Keith Devlin and Jonathan Borwein, two well-known mathematicians with expertise in different mathematical specialties but with a common interest in experimentation in mathematics, have joined forces to create this introduction to experimental mathematics. They cover a variety of topics and examples to give the reader a good sense of the current state of play in the rapidly growing new field of experimental mathematics. The writing is clear and the explanations are enhanced by relevant historical facts and stories of mathematicians and their encounters with the field over time.

Stanford mathematician and NPR Math Guy Keith Devlin explains why, fun aside, video games are the ideal medium to teach middle-school math. Aimed primarily at teachers and education researchers, but also of interest to game developers who want to produce videogames for mathematics education, Mathematics Education for a New Era: Video Games as a Medium for Learning describes exactly what is involved in designing and producing successful math educational videogames that foster the innovative mathematical thinking skills necessary for success in a global economy. Read the author's monthly MAA column Devlin's Angle

Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students. Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead. Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read and enjoy and learn from. About the Author Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,. Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and co

Stanford mathematician and NPR Math Guy Keith Devlin explains why, fun aside, video games are the ideal medium to teach middle-school math. Devlin spent five years as the lead mathematical advisor on a project to develop an MMO game that would teach mathematics to children aged 9 to 12 and be sufficiently compelling that they would actually want to play it. He worked with some very distinguished mathematics educators and videogame designers, and during that time the team learned how to design videogames that do more than try to entice children to practice their basic math skills. Aimed primarily at teachers and education researchers, and game developers who want to produce videogames for mathematics education, Mathematics Education and Video Games describes exactly what is involved in designing and producing successful math educational videogames that foster the innovative mathematical thinking skills necessary for success in a global economy.

This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naive" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.

A mathematician's ten-year quest to tell Fibonacci's story In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci, or the "Book of Calculation," introduced modern arithmetic to the Western world. Although most famous for the Fibonacci numbers-which, it so happens, he didn't discover-Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. Yet Fibonacci was forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Drawing on the diary he kept of his quest, Devlin describes the false starts and disappointments, the unexpected turns, and the occasional lucky breaks he encountered in his search. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him.

In this provocative and ground-breaking book, Keith Devlin argues that in order to obtain a deeper understanding of the nature of intelligence and knowledge acquisition, we must broaden our concept of logic. Classical logic, beginning with the work of Aristotle, has developed into a powerful and rigorous mathematical theory with many applications in mathematics and computer science, but it has proved woefully inadequate in the search for artificial intelligence. The new kind of logic, also mathematically based, outlined by Professor Devlin is the culmination of collaborative research among some of the world's leading logicians, philosophers, linguists, psychologists, and computer scientists. It introduces the concepts of infon, a quantum of information, and situations, a dynamical generalization of sets, and is capable of handling the issues involved in human communication, thought, speech, and machine information processing.

Keith Devlin. You know him. You've read his columns in MAA Online, you've heard him on the radio, and you've seen his popular mathematics books. In between all those activities and his own research, he's been hard at work revising Sets, Functions and Logic, his standard-setting text that has smoothed the road to pure mathematics for legions of undergraduate students.

Now in its third edition, Devlin has fully reworked the book to reflect a new generation. The narrative is more lively and less textbook-like. Remarks and asides link the topics presented to the real world of students' experience. The chapter on complex numbers and the discussion of formal symbolic logic are gone in favor of more exercises, and a new introductory chapter on the nature of mathematics--one that motivates readers and sets the stage for the challenges that lie ahead.

Students crossing the bridge from calculus to higher mathematics need and deserve all the help they can get. Sets, Functions, and Logic, Third Edition is an affordable little book that all of your transition-course students not only can afford, but will actually read…and enjoy…and learn from.

About the Author

Dr. Keith Devlin is Executive Director of Stanford University's Center for the Study of Language and Information and a Consulting Professor of Mathematics at Stanford. He has written 23 books, one interactive book on CD-ROM, and over 70 published research articles. He is a Fellow of the American Association for the Advancement of Science, a World Economic Forum Fellow, and a former member of the Mathematical Sciences Education Board of the National Academy of Sciences,.

Dr. Devlin is also one of the world's leading popularizers of mathematics. Known as "The Math Guy" on NPR's Weekend Edition, he is a frequent contributor to other local and national radio and TV shows in the US and Britain, writes a monthly column for the Web journal MAA Online, and regularly writes on mathematics and computers for the British newspaper The Guardian.

