Keith J. Devlin

In 2000, the Clay Foundation of Cambridge, Massachusetts, 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 $1million in prize money. They encompass many of the most fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. Keith Devlin describes here what the seven problems are, how they came about, and what they mean for mathematics and science. In the hands of Devlin, each Millennium Problem becomes a fascinating window onto the deepest questions in the field.

The Seven Greatest Unsolved Mathematical Puzzles of Our Time

The Millennium Problems

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.

Introduction to Mathematical Thinking

Examines a letter written by Blaise Pascal to Pierre de Fermat in 1654 that speaks of probability and numerical values that have had an impact on the modern world with regard to calculating insurance rates, the housing markets, and car safety.

Pascal, Fermat, and the Seventeenth-century Letter that Made the World Modern

The Unfinished Game

The Maths Gene

A Guide for the Mathematician

The Axiom of Constructibility

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.

The Quest to Rediscover the Forgotten Mathematical Genius who Changed the World

Finding Fibonacci

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the Lα-hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the Jα-hierarchy and the Jensen 'fine-structure theory'.

Constructibility

Keith J Devlin

Presents a survey of advances in mathematics over the past twenty-five years, including such topics as prime numbers, factories, sets, and number systems

The New Golden Age

Mathematics

Wer dieses Musterbuch zur modernen Mathematik liest, wird sich wundern: Mathematik treibt jeder von uns im Alltag, etwa wenn er ein verschlungenes Seil aufdrAselt, wenn er zAhlt, wenn er logisch denkt, wenn er zeitliche VerAnderungen beobachtet oder wenn er Formen, Symmetrien und RegelmAAigkeiten beschreibt. Was den Leser erwartet, ist alles andere als Schulmathematik und beAngstigende Formeln: Es ist die verblA1/4ffende Erfahrung, daA Mathematik ein faszinierender Lebensraum ist, in dem wir uns auch dann leicht wie ein Fisch im Wasser bewegen kAnnen, wenn wir in der Schule das FA1/4rchten vor Formeln gelernt haben. Devlin-Leser werden unmerklich Ihre Einstellung zu Formeln Andern - und vielleicht sogar zu Formelfans mutieren.

Ordnungsgesetze des Geistes und der Natur

Muster der Mathematik

Where does our mathematical ability come from? Our prehistoric ancestors' brains were essentially the same as ours, so they must have had the same underlying ability. What purpose could it serve in 50,000 BC? And what exactly goes on in our brains when we multiply 15 by 36 or prove Fermat's Last Theorem? The answer, according to Keith Devlin, is closely related to the evolutionary changes in the human brain that gave rise to language. It lies within our genes and more specifically with the pattern-making abilities with which we are born. Devlin uses these insights to show why some people loathe mathematics, why others find it so difficult, and why a select few excel at the subject. He also suggests ways in which we can improve our mathematical skills.

Keith J. Devlin

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