Mathematics and Computation
Mathematics and Computation

Author: Avi Wigderson

Publisher: Princeton University Press

Published: 2019-10-29

Total Pages: 434

ISBN-13: 0691189137

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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

Making up Numbers: A History of Invention in Mathematics
Making up Numbers: A History of Invention in Mathematics

Author: Ekkehard Kopp

Publisher: Open Book Publishers

Published: 2020-10-23

Total Pages: 280

ISBN-13: 1800640978

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Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

Creators of Mathematical and Computational Sciences
Creators of Mathematical and Computational Sciences

Author: Ravi P Agarwal

Publisher: Springer

Published: 2014-11-11

Total Pages: 514

ISBN-13: 3319108700

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​The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.

The History of the London Water Industry, 1580–1820
The History of the London Water Industry, 1580–1820

Author: Leslie Tomory

Publisher: JHU Press

Published: 2017-04-25

Total Pages: 331

ISBN-13: 1421422042

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"Beginning in 1580, London companies sold water to consumers through a large network of wooden mains in the expanding metropolis. This new water industry flourished throughout the 1600s, eventually expanding to serve tens of thousands of homes. By the late eighteenth century, more than 80 percent of the city's houses had water connections-making London the best-served metropolis in the world while demonstrating that it was legally, commercially, and technologically possible to run an infrastructure network within the largest city on earth. Leslie Tomory shows how new technologies imported from the Continent, including waterwheel-driven piston pumps, spurred the rapid growth of London's water industry. The business was further sustained by an explosion in consumer demand. Meanwhile, several key local innovations reshaped the industry by enlarging the size of the supply network. By 1800, the success of London's water industry made it a model for other cities in Europe and beyond as they began to build their own water networks, and it inspired builders of other large-scale urban projects, including gas and sewage supply networks."--Provided by the publisher.