This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally from a rigorous answer to the question, "what is a set?" After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of provability in set theory. A final chapter presents an account of an alternative conception of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel. The author is a well-known mathematician and the editor of the "Computers in Mathematics" column in the AMS Notices and of FOCUS, the magazine published by the MAA.

A compelling firsthand account of Keith Devlin's ten-year quest to tell Fibonacci's story In 2000, Keith Devlin set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers--which, it so happens, he didn't invent--Fibonacci's greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci--the "Book of Calculation"--introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death, and it was not until the 1960s that his true achievements were finally recognized. Finding Fibonacci is Devlin's compelling firsthand account of his ten-year quest to tell Fibonacci's story. Devlin, a math expositor himself, kept a diary of the undertaking, which he draws on here to describe the project's highs and lows, its false starts and disappointments, the tragedies and unexpected turns, some hilarious episodes, and the occasional lucky breaks. You will also meet the unique individuals Devlin encountered along the way, people who, each for their own reasons, became fascinated by Fibonacci, from the Yale professor who traced modern finance back to Fibonacci to the Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci's astonishing story. Fibonacci helped to revive the West as the cradle of science, technology, and commerce, yet he vanished from the pages of history. This is Devlin's search to find him.

"One of the best critiques of current mathematics education I have ever seen."--Keith Devlin, math columnist on NPR's "Morning Edition"

A brilliant research mathematician who has devoted his career to teaching kids reveals math to be creative and beautiful and rejects standard anxiety-producing teaching methods. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike and it will alter the way we think about math forever.

Paul Lockhart, has taught mathematics at Brown University and UC Santa Cruz. Since 2000, he has dedicated himself to K-12 level students at St. Ann's School in Brooklyn, New York.

From uncanny movie dinosaurs to the loopy physics of the triple axel, Keith Devlin's vibrantly illustrated book illuminates the mathematics inherent in every human endeavor.

"A beautiful book . . . the aim is not to teach but to entertain, and it succeeds. The view that mathematics is dull is replaced by an image of how math can be both interesting and useful, if not all-powerful."—New Scientist.

"A colorful and exciting introduction to the ways in which mathematics can help [us] to under-stand phenomena. [Devlin] presents fascinating real-world problems posed by real people and shows how mathematics is used to solve them."—Choice.

"Not in many, many years have I seen a book nearly as instructive and enlightening about the beauty of mathematics. Life by the Numbers is superb."—Amir Aczel, author of Fermat's Last Theorem.

"This wondrous book reveals how, on the brink of the millennium, wizards are using math to bring movie dinosaurs to life, to improve tennis stars' serves, to win sailboat races, and to probe the eeriest corners of the cosmos. A pleasurable read for adult and young alike."—Keay Davidson, coauthor of Wrinkles in Time.

"A fascinating account of many of the ways in which mathematical ideas find application in the world around us. Keith Devlin is to be congratulated for bringing these ideas so accessibly to the public."—Sir Roger Penrose, author of The Emperor's New Mind.

Intelligence can be characterised both as the ability to absorb and process information and as the ability to reason. Humans and other animals have both of these abilities to a greater or lesser degree, but the search for artificial intelligence has been hampered by our inability to create a theory that covers both of these characteristics. In this provocative and ground-breaking book, Professor Keith Devlin argues that to obtain a deeper understanding of the nature of intelligence and knowledge acquisition, we must broaden our concept of logic. For these purposes, Devlin introduces the concept of the infon, a quantum of information, and merges it with situations, a mathematical construction generalising the notion of sets developed by Barwise and Perry at Stanford University in order to study the meaning of natural languages. He develops and describes the theory here in general and intuitive terms, and discusses its relevance to a variety of concerns such as artificial intelligence, cognition, natural language and communication.

