Lobachevski Illuminated

Author: Seth Braver
Publisher: Mathematical Association of America
ISBN: 9780883855737
Category: Mathematics
Page: 248
View: 9783

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Lobachevski Illuminated provides a historical introduction to non-Euclidean geometry. Lobachevski's trailblazing explorations of non-Euclidean geometry constitute a crucial episode in the history of mathematics, but they were not widely recognized as such until after his death. Within these pages, readers will be guided step-by-step, through a new translation of Lobachevski's groundbreaking book, The Theory of Parallels. Extensive commentary situates Lobachevski's work in its mathematical, historical and philosophical context, thus granting readers a vision of the mysteries and beautiful world of non-Euclidean geometry as seen through the eyes of one of its discoverers. Although Lobachevski's 170-year-old text is challenging to read on its own, Seth Braver's carefully arranged 'illuminations' render this classic accessible to modern readers (student, professional mathematician or layman).

Lobachevski Illuminated

Author: Seth Braver
Publisher: MAA
ISBN: 0883859793
Page: 400
View: 2644

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A historical introduction to non-Euclidean geometry.

Convexity and Its Applications

Publisher: Birkhäuser
ISBN: 3034858582
Category: Science
Page: 421
View: 3202

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This collection of surveys consists in part of extensions of papers presented at the conferences on convexity at the Technische Universitat Wien (July 1981) and at the Universitat Siegen (July 1982) and in part of articles written at the invitation of the editors. This volume together with the earlier volume «Contributions to Geometry» edited by Tolke and Wills and published by Birkhauser in 1979 should give a fairly good account of many of the more important facets of convexity and its applications. Besides being an up to date reference work this volume can be used as an advanced treatise on convexity and related fields. We sincerely hope that it will inspire future research. Fenchel, in his paper, gives an historical account of convexity showing many important but not so well known facets. The articles of Papini and Phelps relate convexity to problems of functional analysis on nearest points, nonexpansive maps and the extremal structure of convex sets. A bridge to mathematical physics in the sense of Polya and Szego is provided by the survey of Bandle on isoperimetric inequalities, and Bachem's paper illustrates the importance of convexity for optimization. The contribution of Coxeter deals with a classical topic in geometry, the lines on the cubic surface whereas Leichtweiss shows the close connections between convexity and differential geometry. The exhaustive survey of Chalk on point lattices is related to algebraic number theory. A topic important for applications in biology, geology etc.

The Value of Science

Author: Henri Poincaré,George Bruce Halsted
Publisher: N.A
Category: Science
Page: 147
View: 3692

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Relativistic Cosmology

Author: George F. R. Ellis,Roy Maartens,Malcolm A. H. MacCallum
Publisher: Cambridge University Press
ISBN: 1139642952
Category: Science
Page: N.A
View: 6772

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Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

Mathematics for Physics

A Guided Tour for Graduate Students
Author: Michael Stone,Paul Goldbart
Publisher: Cambridge University Press
ISBN: 1139480618
Category: Science
Page: N.A
View: 446

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An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Indiscrete Thoughts

Author: Gian-Carlo Rota
Publisher: Springer Science & Business Media
ISBN: 9780817647810
Category: Mathematics
Page: 280
View: 8754

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Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.

Springer Handbook of Spacetime

Author: Abhay Ashtekar,Vesselin Petkov
Publisher: Springer
ISBN: 3642419925
Category: Science
Page: 950
View: 6499

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The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.

A Unified Grand Tour of Theoretical Physics, Third Edition

Author: Ian D. Lawrie
Publisher: CRC Press
ISBN: 1439884463
Category: Science
Page: 711
View: 8581

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A Unified Grand Tour of Theoretical Physics invites its readers to a guided exploration of the theoretical ideas that shape our contemporary understanding of the physical world at the fundamental level. Its central themes, comprising space-time geometry and the general relativistic account of gravity, quantum field theory and the gauge theories of fundamental forces, and statistical mechanics and the theory of phase transitions, are developed in explicit mathematical detail, with an emphasis on conceptual understanding. Straightforward treatments of the standard models of particle physics and cosmology are supplemented with introductory accounts of more speculative theories, including supersymmetry and string theory. This third edition of the Tour includes a new chapter on quantum gravity, focusing on the approach known as Loop Quantum Gravity, while new sections provide extended discussions of topics that have become prominent in recent years, such as the Higgs boson, massive neutrinos, cosmological perturbations, dark energy and matter, and the thermodynamics of black holes. Designed for those in search of a solid grasp of the inner workings of these theories, but who prefer to avoid a full-scale assault on the research literature, the Tour assumes as its point of departure a familiarity with basic undergraduate-level physics, and emphasizes the interconnections between aspects of physics that are more often treated in isolation. The companion website at www.unifiedgrandtours.org provides further resources, including a comprehensive manual of solutions to the end-of-chapter exercises.

