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What Are the Arts and Sciences?
What constitutes the study of philosophy or physics? What exactly does an anthropologist do, or a geologist or historian? In short, what are the arts and sciences? While many of us have been to college and many aspire to go, we may still wonder just what the various disciplines represent and how they interact. What are their origins, methods, applications, and unique challenges? What kind of people elect to go into each of these fields, and what are the big issues that motivate them? Curious to explore these questions himself, Dartmouth College professor and mathematician Dan Rockmore asked his colleagues to explain their fields and what it is that they do. The result is an accessible, entertaining, and enlightening survey of the ideas and subjects that contribute to a liberal education. The book offers a doorway to the arts and sciences for anyone intrigued by the vast world of ideas.
Stalking The Riemann Hypothesis
Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scatt...
99 Variations on a Proof
An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond ...
Modern Signal Processing
A description of the mathematical basis of signal processing, and many areas of application.
Music and Computers
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Law as Data
In recent years, the digitization of legal texts and developments in the fields of statistics, computer science, and data analytics have opened entirely new approaches to the study of law. This volume explores the new field of computational legal analysis, an approach marked by its use of legal texts as data. The emphasis herein is work that pushes methodological boundaries, either by using new tools to study longstanding questions within legal studies or by identifying new questions in response to developments in data availability and analysis. By using the text and underlying data of legal documents as the direct objects of quantitative statistical analysis, Law as Data introduces the legal world to the broad range of computational tools already proving themselves relevant to law scholarship and practice, and highlights the early steps in what promises to be an exciting new approach to studying the law.
Applied Fourier Analysis
The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis ...
The Weil Conjectures
_______________ 'Beguiling ... I was riveted. Olsson is evocative on curiosity as an appetite of the mind, on the pleasure of glutting oneself on knowledge' - New York Times 'A wonderful book ... Reading it is akin to kicking a can along the road of higher learning' - Patti Smith 'A remarkable tour de force' - Standpoint _______________ Simone Weil: philosopher, political activist, mystic - and sister to André, one of the most influential mathematicians of the twentieth century. These two extraordinary siblings formed an obsession for Karen Olsson, who studied mathematics at Harvard, only to turn to writing as a vocation. When Olsson got hold of the 1940 letters between the siblings, she found they shared a curiosity about the inception of creative thought - that flash of insight - that Olsson experienced as both a mathematics student, and later, a novelist. Following this thread of connections, The Weil Conjectures explores the lives of Simone and André, the lore and allure of mathematics, and its significance in Olsson's own life.
Heads in Grammatical Theory
A study of the idea of the 'head' or dominating element of a phrase.
Introduction to Probability
This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject.
