"So goes the legend of the tricky knot of Gordius, king of Phrygia. Many had tried, many had failed, but Alexander the Great simply cut the knot with his sword. He went on to conquer most of Asia, eventually reaching as far east as Northern India. This book of probability riddles curated to challenge the mind and expand mathematical and logical thinking skills. First housed on cut-the-knot.org, these puzzles and their solutions represent the efforts of great minds around the world. Follow along as Alexander Bogomolny presents these selected riddles by topical progression. Try them for yourself before reading their solutions. Just like it was for Alexander the Great, the non-trivial, unexpected solution might be exactly the one you need." -- from amazon.com

Published with the aid of a grant from the National Endowment for the Humanities. Contains the only complete English-language text of The Concept of Truth in Formalized Languages. Tarski made extensive corrections and revisions of the original translations for this edition, along with new historical remarks. It includes a new preface and a new analytical index for use by philosophers and linguists as well as by historians of mathematics and philosophy.

Astronomy is a fortunate science; it needs no embellishments, said the French savant Arago. So fascinating are its achievements that no special effort is needed to attract attention. Nonetheless, the science of the heavens is not only a collection of astonishing revelations and daring theories. Ordinary facts, things that happen, day by day, are its substance. Most laymen have, generally speaking, a rather hazy notion of this prosaic aspect of astronomy. They find it of little interest, for it is indeed hard to concentrate on what is always before the eye.Everyday happenings in the sky are the contents of this book, free from professional terminology with easy reading. Its purpose is to initiate the reader into the basic facts of astronomy. Ordinary facts with which you may be acquainted are couched here in unexpected paradoxes, or slanted from an odd and unexpected angle solely to excite the imagination and quicken your interest. The daily aspect of the science of the skies, its beginnings, not later findings that mainly form the contents of Astronomy for Entertainment. The purpose of the book is to initiate the reader into the basic facts of astronomy. Ordinary facts with which you may be acquainted are couched here in unexpected paradoxes, or slanted from an odd and unexpected angle. The theme is, as far as possible, free from "terminology" and technical paraphernalia that so often make the reader shy of books on astronomy.Books on popular science are often rebuked for not being sufficiently serious. In a way the rebuke is just, and support for it can be found (if one has in mind the exact natural sciences) in the tendency to avoid calculations in any shape or form. And yet the reader can really master his subject only by learning how to reckon, even though in a rudimentary fashion. True, he has taken care to present them in an easy form, well within the reach of all who have studied mathematics at school. It is his conviction that these exercises help not only retain the knowledge acquired; they are also a useful introduction to more serious reading.This book contains chapters relating to the Earth, the Moon, planets, stars and gravitation. The author has concentrated in the main on materials not usually discussed in works of this nature. Subjects omitted in the present book, will, he hopes, be treated in a second volume. The book, it should be said, makes no attempt to analyze in detail the rich content of modern astronomy.Unfortunately Y. Perelman never wrote the continuation he had planned for this book, as untimely death in war bound Leningrad in 1942 interrupted his labours.

The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''

Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra.

This collection of manuscripts was posted off by Wittgenstein to be considered for publication during World War 2, in October 1941. None of it was published and it remained hidden for over two generations. Upon its rediscovery, Professor Gibson was invited to research, prepare and edit the Archive to appear as this book, encouraged by Trinity College Cambridge and The Mathematical Association. Niamh O'Mahony joined him in co-editing and bring this book to publication. In this volume we witness Wittgenstein in the act of composing and experimenting with his new visions in philosophy. The book includes key explanations of the origin and background of these previously unknown manuscripts. It investigates how Wittgenstein's philosophical thought-processes are revealed in his dictation to, as well as his editing and revision with Francis Skinner, in the latter's role of amanuensis. The book displays a considerable wealth and variety of Wittgenstein's fundamental experiments in philosophy across a wide array of subjects that include the mind, pure and applied mathematics, metaphysics, the identities of ordinary and creative language, as well as intractable problems in logic and life. He also periodically engages with the work of Newton, Fermat, Russell and others. The book shows Wittgenstein strongly battling against the limits of understanding and the bewitchment of institutional and linguistic customs. The reader is drawn in by Wittgenstein as he urges us to join him in his struggles to equip us with skills, so that we can embark on devising new pathways beyond confusion. -- Back cover.

Originally written in 1950, then revised and first published in 1992, The Dwarfs is Harold Pinter's only novel. Set in postwar Britain, The Dwarfs describes the intertwined lives and concerns of four young Londoners: Len, working at the Euston train station but fascinated by abstract mathematics; Mark, a sometime actor; and Virginia and Pete, a young couple trying to define their relationship amid the powerful, sometimes destructive forces at work among the four. In the evolution of this quadrilateral friendship and the strains it creates, Harold Pinter explores how ordinary lives are molded by the limitations and boundaries of sexuality, intimacy, and mortality. It is a world populated by dwarfs -- young people who have departed, only to leave emptiness. Funny, vivid, and haunting, The Dwarfs is a brilliantly intriguing and chillingly perceptive novel by a writer whose imagination has shaped our lives.