Number Theory

An Introduction to Mathematics
Author: W.A. Coppel
Publisher: Springer Science & Business Media
ISBN: 0387894861
Category: Mathematics
Page: 610
View: 3944

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Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.

Ancient Riddles of Solar Eclipses

Asymmetric Astronomy
Author: Igor Taganov,Ville Saari
Publisher: Klaava Media
ISBN: 9527074452
Category: Science
Page: 114
View: 4899

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Ancient astronomical manuscripts in addition to priceless chronicles of solar and lunar eclipses contain curious riddles, which are sometimes difficult to interpret by science. Astronomers and historians Igor Taganov and Ville Saari confirmed intuitive guesses of medieval Indian and Chinese astronomers and discovered the calendar cycles – the probabilities of total solar eclipse are larger in summer months and in southern regions. Moreover, analyzing the ancient chronicles of solar and lunar eclipses they found the sensational evidence of slow deceleration of the pace of time that can radically change our world outlook.

Symmetries and Laplacians

Introduction to Harmonic Analysis, Group Representations and Applications
Author: David Gurarie
Publisher: Courier Corporation
ISBN: 0486462889
Category: Mathematics
Page: 453
View: 8766

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Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.

Distant View of a Minaret

And Other Stories
Author: Alifa Rifaat,Denys Johnson-Davies
Publisher: Heinemann
ISBN: 9780435909123
Category: Fiction
Page: 116
View: 8817

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Alifa Rifaat, an Egyptian, lifts the veil on what it means to be a woman living within a traditional Muslim society.

Heinrich Hertz: Classical Physicist, Modern Philosopher

Author: D. Baird,R.I. Hughes,Alfred Nordmann
Publisher: Springer Science & Business Media
ISBN: 9401588554
Category: Science
Page: 324
View: 7624

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The sub-title of this symposium is accurate and, in a curious way, promises more than it states: Classical Physicist, Modem Philosopher. Heinrich Hertz, as the con summate experimentalist of 19th century technique and as brilliant clarifying critic of physical theory of his time, achieved one of the fulfilments but at the same time opened one of the transition points of classical physics. Thus, in his 'popular' lecture 'On the Relations Between Light and Electricity' at Heidelberg in the Fall of 1889, Hertz identified the ether as henceforth the most fundamental problem of physics, as the conceptual mystery but also the key to understanding mass, electric ity, and gravity. Of Hertz's demonstration of electric waves, Helmholtz told the Physical Society of Berlin: "Gentlemen! I have to communicate to you today the most important physical discovery of the century. " Hertz, philosophizing in his direct, lucid, pithy style, once wrote "We have to imagine". Perhaps this is metaphysics on the horizon? In the early pages of his Principles of Mechanics, we read A doubt which makes an impression on our mind cannot be removed by calling it metaphysical: every thoughtful mind as such has needs which scientific men are accustomed to denote as metaphysical. (PM23) And at another place, concerning the terms 'force' and 'electricity' and the alleged mystery of their natures, Hertz wrote: We have an obscure feeling of this and want to have things cleared up.

Wrinkles in Time

Witness to the Birth of the Universe
Author: George Smoot,Keay Davidson
Publisher: Harper Collins
ISBN: 0061344443
Category: Science
Page: 352
View: 1642

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Astrophysicist George Smoot spent decades pursuing the origin of the cosmos, "the holy grail of science," a relentless hunt that led him from the rain forests of Brazil to the frozen wastes of Antarctica. In his search he struggled against time, the elements, and the forces of ignorance and bureaucratic insanity. Finally, after years of research, Smoot and his dedicated team of Berkeley researchers succeeded in proving the unprovable—uncovering, inarguably and for all time, the secrets of the creation of the universe. Wrinkles in Time describes this startling discovery that would usher in a new scientific age—and win Smoot the Nobel Prize in Physics.

