An exploration of the scientific limits of knowledge that challenges our deep-seated beliefs about our universe, our rationality, and ourselves.
Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes.
Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known.
Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.
Автор: Flood, Raymond; Rice, Adrian; Wilson, Robin Название: Mathematics in Victorian Britain ISBN: 0199601399 ISBN-13(EAN): 9780199601394 Издательство: Oxford Academ Рейтинг: Цена: 45830.00 T Наличие на складе: Есть Описание: With a foreword by Adam Hart-Davis, this book constitutes perhaps the first general survey of the mathematics of the Victorian period. It charts the institutional development of mathematics as a profession, as well as exploring the numerous innovations made during this time, many of which are still familiar today.
Автор: Walling Название: Modern Mathematics ISBN: 131661266X ISBN-13(EAN): 9781316612668 Издательство: Cambridge Academ Рейтинг: Цена: 31670.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Originally published in 1948, this book was written to provide students with an accessible guide to various elements of mathematics. The text was created for individual working rather than group learning situations. Numerous exercises are included.
Автор: Carr Название: A Synopsis of Elementary Results in Pure and Applied Mathematics ISBN: 1108050670 ISBN-13(EAN): 9781108050678 Издательство: Cambridge Academ Рейтинг: Цена: 29570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Originally published between 1880 and 1886, this two-volume work by George Shoobridge Carr (1837-1914) was intended as an aid to students preparing for the Cambridge Mathematical Tripos. Most notably, it played an important part in the mathematical education of the Indian prodigy Srinivasa Ramanujan (1887-1920).
Автор: Chemla, Karine; Chorlay, Renaud; Rabouin, David Название: The Oxford Handbook of Generality in Mathematics and the Sciences ISBN: 0198777264 ISBN-13(EAN): 9780198777267 Издательство: Oxford Academ Рейтинг: Цена: 126720.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This collection of original essays aims to inquire into the diversity of Generality. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts.
Автор: Michael K. J. Goodman Название: An Introduction to the Early Development of Mathematics ISBN: 1119104971 ISBN-13(EAN): 9781119104971 Издательство: Wiley Рейтинг: Цена: 64360.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: An easy-to-read presentation of the early history of mathematics Engaging and accessible, An Introduction to the Early Development of Mathematics provides a captivating introduction to the history of ancient mathematics in early civilizations for a nontechnical audience.
Автор: Case Bettye Anne Название: Complexities: Women in Mathematics ISBN: 0691171092 ISBN-13(EAN): 9780691171098 Издательство: Wiley Рейтинг: Цена: 33790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Sophie Germain taught herself mathematics by candlelight, huddled in her bedclothes. Ada Byron Lovelace anticipated aspects of general-purpose digital computing by more than a century. Cora Ratto de Sadosky advanced messages of tolerance and equality while sharing her mathematical talents with generations of students.
This captivating book gives voice to women mathematicians from the late eighteenth century through to the present day. It documents the complex nature of the conditions women around the world have faced--and continue to face--while pursuing their careers in mathematics. The stories of the three women above and those of many more appear here, each one enlightening and inspiring. The earlier parts of the book provide historical context and perspective, beginning with excursions into the lives of fifteen women born before 1920. Included are histories of collective efforts to improve women's opportunities in research mathematics. In addition, a photo essay puts a human face on the subject as it illustrates women's contributions in professional associations.
More than eighty women from academe, government, and the private sector provide a rich melange of insights and strategies for creating workable career paths while maintaining rewarding personal lives. The book discusses related social and cultural issues, and includes a summary of recent comparative data relating to women and men in mathematics and women from other sciences. First-person accounts provide explicit how-tos; many narratives demonstrate great determination and perseverance. Talented women vividly portray their pleasure in discovering new mathematics. The senior among them speak out candidly, interweaving their mathematics with autobiographical detail. At the beginning of a new century, women at all stages of their careers share their outlooks and experiences.
Clear, engaging, and meticulously researched, "Complexities" will inspire young women who are contemplating careers in mathematics and will speak to women in many fields of endeavor and walks of life."
Автор: Williams, Kim Название: Architecture and mathematics from antiquity to the future: v.I: Antiquity to the 1500s ISBN: 3319001361 ISBN-13(EAN): 9783319001364 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order.
Автор: Stillwell John Название: Reverse Mathematics: Proofs from the Inside Out ISBN: 0691177171 ISBN-13(EAN): 9780691177175 Издательство: Wiley Рейтинг: Цена: 23230.00 T Наличие на складе: Поставка под заказ. Описание:
This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic.
Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it.
By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.
Автор: Weyl, Hermann Название: Philosophy of mathematics and natural science ISBN: 0691141207 ISBN-13(EAN): 9780691141206 Издательство: Wiley Рейтинг: Цена: 58080.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Examines how advances in philosophy were led by scientific discoveries - the more humankind understood about the physical world, the more curious we became. Drawing on work by Descartes, Galileo, Hume, Kant, Leibniz, and Newton, this book helps readers understand science through the lens of philosophy.
Автор: Friedman, Michael. Название: A history of folding in mathematics : ISBN: 331972486X ISBN-13(EAN): 9783319724867 Издательство: Springer Рейтинг: Цена: 204970.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: While it is well known that the Delian problems are impossible to solve with a straightedge and compass – for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments – the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised?Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete.In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
Автор: Struik Dirk Jan Название: A Source Book in Mathematics, 1200-1800 ISBN: 0691610517 ISBN-13(EAN): 9780691610511 Издательство: Wiley Рейтинг: Цена: 79200.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: These selected mathematical writings cover the years when the foundations were laid for the theory of numbers, analytic geometry, and the calculus. Originally published in 1986. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton
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