This volume contains some of Professor Wigner's more popular papers, which, in their diversity of subject and clarity of style, reflect the author's deep analytical powers and the remarkable scope of his interests. Included are articles on the nature of physical symmetry, invariance and conservation principles, the structure of solid bodies and of the compound nucleus, the theory of nuclear fission, the effects of radiation on solids, and epistemological problems of quantum mechanics. Other articles deal with the story of the first man-made nuclear chain reaction, the long-term prospects of nuclear energy, the problems of Big Science, and the role of mathematics in the natural sciences. In addition, the book contains statements of Wigner's convictions and beliefs, as well as memoirs of his friends, Enrico Fermi and John von Neumann.

Presents an outline of the knowledge that, according to the Cultural Literacy Foundation, should be acquired by the end of sixth grade, in such categories as literature, religion and philosophy, history, geography, mathematics, science, and technology.

This book provides relevant theoretical frameworks and the latest empirical research findings in Operations Research (OR) and Management Science (MS) as applied to sustainability. Its goal is to identify and describe ways in which OR and MS have been applied to and influenced the development of sustainability. Many of the issues we face today stem from the interconnectivity of the economy, society, and the environment, and from how both the economy and society are affecting the environment. In response, there have been a range of local and global efforts to advance society without harming the natural environment. The book showcases how OR/MS can help to address these issues, specifically with regard to renewable energy, smart industry, smart cities, transportation, smart homes and devices, etc. This book is intended for professionals in the fields of energy, engineering, information science, mathematics and economics, and for researchers who wish to develop new skills in connection with sustainability, or whose work involves sustainability.

With extraordinary concision and clarity, A. J. Ayer gives an account of the major incidents of Bertrand Russell's life and an exposition of the whole range of his philosophy. "Ayer considers Russell to be, except possibly for Wittgenstein, the most influential philosopher of our time. In this book [he] gives a lucid account of Russell's philosophical achievements."—James Rachels, New York Times Book Review "I am sure [this] is the best introduction of any length to Russell, and I suspect that it might serve as one of the best introductions to modern philosophy. . . . Ayer begins with a brief, austere, and balanced account of Russell's life: as in Russell's autobiography this means his thought, books, women, and politics. Tacitus (and Russell) would have found the account exemplary. Ayer ends with a sympathetic and surprisingly detailed survey of Russell's social philosophy. But the bulk of this book consists of a chapter on Russell's work in logic and the foundations of mathematics, followed by a chapter on his epistemological views and one on metaphysics. . . . I find it impossible to imagine that this book will not remain indefinitely the very best book of its sort."— Review of Metaphysics "The confrontation or conjunction of Ayer and Russell is a notable event and has produced a remarkable book—brilliantly argued and written."—Martin Lebowitz, The Nation

Sixth-grade mathematical genius Charlie Lewis, the Whiz Kids, and new friends follow their hunch that eccentric billionnaire Blake Headstrom is importing mammoth tusks for sinister purposes.

First published in 1971, Professor Putnam's essay concerns itself with the ontological problem in the philosophy of logic and mathematics - that is, the issue of whether the abstract entities spoken of in logic and mathematics really exist. He also deals with the question of whether or not reference to these abstract entities is really indispensible in logic and whether it is necessary in physical science in general.

This book introduces the basic concepts of parallel and vector computing in the context of an introduction to numerical methods. It contains chapters on parallel and vector matrix multiplication and solution of linear systems by direct and iterative methods. It is suitable for advanced undergraduate and beginning graduate courses in computer science, applied mathematics, and engineering. Ideally, students will have access to a parallel or Vector computer, but the material can be studied profitably in any case.

"Practical, scientific, philosophical & artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these-the search for beauty. Mathematics is an art, & as such affords the pleasures which all the arts afford."--The Author Preface Why mathematics? A historical orientation Logic & mathematics Number: the fundamental concept Algebra, the higher arithmetic The nature & uses of Euclidean geometry Charting the earth & the heavens The mathematical order of nature The awakening of Europe Mathematics & painting in the Renaissance Projective geometry Coordinate geometry The simplest formulas in action Parametric equations & curvilinear motion The application of formulas to gravitation The differential calculus The integral calculus Trigonometric functions & oscillatory motion The trigonometric analysis of musical sounds Non-Euclidean geometries & their significance Arithmetics & their algebras The statistical approach to the social & biological sciences The theory of probability The nature & values of mathematics Table of Trigonometic Ratios Answers to Selected & Review Exercises Additional Answers & Solutions Index

Slight shelf wear. Marker mark fore edge. Pages are clean. Binding is tight.

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

The Langlands Program was conceived initially as a bridge between Number Theory and Automorphic Representations, and has now expanded into such areas as Geometry and Quantum Field Theory, tying together seemingly unrelated disciplines into a web of tantalizing conjectures. A new chapter to this grand project is provided in this book. It develops the geometric Langlands Correspondence for Loop Groups, a new approach, from a unique perspective offered by affine Kac-Moody algebras. The theory offers fresh insights into the world of Langlands dualities, with many applications to Representation Theory of Infinite-dimensional Algebras, and Quantum Field Theory. This accessible text builds the theory from scratch, with all necessary concepts defined and the essential results proved along the way. Based on courses taught at Berkeley, the book provides many open problems which could form the basis for future research, and is accessible to advanced undergraduate students and beginning graduate students.