Kirjahaku

Mathematicians do not know in advance if their assertions are true, so they need to verify assertions with rigorous proofs or produce counterexamples, then attempt to salvage the assertions by transforming them into theorems. Extending the Frontiers of Mathematics: Inquiries into proof and argumentation invites students to experience this progression of mathematical discovery. Burger's informal, humorous writing style and intriguing puzzles engage students throughout the learning process. The innovative text offers a discovery-based approach that is ideally suited for use in a proofs course, a discrete math course, or any bridge course to more abstract mathematics.

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.

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.

Transform your mathematics course into an engaging and mind-opening experience for even your most math-phobic students. Now in its Fourth Edition, The Heart of Mathematics: An Invitation to Effective Thinking succeeds at reaching non-math, non-science-oriented majors, encouraging them to discover the mathematics inherent in the world around them. Infused with the authors' humor and enthusiasm throughout, The Heart of Mathematics introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.