In the twenty-first century, everyone can benefit from being able to think mathematically. This is not the same as "doing math." The latter usually involves the application of formulas, procedures, and symbolic manipulations; mathematical thinking is a powerful "way of thinking" about things in the world -- logically, analytically, quantitatively, and with precision. It is not a natural way of thinking, but it can be learned. Mathematicians, scientists, and engineers need to "do math," and it takes many years of college-level education to learn all that is required. Mathematical thinking is valuable to everyone, and can be mastered in about six weeks by anyone who has completed high school mathematics. Mathematical thinking does not have to be about mathematics at all, but parts of mathematics provide the ideal target domain to learn how to think that way, and that is the approach taken by this short but valuable book. The book is written "primarily" for first and second year students of science, technology, engineering, and mathematics (STEM) at colleges and universities, and for high school students intending to study a STEM subject at university. Many students encounter difficulty going from high school math to college-level mathematics. Even if they did well at math in school, most are knocked off course for a while by the shift in emphasis, from the K-12 focus on mastering procedures to the "mathematical thinking" characteristic of much university mathematics. Though the majority survive the transition, many do not. To help them make the shift, colleges and universities often have a "transition course." This book could serve as a textbook or a supplementary source for such a course. Because of the widespread applicability of mathematical thinking, however, the book has been kept short and written in an engaging style, to make it accessible to anyone who seeks to extend and improve their analytic thinking skills. Going beyond a basic grasp of analytic thinking that everyone can benefit from, the STEM student who truly masters mathematical thinking will find that college-level mathematics goes from being confusing, frustrating, and at times seemingly impossible, to making sense and being hard but "doable." Dr. Keith Devlin is a professional mathematician at Stanford University and the author of 31 previous books and over 80 research papers. His books have earned him many awards, including the Pythagoras Prize, the Carl Sagan Award, and the Joint Policy Board for Mathematics Communications Award. He is known to millions of NPR listeners as "the Math Guy" on "Weekend Edition" with Scott Simon. He writes a popular monthly blog "Devlin's Angle" for the Mathematical Association of America, another blog under the name "profkeithdevlin," and also blogs on various topics for the Huffington Post.

In 2000, the Clay Foundation announced a historic competition: whoever could solve any of seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money. There was some precedent for doing this: In 1900 the mathematician David Hilbert proposed twenty-three problems that set much of the agenda for mathematics in the twentieth century. The Millennium Problems--chosen by a committee of the leading mathematicians in the world--are likely to acquire similar stature, and their solution (or lack of it) is likely to play a strong role in determining the course of mathematics in the twenty-first century. Keith Devlin, renowned expositor of mathematics and one of the authors of the Clay Institute's official description of the problems, here provides the definitive account for the mathematically interested reader.

Mind, Brain, and Education: Neuroscience Implications for the Classroom is the sixth book in the Leading Edge series. The Leading Edge series unites education authorities from around the globe and asks them to confront the important issues that affect teachers and administratorsthe issues that profoundly impact student success.

Mind, Brain, and Education is a landmark publication in the emerging science of educational neuroscience. The leading researchers who contribute to the volume use neuroscience's growing knowledge of how the brain functions and develops to explore the field's implications for pedagogy and the classroom. The contributors investigate such questions as the following:

What are the neurological foundations of learning and of individual differences in learning?

How did educators get involved with neuroscience, and where might this involvement lead?

What does neuroscience reveal about the brain's ability to use written and spoken language, to use mathematics, and to think creatively?

How can educational neuroscience improve the teaching of these abilities?

Papier und Bleistift wurden lange als die einzigen Hilfsmittel der Mathematiker betrachtet (einige wurden hier auch noch den Papierkorb dazuzahlen). Wie in vielen anderen Gebieten auch, hat allerdings in den letzten Jahren der Einsatz von Computern in der Mathematik stark zugenommen und somit die Rolle des Experiments in der Mathematik erweitert und legitimiert. Wie konnen Mathematiker den Computer als Werkzeug benutzen? Und kann er vielleicht nicht nur als Werkzeug, sondern sogar als Mitarbeiter eingesetzt werden?

Keith Devlin und Jonathan Borwein, zwei bekannte Mathematiker mit Expertise in unterschiedlichen mathematischen Spezialgebieten, aber mit einem gemeinsamen Interesse am Experimentieren in der Mathematik, haben sich fur diese Einfuhrung in die experimentelle Mathematik zusammengetan. Sie behandeln eine Vielfalt an Themen und Beispielen, um dem Leser einen guten Einblick in die aktuelle Entwicklung dieses rasch wachsenden neuen Gebietes zu geben. Die Darstellung ist klar und ubersichtlich; die Erlauterungen sind durch historische Fakten und Geschichten von Mathematikern und deren Begegnungen mit dem Gebiet der experimentellen Mathematik angereichert.

