Drawings and writings by Archimedes, previously thought to have been destroyed, have been uncovered beneath the pages of a 13th-century monk's prayer book. These hidden texts, slowly being retrieved and deciphered by scientists, show that Archimedes' thinking (2,200 years ago) was even ahead of Isaac Newton in the 17th century. Archimedes discovered the value of Pi, he developed the theory of specific gravity and made steps towards the development of calculus. Everything we know about him comes from three manuscripts, two of which have disappeared. The third, currently in the Walters Art Museum, is a palimpsest - the text has been scraped off, the book taken apart and its parchment re-used, in this case as a prayer book. William Noel, the project director, and Reviel Netz, a historian of ancient mathematics, tell the enthralling story of the survival of that prayer book from 1229 to the present, and examine the process of recovering the invaluable text underneath as well as investigating into why that text is so important. Combining intrigue, lost books, academic detection and final revelations which rewrite the history of science and mathematics, The Archimedes Codex will be a major publishing event.

In the early 1980's, Leonard Mlodinow came to the California Institute of Technology to begin a postdoctoral fellowship. Mlodinow had written a groundbreaking Ph.D. thesis, but he was afraid he was simply not smart enough to be at Caltech. In danger of losing himself watching hours of Rockford Files reruns while waiting for one good idea, Mlodinow took his doubts and insecurities to Caltech's intimidating resident genius and iconoclast, Richard Feynman. So began a pivotal year in a young man's life and a year of awakening. In the funny, inspiring, and revelatory book, Leonard Mlodinow looks back at the time he shared with Feynman: the ideas they explored, the views of life and physics they exchanged, and what Mlodinow learned from a mentor who had not only helped shape the landscape of physics, but whose mind was drawn to all aspects of human experience. In a series of fascinating, sprawling exchanges, Feynman delved into the nature of science, creativity, love, mathematics, happiness, God, art, pleasures and ambition. And as the relationship between the older scientist and Mlodinow deepened - at one point the two crashed a wedding buffet together - their conversations took on a sense of urgency. For while Mlodinow was floundering, Feynman was battling cancer - and confronting his own mortality.

Text book for a freshman course that allows students to learn a mathematics background that supports various disciplines.

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This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.

Mathematical Foundations of Quantum Mechanics was a revolutionary book that caused a sea change in theoretical physics. Here, John von Neumann, one of the leading mathematicians of the twentieth century, shows that great insights in quantum physics can be obtained by exploring the mathematical structure of quantum mechanics. He begins by presenting the theory of Hermitean operators and Hilbert spaces. These provide the framework for transformation theory, which von Neumann regards as the definitive form of quantum mechanics. Using this theory, he attacks with mathematical rigor some of the general problems of quantum theory, such as quantum statistical mechanics as well as measurement processes. Regarded as a tour de force at the time of publication, this book is still indispensable for those interested in the fundamental issues of quantum mechanics.

Were it not for the calculus, mathematicians would have no way to describe the acceleration of a motorcycle or the effect of gravity on thrown balls and distant planets, or to prove that a man could cross a room and eventually touch the opposite wall. Just how calculus makes these things possible and in doing so finds a correspondence between real numbers and the real world is the subject of this dazzling book by a writer of extraordinary clarity and stylistic brio. Even as he initiates us into the mysteries of real numbers, functions, and limits, Berlinski explores the furthest implications of his subject, revealing how the calculus reconciles the precision of numbers with the fluidity of the changing universe. "An odd and tantalizing book by a writer who takes immense pleasure in this great mathematical tool, and tries to create it in others."--New York Times Book Review

'In many ways it s the ultimate question in natural science: How does our universe work? Is there a fundamental theory? An incredible amount has been figured out about physics over the past few hundred years. But even with everything that s been done and it's very impressive - we still, after all this time, don t have a truly fundamental theory of physics.' The Wolfram Physics Project is a bold effort to find the fundamental theory of physics. It combines new ideas with the latest research in physics, mathematics and computation in the push to achieve this ultimate goal of science. Written with Stephen Wolfram's characteristic expository flair, this book provides a unique opportunity to learn about a historic initiative in science right as it is happening. A Project to Find the Fundamental Theory of Physics includes: The announcement of the project; A technical introduction; A history section that outlines the backstory which led Wolfram to this point; Background information from computational essays published by the author in 2015 and 2017; Foundational information, including historical notes and an excerpt from Wolfram's; 2002 New York Times Best Seller A New Kind of Science; Hundreds of beautiful full-colour visualisations. Stephen Wolfram is a distinguished scientist and best-selling author, and the creator of some of the world's most respected software systems, including Mathematica, Wolfram|Alpha and Wolfram Language. For more than 30 years he has been the CEO of the global technology company Wolfram Research.

