James W. Cannon's Books

Topology as Fluid Geometry

By: James W. Cannon

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This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two proofs), the No Retraction Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem, the Open Mapping Theorem, the Riemann-Hurwitz Theorem, and the Classification Theorem for Compact 2-manifolds. Volume 2 also includes a number of theorems usually assumed without proof since their proofs are not readily available, for example, the Zippin Characterization Theorem for 2-dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2-manifolds, and the R. L. Moore's Decomposition Theorem so useful in understanding fractal sets.

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Page Count

181

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470437155

ISBN 13

9781470437152

Non-Euclidean Geometry and Curvature

By: James W. Cannon

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Non-Euclidean Geometry and Curvature

By: James W. Cannon

This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, which explains a more classical view of hyperbolic non-Euclidean geometry in all dimensions. Finally, the author explains a natural intrinsic obstruction to flattening a triangulated polyhedral surface into the plane without distorting the constituent triangles. That obstruction extends intrinsically to smooth surfaces by approximation and is called curvature. Gauss's original definition of curvature is extrinsic rather than intrinsic. The final two chapters show that the book's intrinsic definition is equivalent to Gauss's extrinsic definition (Gauss's “Theorema Egregium” (“Great Theorem”)).

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Page Count

119

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470437163

ISBN 13

9781470437169

Modular Forms

A Classical and Computational Introduction

By: Lloyd James Peter Kilford

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Modular Forms

A Classical and Computational Introduction

By: Lloyd James Peter Kilford

This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.

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Page Count

237

Publisher

Imperial College Press

Published Date

ISBN 10

1848162146

ISBN 13

9781848162143

Geometry of Lengths, Areas, and Volumes

By: James W. Cannon

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Geometry of Lengths, Areas, and Volumes

By: James W. Cannon

This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of and , of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.

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Page Count

133

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470437147

ISBN 13

9781470437145

Chase, Chance, and Creativity

The Lucky Art of Novelty

By: James H. Austin

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Chase, Chance, and Creativity

The Lucky Art of Novelty

By: James H. Austin

A personal story of the ways in which persistence, chance, and creativity interact in biomedical research. This first book by the author of Zen and the Brain examines the role of chance in the creative process. James Austin tells a personal story of the ways in which persistence, chance, and creativity interact in biomedical research; the conclusions he reaches shed light on the creative process in any field. Austin shows how, in his own investigations, unpredictable events shaped the outcome of his research and brought about novel results. He then goes beyond this story of serendipity to propose a new classification of the varieties of chance, drawing on his own research and examples from the history of science—including the famous accidents that led Fleming to the discovery of penicillin. Finally, he explores the nature of the creative process, considering not only the environmental and neurophysiological correlates of creativity but also the role of intuition in both scientific discoveries and spiritual quests. This updated MIT Press paperback edition includes a new introduction and recent material on medical research, creativity, and spirituality.

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Page Count

278

Publisher

MIT Press

Published Date

ISBN 10

0262250101

ISBN 13

9780262250108

Dynamics of Human Reproduction

Biology, Biometry, Demography

By: James W. Wood

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Dynamics of Human Reproduction

Biology, Biometry, Demography

By: James W. Wood

Awarded the W. W. Howells Award for the Outstanding Book in Biological Anthropology, this volume presents a comprehensive, integrated, and up-to-date overview of the major physiological and behavioral factors affecting human reproduction. In attempting to identify the most important causes of variation in fertility within and among human populations, Wood summarizes data from a wide range of societies. Trained as an anthropologist as well as a demographer, he devotes special attention to so-called ""natural fertility"" populations, in which modern contraceptives and induced abortion are not used to limit reproductive output. Such an emphasis enables him to study the interaction of biology and behavior with particular clarity.The volume weaves together the physiological, demographic, and biometric approaches to human fertility in a way that will encourage future interdisciplinary research. Instead of offering a general overview, the focus is to answer one question: Why does fertility and the number of live births vary from couple to couple within any particular population, and from population to population across the human species as a whole?Topics covered include ovarian function, conception and pregnancy, intrauterine mortality, reproductive maturation and senescence, coital frequency and the waiting time to conception, marriage patterns and the initiation of reproduction, the fertility-reducing effects of breastfeeding, the impact of maternal nutrition on reproduction, and reproductive seasonality. This unique combination of comprehensive subject matter and an integrated analytical approach makes the book ideally suited both as a graduate-level textbook and as a reference work.

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Page Count

669

Publisher

Routledge

Published Date

ISBN 10

1351521470

ISBN 13

9781351521475

Interferometry and Synthesis in Radio Astronomy

By: A. Richard Thompson,James M. Moran,George W. Swenson, Jr.

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Interferometry and Synthesis in Radio Astronomy

By: A. Richard Thompson,James M. Moran,George W. Swenson, Jr.

In this second edition of Interferometry and Synthesis in Radio Astronomy, three leading figures in the development of large imaging arrays, including very-long-baseline interferometry (VLBI), describe and explain the technology that provides images of the universe with an angular resolution as fine as 1/20,000 of an arcsecond. This comprehensive volume begins with a historical review followed by detailed coverage of the theory of interferometry and synthesis imaging, analysis of interferometer response, geometrical relationships, polarimetry, antennas, and arrays. Discussion of the receiving system continues with analysis of the response to signals and noise, analog design requirements, and digital signal processing. The authors detail special requirements of VLBI including atomic frequency standards, broadband recording systems, and antennas in orbit. Further major topics include: Calibration of data and synthesis of images Image enhancement using nonlinear algorithms Techniques for astrometry and geodesy Propagation in the neutral atmosphere and ionized media Radio interference Related techniques: intensity interferometry, moon occultations, antenna holography, and optical interferometry ”This edition meets current demands by providing a comprehensive account of the techniques used today.“ (La Doc STI) [...] The up-to-date edition of Thompson [...] with its exhaustive bibliography, becomes the indispensable source of background for those already in, or considering, radio astronomy.“ (The Observatory)

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Page Count

723

Publisher

John Wiley & Sons

Published Date

ISBN 10

3527414525

ISBN 13

9783527414529

Book's by James W. Cannon

Topology as Fluid Geometry

Topology as Fluid Geometry

Non-Euclidean Geometry and Curvature

Non-Euclidean Geometry and Curvature

Modular Forms

Modular Forms

Geometry of Lengths, Areas, and Volumes

Geometry of Lengths, Areas, and Volumes

Chase, Chance, and Creativity

Chase, Chance, and Creativity

Dynamics of Human Reproduction

Dynamics of Human Reproduction

Interferometry and Synthesis in Radio Astronomy

Interferometry and Synthesis in Radio Astronomy

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