: While essen­ tially all numbers are transcendental, establishing the transcendence of a particular number is a monumental task. Thus transcendental numbers are an enigmatic species of number: We know they are all around us and yet it requires enormous effort to catch one. More often than not, they slip through our fingers and dissappear back into the dense jungle of numbers. Here we will venture to tame a few of these incredible creatures. In the pages ahead we offer an approach to transcendence that not only includes the intricate analysis but also the beautiful ideas behind the technical details. The phrase "classical transcendental number theory" in the title of this book refers to the most widely known results that were obtained in the nineteenth and early twentieth centuries. The reason for this focus is threefold. Firstly, this body of work requires only the mathematical techniques and tools familiar to advanced undergraduate mathematics students, and thus this area can be appreciated by a wide range of readers. Secondly, the ideas behind modem transcendence results are almost always an elaboration of the classical arguments we will explore here. And finally, and perhaps more importantly, this early work yields the transcendence of such admired and well-known numbers as e, rr, and even 2v''2.