Mathematics: The New Golden Age offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hilbert's tenth problem and the four-color theorem, Gaussian integers, chaotic dynamics and the Mandelbrot set, infinite numbers, and strange number systems. Why a "new golden age"? According to Keith Devlin, we are currently witnessing an astronomical amount of mathematical research. Charting the most significant developments that have taken place in mathematics since 1960, Devlin expertly describes these advances for the interested layperson and...
Mathematics: The New Golden Age offers a glimpse of the extraordinary vistas and bizarre universes opened up by contemporary mathematicians: Hi...
This book provides an account of those parts of contemporary set theory of direct relevance to other areas of pure mathematics. The intended reader is either an advanced-level mathematics undergraduate, a beginning graduate student in mathematics, or an accomplished mathematician who desires or needs some familiarity with modern set theory. The book is written in a fairly easy-going style, with minimal formalism. In Chapter 1, the basic principles of set theory are developed in a 'naive' manner. Here the notions of 'set', 'union', 'intersection', 'power set', 'rela- tion', 'function', etc.,...
This book provides an account of those parts of contemporary set theory of direct relevance to other areas of pure mathematics. The intended reader is...
Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's 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 breathtakingly new theory of language development--that language evolved in two stages, and its main purpose was not communication--to show that...
Why is math so hard? And why, despite this difficulty, are some people so good at it? If there's some inborn capacity for mathematical thinking--which...
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...
In 2000, the Clay Foundation announced a historic competition: whoever could solve any of seven extraordinarily difficult mathematical problems, and h...
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...
In this provocative and ground-breaking book, Keith Devlin argues that in order to obtain a deeper understanding of the nature of intelligence and kno...
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...
In this provocative and ground-breaking book, Keith Devlin argues that in order to obtain a deeper understanding of the nature of intelligence and kno...
"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematics." In The Language of Mathematics, award-winning author Keith Devlin reveals the vital role mathematics plays in our eternal quest to understand who we are and the world we live in. More than just the study of numbers, mathematics provides us with the eyes to recognize and describe the hidden patterns of life--patterns that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts...
"The great book of nature," said Galileo, "can be read only by those who know the language in which it was written. And this language is mathematic...
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...
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...
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'...
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 be...
Why do leopards grow spots when tigers grow stripes? Is the universe round, square, or some other shape? How do the dimples in a golf ball give it greater lift? Is there such a thing as a public mood? If so, how can we accurately take its pulse?
Only one tool of the human mind has the power and versatility to answer so many questions about our world--mathematics. Far from a musty set of equations and proofs, mathematics is a vital and creative way of thinking and seeing. It is the most powerful means we have of exploring our world and how it works, from the darkest depths of the oceans to...
Why do leopards grow spots when tigers grow stripes? Is the universe round, square, or some other shape? How do the dimples in a golf ball give it gre...