2011 Reprint of 1960 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." - "Philosophy and Phenomenological Research".

This book brings together - in an informal and tutorial fashion - the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields. Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. No prior knowledge of GAs or genetics is assumed, and only a minimum of computer programming and mathematics background is required. 0201157675B07092001

When Mr Ruche, a reclusive Parisian bookseller, receives a letter from a long lost friend in the Amazon bequesting him a vast library of mathematical books, he is propelled into a great exploration of the story of maths, from brilliant Greek thinkers, such as Archimedes and Pythagoras, to the modern-day genius Fermat. Meanwhile Max, a deaf boy whose dysfunctional family live with Mr Ruche, finds a voluble parrot in a local fleamarket. He turns out to be a bird who discusses maths with anyone who will listen. So when Mr Ruche learns of his friend's mysterious death in the rainforests of Brazil he decides that with the parrot's help he will use these books to teach Max and his twin brother and sister the mysteries and wonders of numbers and shapes. Charming, fresh, with a narrative which races along, the novel takes the reader on a delightful journey through the history of mathematics.

This manuscript portrays optimization as a process. In many practical applications the environment is so complex that it is infeasible to lay out a comprehensive theoretical model and use classical algorithmic theory and mathematical optimization. It is necessary as well as beneficial to take a robust approach, by applying an optimization method that learns as one goes along, learning from experience as more aspects of the problem are observed. This view of optimization as a process has become prominent in varied fields and has led to some spectacular success in modeling and systems that are now part of our daily lives.

This book, suitable for both course work and self-study, brings together for the first time, in an informal, tutorial fashion, the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields: programmers, scientists, engineers, mathematicians, statisticians and management scientists will all find interesting possibilities here. Major concepts are illustrated with running examples, and major algorithms are illustrated by Pascal computer programs. Chapter concludes with exercises and computer assignments. No prior knowledge of Gas or genetics is assumed.

Clifton Fadiman's classic collection of mathematical stories, essays and anecdotes is now once again available. Ranging from the poignant to the comical via the simply surreal, these selections include writing by Aldous Huxley, Martin Gardner, H.G. Wells, George Gamow, G.H. Hardy, Robert Heinlein, Arthur C. Clarke, and many others. Humorous, mysterious, and always entertaining, this collection is sure to bring a smile to the faces of mathematicians and non-mathematicians alike.

Revision of the classic text in the field, adding two new chapters and thoroughly updating all others. The original structure is retained, and the book continues to serve as a combined text/reference.

Looks at coincidences and unlikely occurrences, delving into the mathematical concepts of probability and sharing stories of striking flukes and coincidences from around the world.

"Weinberg takes us across centuries from ancient Miletus to medieval Baghdad and Oxford, from Plato's Academy and the Museum of Alexandria to the cathedral school of Chartres and the Royal Society of London. He shows that the scientists of ancient and medieval times not only did not understand what we understand about the world--they did not understand what there is to understand, or how to understand it. Yet over the centuries, through the struggle to solve such mysteries as the curious backward movement of the planets and the rise and fall of the tides, the modern discipline of science eventually emerged"--Amazon.com ; Presents a commentary on the history of science that examines historic clashes and collaborations between science and the competing realms of religion, technology, poetry, mathematics, and philosophy

This is a unique kind of psychological self-help book. In it Dr. Flesch has summarized for the general reader the relation of scientific findings to thinking and problem-solving. Drawing from psychology, linguistics, anthropology, and mathematics, he has produced an expert guide to clear and constructive thinking. The book is packed with useful suggestions, including shortcuts to mathematics, a system for speedy note-taking, and tips on how to solve puzzles and problems. Moreover, it is written with zest and enthusiasm, continually delving into such fascinating matters as strange coincidences, romantic love, the differences between wit and humor, and the thinking processes of children, pollsters, Eskimos, computers, mystery writers, jurors, chimpanzees, and executives.