Stimme zur Originalausgabe: "Das Buch wird fur jeden Leser fur Interesse sein, der anhand Kostproben kennen lernen mochte, wie man mathematische Problem mit einem Computer lost. Es macht nichts, wenn die Leser nicht viele mathematische Kenntnisse mitbringen: Sie konnen das Wesentliche des Buchs verstehen und Spa dabei haben, einige Fragestellungen experimentell zu erforschen." Valentina Dagiene, Zentralblatt MATH

There are two kinds of math: the hard kind and the easy kind. The easy kind, practiced by ants, shrimp, Welsh Corgis -- and us -- is innate. But what innate calculating skills do we humans have? Leaving aside built-in mathematics, such as the visual system, ordinary people do just fine when faced with mathematical tasks in the course of the day. Yet when they are confronted with the same tasks presented as "math," their accuracy often drops. If we have innate mathematical ability, why do we have to teach math and why do most of us find it so hard to learn? Are there tricks or strategies that the ordinary person can do to improve mathematical ability? Can we improve our math skills by learning from dogs, cats, and other creatures that "do math?" The answer to each of these questions is a qualified yes. All these examples of animal math suggest that if we want to do better in the formal kind of math, we should see how it arises from natural mathematics. From NPR's "Math Guy," The Math Instinct is a real celebration of innate math sense and will provide even the most number-phobic readers with confidence in their own mathematical abilities.

This work about maths and language is from the NPR commentator Keith Devlin. Why is maths so hard? And why, despite this difficulty, are some people so good at it? If there is some inborn capacity for mathematical thinking which there must be, otherwise no one could do it, why can't we all do it well? Keith Devlin has answers to all these difficult questions, and in giving them shows us how mathematical ability evolved, why it's a part of language ability, and how we can make better use of this innate talent. He also offers a theory of language development - that language evolved in two stages, and its main purpose was not communication. Devlin goes on to show that the ability to think mathematically arose out of the same symbol-manipulating ability that was so crucial to the emergence of true language. Why, then, can't we do maths as well as we can speak? The answer, says Devlin, is that we can and do, we just don't recognize when we're using mathematical reasoning.

In the early seventeenth century, the outcome of something as simple as a dice roll was consigned to the realm of unknowable chance. Mathematicians largely agreed that it was impossible to predict the probability of an occurrence. Then, in 1654, Blaise Pascal wrote to Pierre de Fermat explaining that he had discovered how to calculate risk. The two collaborated to develop what is now known as probability theory--a concept that allows us to think rationally about decisions and events.

In "The Unfinished Game," Keith Devlin masterfully chronicles Pascal and Fermat's mathematical breakthrough, connecting a centuries-old discovery with its remarkable impact on the modern world.

People are very creative in their use of language. This observation was made convincingly by Chomsky in the 1950s and is generally accepted in the scientific communities concerned with the study of language. Computers, on the other hand, are neither creative, flexible, nor adaptable. This is in spite of the fact that their ability to process language is based largely on the grammars developed by linguists and computer scientists. Thus, there is a mismatch between the observed human creativity and our ability as theorists to explain it. Language at Work examines grammars and other descriptions of language by combining the scientific and the practical. The scientific motivation is to unite distinct intellectual traditions, mathematics and descriptive social science, which have tried to provide an adequate explanation of language and its use on their own to no avail. This volume argues that Situation Theory, a theory of information couched in mathematics, has provided a uniform framework for the investigation of the creative aspects of language use. The application of Situation Theory in the study of language use in everyday communication to improve human/computer interaction is explored and espoused.

People are very creative in their use of language. This observation was made convincingly by Chomsky in the 1950s and is generally accepted in the scientific communities concerned with the study of language. Computers, on the other hand, are neither creative, flexible, nor adaptable. This is in spite of the fact that their ability to process language is based largely on the grammars developed by linguists and computer scientists. Thus, there is a mismatch between the observed human creativity and our ability as theorists to explain it. Language at Work examines grammars and other descriptions of language by combining the scientific and the practical. The scientific motivation is to unite distinct intellectual traditions, mathematics and descriptive social science, which have tried to provide an adequate explanation of language and its use on their own to no avail. This volume argues that Situation Theory, a theory of information couched in mathematics, has provided a uniform framework for the investigation of the creative aspects of language use. The application of Situation Theory in the study of language use in everyday communication to improve human/computer interaction is explored and espoused.