The Mathematical Revolution Inspired By Computing
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| Author | : Jeffrey Johnson |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 352 |
| Release | : 1991 |
| Genre | : Computers |
| ISBN | : |
The impact that computers has had on mathematics and mathematicians is profound. This volume presents a survey of the many ways in which this influence has been felt and the implications these have for the future development of mathematics. Individual chapters cover topics as diverse as automated theorem proving, computational algebra, word-processing algorithms, the Z specification language for computer systems, the use of types in computing, neural networks, and dynamical systems. All the contributors are experts in their respective fields and, as a result, not only does the volume provide insights into how computers are used in mathematics, but also, (perhaps more significantly) how the advent of computers has changed both the way mathematicians work and the nature of the problems that they study.
| Author | : Avi Wigderson |
| Publisher | : Princeton University Press |
| Total Pages | : 434 |
| Release | : 2019-10-29 |
| Genre | : Computers |
| ISBN | : 0691189137 |
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
| Author | : Douglas S. Robertson |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 220 |
| Release | : 2003 |
| Genre | : Mathematics |
| ISBN | : 9780195157482 |
Robertson's earlier work, The New Renaissance projected the likely future impact of computers in changing our culture. Phase Change builds on and deepens his assessment of the role of the computer as a tool driving profound change by examining the role of computers in changing the face of the sciences and mathematics. He shows that paradigm shifts in understanding in science have generally been triggered by the availability of new tools, allowing the investigator a new way of seeing into questions that had not earlier been amenable to scientific probing.
| Author | : J. H. Johnson |
| Publisher | : |
| Total Pages | : 329 |
| Release | : 1991 |
| Genre | : |
| ISBN | : |
| Author | : Robin Wilson |
| Publisher | : Princeton University Press |
| Total Pages | : 218 |
| Release | : 2021-10-12 |
| Genre | : Mathematics |
| ISBN | : 0691237565 |
On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map. This new edition features many color illustrations. It also includes a new foreword by Ian Stewart on the importance of the map problem and how it was solved.
| Author | : Steve Nadis |
| Publisher | : Harvard University Press |
| Total Pages | : 272 |
| Release | : 2013-11-01 |
| Genre | : Mathematics |
| ISBN | : 0674727894 |
In the twentieth century, American mathematicians began to make critical advances in a field previously dominated by Europeans. Harvard’s mathematics department was at the center of these developments. A History in Sum is an inviting account of the pioneers who trailblazed a distinctly American tradition of mathematics—in algebraic geometry and topology, complex analysis, number theory, and a host of esoteric subdisciplines that have rarely been written about outside of journal articles or advanced textbooks. The heady mathematical concepts that emerged, and the men and women who shaped them, are described here in lively, accessible prose. The story begins in 1825, when a precocious sixteen-year-old freshman, Benjamin Peirce, arrived at the College. He would become the first American to produce original mathematics—an ambition frowned upon in an era when professors largely limited themselves to teaching. Peirce’s successors—William Fogg Osgood and Maxime Bôcher—undertook the task of transforming the math department into a world-class research center, attracting to the faculty such luminaries as George David Birkhoff. Birkhoff produced a dazzling body of work, while training a generation of innovators—students like Marston Morse and Hassler Whitney, who forged novel pathways in topology and other areas. Influential figures from around the world soon flocked to Harvard, some overcoming great challenges to pursue their elected calling. A History in Sum elucidates the contributions of these extraordinary minds and makes clear why the history of the Harvard mathematics department is an essential part of the history of mathematics in America and beyond.
| Author | : K. Vela Velupillai |
| Publisher | : Routledge |
| Total Pages | : 514 |
| Release | : 2012-07-26 |
| Genre | : Business & Economics |
| ISBN | : 1134253362 |
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode completely non-algorithmic, which means it is numerically meaningless. The book provides a systematic attempt to dissect and expose the non-algorithmic content of orthodox mathematical economics and game theory and suggests a reformalization on the basis of a strictly rigorous algorithmic mathematics. This removes the current schizophrenia in mathematical economics and game theory, where theory is entirely divorced from algorithmic applicability – for experimental and computational exercises. The chapters demonstrate the uncomputability and non-constructivity of core areas of general equilibrium theory, game theory and recursive macroeconomics. The book also provides a fresh look at the kind of behavioural economics that lies behind Herbert Simon’s work, and resurrects a role for the noble classical traditions of induction and verification, viewed and formalised, now, algorithmically. It will therefore be of particular interest to postgraduate students and researchers in algorithmic economics, game theory and classical behavioural economics.
| Author | : Anthony J. G. Hey |
| Publisher | : Cambridge University Press |
| Total Pages | : 415 |
| Release | : 2015 |
| Genre | : Computers |
| ISBN | : 0521766451 |
This exciting and accessible book takes us on a journey from the early days of computers to the cutting-edge research of the present day that will shape computing in the coming decades. It introduces a fascinating cast of dreamers and inventors who brought these great technological developments into every corner of the modern world, and will open up the universe of computing to anyone who has ever wondered where his or her smartphone came from.
| Author | : G. E. Tupholme |
| Publisher | : Clarendon Press/Institute of Mathematics and its Applications |
| Total Pages | : 361 |
| Release | : 1998-07-09 |
| Genre | : |
| ISBN | : 0191590908 |
During this century, as no other, the two themes of mathematics and heat transfer have become inextricably intertwined, and it was with this underlying sentiment that this volume was conceived. It includes contributions from fifteen countries throughout the world, covering various problems in heat transfer. The contributors work in diverse fields and include mathematicians, theoretical engineers, experimentalists and industrialists.
| Author | : Jing-zhong Zhang |
| Publisher | : World Scientific |
| Total Pages | : 488 |
| Release | : 1994-04-06 |
| Genre | : Mathematics |
| ISBN | : 981450260X |
This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