Cooperative Work and Coordinative Practices

Contributions to the Conceptual Foundations of Computer-Supported Cooperative Work (CSCW)
Author: Kjeld Schmidt
Publisher: Springer Science & Business Media
ISBN: 9781848000681
Category: Computers
Page: 472
View: 7739

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Information technology has been used in organisational settings and for organisational purposes such as accounting, for a half century, but IT is now increasingly being used for the purposes of mediating and regulating complex activities in which multiple professional users are involved, such as in factories, hospitals, architectural offices, and so on. The economic importance of such coordination systems is enormous but their design often inadequate. The problem is that our understanding of the coordinative practices for which these systems are developed is deficient, leaving systems developers and software engineers to base their designs on commonsensical requirements analyses. The research reflected in this book addresses these very problems. It is a collection of articles which establish a conceptual foundation for the research area of Computer-Supported Cooperative Work.

Recent Developments in General Relativity

Author: B. Casciaro,D. Fortunato,M. Francaviglia,A. Masiello
Publisher: Springer Science & Business Media
ISBN: 8847021138
Category: Science
Page: 521
View: 2829

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The 13th Italian Conference on General Relativity and Gravitational Physics was held in Cala Corvino-Monopoli (Bari) from September 21to September 25, 1998. The Conference, which is held every other year in different Italian locations, has brought together, as in the earlier conferences in this series, those scientists who are interested and actively work in all aspects of general relativity, from both the mathematical and the physical points of view: from classical theories of gravitation to quantum gravity, from relativistic astrophysics and cosmology to experiments in gravitation. About 70 participants came from Departments of Astronomy and Astrophysics, Departments of Mathematics and Departments of Experimental and Theoretical Physics from all over the Country; in addition a few Italian scientists working abroad kindly accepted invitations from the Scientific Committee. The good wishes of the University and of the Politecnico di Bari were conveyed by the director of Diparti mento Interuniversitario di Matematica, Prof. Franco Altomare. These proceedings contain the contributions of the two winners of the SIGRAV prizes, the invited talks presented at the Conference and most of the contributed talks. We thank all of our colleagues, who did their best to prepare their manuscripts. The pleasant atmosphere induced by the beauty of the place was greatlyenhanced not only by the participation of so many colleagues, who had lively discussions about science well beyond Conference hours, but also by the feeling of hospitalityextended to the participants by the staff of the Cala Corvino Hotel, where the Conference was held.


The Science of the Universe
Author: Edward Harrison
Publisher: Cambridge University Press
ISBN: 1139643452
Category: Science
Page: N.A
View: 9851

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Cosmology: The Science of the Universe is an introduction to past and present cosmological theory. For much of the world's history, cosmological thought was formulated in religious or philosophical language and was thus theological or metaphysical in nature. However, cosmological speculation and theory has now become a science in which the empirical discoveries of the astronomer, theoretical physicist, and biologist are woven into intricate models that attempt to account for the universe as a whole. Professor Harrison draws on the discoveries and speculations of these scientists to provide a comprehensive survey of man's current understanding of the universe and its history. Tracing the rise of the scientific method, the major aim of this book is to provide an elementary understanding of the physical universe of modern times. Thoroughly revised and updated, this second edition extends the much acclaimed first edition taking into account the many developments that have occurred.

Concepts of Space

The History of Theories of Space in Physics: Third, Enlarged Edition
Author: Max Jammer
Publisher: Courier Corporation
ISBN: 0486166473
Category: History
Page: 288
View: 1682

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Historical surveys consider Judeo-Christian notions of space, Newtonian absolute space, perceptions from 18th century to the present, more. Numerous quotations and references. "Admirably compact and swiftly paced style." — Philosophy of Science.

Travels in Four Dimensions

The Enigmas of Space and Time
Author: Robin Le Poidevin
Publisher: Peterson's
ISBN: 9780198752547
Category: Philosophy
Page: 275
View: 9963

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A metaphysics professor offers a profound but accessible look at some of the most baffling puzzles of the universe, including time travel, parallel worlds, the edge of the universe, the mysteries of time and space, in a volume that draws on a variety of examples from the fields of philosophy, science, history, and literature. (Philosophy)