A Mathematical Space Odyssey

Author : Claudi Alsina,Roger B. Nelsen
Publisher : The Mathematical Association of America
Page : 288 pages
File Size : 50,5 Mb
Release : 2015-08-21
Category : Mathematics
ISBN : 9780883853580

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A Mathematical Space Odyssey by Claudi Alsina,Roger B. Nelsen Pdf

Solid geometry is the traditional name for what we call today the geometry of three-dimensional Euclidean space. Courses in solid geometry have largely disappeared from American high schools and colleges. The authors are convinced that a mathematical exploration of three-dimensional geometry merits some attention in today’s curriculum. A Mathematical Space Odyssey: Solid Geometry in the 21st Century is devoted to presenting techniques for proving a variety of mathematical results in three-dimensional space, techniques that may improve one’s ability to think visually. Special attention is given to the classical icons of solid geometry (prisms, pyramids, platonic solids, cones, cylinders, and spheres) and many new and classical results: Cavalieri’s principle, Commandino’s theorem, de Gua’s theorem, Prince Rupert’s cube, the Menger sponge, the Schwarz lantern, Euler’s rotation theorem, the Loomis-Whitney inequality, Pythagorean theorems in three dimensions, etc. The authors devote a chapter to each of the following basic techniques for exploring space and proving theorems: enumeration, representation, dissection, plane sections, intersection, iteration, motion, projection, and folding and unfolding. In addition to many figures illustrating theorems and their proofs, a selection of photographs of three-dimensional works of art and architecture are included. Each chapter includes a selection of Challenges for the reader to explore further properties and applications. It concludes with solutions to all the Challenges in the book, references, and a complete index. Readers should be familiar with high school algebra, plane and analytic geometry, and trigonometry. While brief appearances of calculus do occur, no knowledge of calculus is necessary to enjoy this book.

Author : Ivars Peterson,Nancy Henderson
Publisher : Turtleback
Page : 128 pages
File Size : 48,5 Mb
Release : 2000-10
Category : Electronic
ISBN : 0613845633

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Math Trek 2 by Ivars Peterson,Nancy Henderson Pdf

Take a wild and wonderful voyage through the world of mathematics with this fun book filled with intriguing math concepts that's also packed with plenty of art, projects, historical profiles, and challenges. 70 illustrations.

Author : Ivars Peterson,Nancy Henderson
Publisher : Jossey-Bass
Page : 0 pages
File Size : 51,8 Mb
Release : 2000-10-26
Category : Juvenile Nonfiction
ISBN : 0471315710

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Math Trek 2 by Ivars Peterson,Nancy Henderson Pdf

Take a wild and Wonderful Voyage Through the Universe of Mathematics! Just imagine how much fun it would be to explore the fourth dimension! Play baseball on an asteroid! Ride an alien bike with square wheels! Let Math Trek 2 take you on an intergalactic excursion as you master dizzying mathematical concepts on your home planet of Earth! While playing games and solving puzzles, you can explore mind-boggling mental mysteries and investigate hidden patterns in the universe. From strange number sequences and bizarre buckyballs to random walks, you’ll be amazed at the mathematical concepts you’ll soon comprehend. So let Math Trek 2 take you on a fantastic space odyssey where you can look for a pi in the sky, get stuck in galactic gridlock, and sail away to the planet of the shapes!

Author : Raymond Mortini,Rudolf Rupp
Publisher : Springer Nature
Page : 2197 pages
File Size : 41,5 Mb
Release : 2021-08-02
Category : Mathematics
ISBN : 9783030738723

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Extension Problems and Stable Ranks by Raymond Mortini,Rudolf Rupp Pdf

This self-contained encyclopedic monograph gives a detailed introduction to Bézout equations and stable ranks, encompassing and explaining needed topological, analytical, and algebraic tools and methods. Some of the highlights included are Carleson's corona theorem and the Bass, topological, and matricial stable ranks. The first volume focusses on topological structures, Banach algebras, and advanced function theory, thus preparing the stage for the algebraic structures in the second volume towards examining stable ranks with analytic methods. The main emphasis is laid on algebras of holomorphic functions. Often a new approach is presented or at least a different angle of sight, which makes the book attractive both for researchers and students interested in these active fields of research.

Author : Arthur C. Clarke,Frederik Pohl
Publisher : Del Rey
Page : 337 pages
File Size : 49,6 Mb
Release : 2009-08-18
Category : Fiction
ISBN : 9780345470232

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The Last Theorem by Arthur C. Clarke,Frederik Pohl Pdf

When Ranjit Subramanian, a Sri Lankan with a special gift for numbers, writes a three-page proof of the coveted “Last Theorem,” which French mathematician Pierre de Fermat claimed to have discovered (but never recorded) in 1637, Ranjit’s achievement is hailed as a work of genius, bringing him fame and fortune. But it also brings him to the attention of the National Security Agency and a shadowy United Nations outfit called Pax per Fidem–or Peace Through Transparency–whose secretive workings belie its name. Suddenly Ranjit–along with his family–finds himself swept up in world-shaking events, his genius for abstract mathematical thought put to uses that are both concrete and potentially deadly.

Author : Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands)
Publisher : Unknown
Page : 642 pages
File Size : 55,7 Mb
Release : 1994
Category : Computer science
ISBN : 9061964504

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From Universal Morphisms to Megabytes by Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands) Pdf

Author : Ignazio Ciufolini,Daniele Dominici,L. Lusanna
Publisher : World Scientific
Page : 528 pages
File Size : 45,6 Mb
Release : 2003
Category : Science
ISBN : 9812380892

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2001, a Relativistic Spacetime Odyssey by Ignazio Ciufolini,Daniele Dominici,L. Lusanna Pdf

This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity.

Author : Ignazio Ciufolini,Daniele Dominici,Luca Lusanna
Publisher : World Scientific
Page : 524 pages
File Size : 45,7 Mb
Release : 2003-01-16
Category : Science
ISBN : 9789814487986

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2001: A Relativistic Spacetime Odyssey by Ignazio Ciufolini,Daniele Dominici,Luca Lusanna Pdf

This volume offers a comprehensive overview of our understanding of gravity at both the experimental and the theoretical level. Critical reviews by experts cover topics ranging from astrophysics (anisotropies in the cosmic microwave background, gamma ray bursts, neutron stars and astroparticles), cosmology, the status of gravitational wave sources and detectors, verification of Newton's law at short distances, the equivalence principle, gravito-magnetism, measurement theory, time machines and the foundations of Einstein's theory, to string theory and loop quantum gravity. Contents:Foundations and Classical General Relativity:Space–Time, General Covariance, Dirac–Bergmann Observables and Non-Inertial Frames (L Lusanna)Physics in the Presence of a Time Machine (I D Novikov)Frame-Dragging and Gravitomagnetism: Theory and Experiment (I Ciufolini)New Tests of the Strong Equivalence Principle and of the Inverse Square Law (E G Adelberger)Cosmology:The Inflationary Universe (A Riotto)Imaging the Early Universe with the BOOMERANG Experiment (P De Bernardis et al.)Gravitational Waves:Gravitational Radiation: A Tool for Testing General Relativity (C M Will)What Gravitational Signals Say about the Structure and the Evolution of Astrophysical Sources (V Ferrari)Astrophysics:Computational Relativity: Collisions of Black Holes (R Matzner)Gamma Ray Bursts: Some Facts and Ideas (G Ghisellini)Quantum Gravity:Spin Foams as Feynman Diagrams (M Reisenberger & C Rovelli)Physics with Large Extra Dimensions (I Antoniadis)Field Theories on Canonical and Lie-Algebra Noncommutative Spacetimes (G Amelino-Camelia et al.)and other papers Readership: Quantum, astro-, high-energy and theoretical physicists. Keywords:

Author : Michigan Center for Theoretical Physics. Inaugural Conference
Publisher : World Scientific
Page : 244 pages
File Size : 45,6 Mb
Release : 2002
Category : Science
ISBN : 9812382313

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2001, a Spacetime Odyssey by Michigan Center for Theoretical Physics. Inaugural Conference Pdf

Two theories revolutionized the 20th century view of space and time: Einstein's general theory of relativity and quantum mechanics. Their union has given rise to elementary particle theories with extra spacetime dimensions, the inflationary model of big bang cosmology, the hypothesis of dark matter in the universe, the discovery of radiation from quantum black holes, and the fuzzy spacetime geometry of superstrings and M-theory. In this important book, experts present the latest developments in cosmology, theoretical physics and mathematics, as well as share their thoughts on the future of spacetime physics.

Author : Steven G. Krantz,Harold R. Parks
Publisher : Springer
Page : 392 pages
File Size : 46,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781461489399

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A Mathematical Odyssey by Steven G. Krantz,Harold R. Parks Pdf

Mathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone. This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe. Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths.

Author : Mircea Pitici
Publisher : Princeton University Press
Page : 408 pages
File Size : 54,6 Mb
Release : 2017-02-14
Category : Mathematics
ISBN : 9781400885602

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The Best Writing on Mathematics 2016 by Mircea Pitici Pdf

The year's finest mathematics writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Burkard Polster shows how to invent your own variants of the Spot It! card game, Steven Strogatz presents young Albert Einstein's proof of the Pythagorean Theorem, Joseph Dauben and Marjorie Senechal find a treasure trove of math in New York's Metropolitan Museum of Art, and Andrew Gelman explains why much scientific research based on statistical testing is spurious. In other essays, Brian Greene discusses the evolving assumptions of the physicists who developed the mathematical underpinnings of string theory, Jorge Almeida examines the misperceptions of people who attempt to predict lottery results, and Ian Stewart offers advice to authors who aspire to write successful math books for general readers. And there's much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Author : Sven Ove Hansson
Publisher : Springer
Page : 373 pages
File Size : 55,8 Mb
Release : 2018-10-24
Category : Philosophy
ISBN : 9783319937793

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Technology and Mathematics by Sven Ove Hansson Pdf

This volume is the first extensive study of the historical and philosophical connections between technology and mathematics. Coverage includes the use of mathematics in ancient as well as modern technology, devices and machines for computation, cryptology, mathematics in technological education, the epistemology of computer-mediated proofs, and the relationship between technological and mathematical computability. The book also examines the work of such historical figures as Gottfried Wilhelm Leibniz, Charles Babbage, Ada Lovelace, and Alan Turing.

Author : Dennis S. Bernstein
Publisher : Princeton University Press
Page : 1600 pages
File Size : 50,7 Mb
Release : 2018-02-27
Category : Mathematics
ISBN : 9781400888252

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Scalar, Vector, and Matrix Mathematics by Dennis S. Bernstein Pdf

The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index

Author : Dirk Huylebrouck
Publisher : Springer
Page : 229 pages
File Size : 53,7 Mb
Release : 2019-03-30
Category : Mathematics
ISBN : 9783030040376

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Africa and Mathematics by Dirk Huylebrouck Pdf

This volume on ethnomathematics in Central Africa fills a gap in the current literature, focusing on a region rarely explored by other publications. It highlights the discovery of the Ishango rod, which was found to be the oldest mathematical tool in humanity's history, thereby shifting the origin of mathematics to the heart of Africa, and explores the different scientific hypotheses that emerged as a result. While it contains some high-level mathematics, the non-mathematical reader can easily skip these portions and enjoy the book’s survey of African history, culture, and art.

Author : Roger B. Nelsen
Publisher : American Mathematical Soc.
Page : 187 pages
File Size : 52,9 Mb
Release : 2015-12-31
Category : Mathematics
ISBN : 9780883857908

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Proofs Without Words III by Roger B. Nelsen Pdf

Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.