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Author: Felipe Cucker
Publisher: Cambridge University Press
ISBN: 1107354498
Category : Mathematics
Languages : en
Pages : 427
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Book Description
Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.
Author: Felipe Cucker
Publisher: Cambridge University Press
ISBN: 1107354498
Category : Mathematics
Languages : en
Pages : 427
Get Book Here
Book Description
Most works of art, whether illustrative, musical or literary, are created subject to a set of constraints. In many (but not all) cases, these constraints have a mathematical nature, for example, the geometric transformations governing the canons of J. S. Bach, the various projection systems used in classical painting, the catalog of symmetries found in Islamic art, or the rules concerning poetic structure. This fascinating book describes geometric frameworks underlying this constraint-based creation. The author provides both a development in geometry and a description of how these frameworks fit the creative process within several art practices. He furthermore discusses the perceptual effects derived from the presence of particular geometric characteristics. The book began life as a liberal arts course and it is certainly suitable as a textbook. However, anyone interested in the power and ubiquity of mathematics will enjoy this revealing insight into the relationship between mathematics and the arts.
Author: Adam Roberts
Publisher: Open Book Publishers
ISBN: 1800641613
Category : Literary Criticism
Languages : en
Pages : 144
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Book Description
In Middlemarch, George Eliot draws a character passionately absorbed by abstruse allusion and obscure epigraphs. Casaubon’s obsession is a cautionary tale, but Adam Roberts nonetheless sees in him an invitation to take Eliot’s use of epigraphy and allusion seriously, and this book is an attempt to do just that. Roberts considers the epigraph as a mirror that refracts the meaning of a text, and that thus carries important resonances for the way Eliot’s novels generate their meanings. In this lively and provoking study, he tracks down those allusions and quotations that have hitherto gone unidentified by scholars, examining their relationship to the text in which they sit to unfurl a broader argument about the novel – both this novel, and the novel form itself. Middlemarch: Epigraphs and Mirrors is both a study of George Eliot and a meditation on the textuality of fiction. It is essential reading for specialists and students of George Eliot, the nineteenth century novel, and intertextuality. It will also richly reward anyone who has ever taken pleasure in Middlemarch.
Author: Shing-Tung Yau
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 526
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Book Description
Vol. 1 represents a new ed. of papers which were originally published in Essays on mirror manifolds (1992); supplemented by the additional volume: Mirror symmetry 2 which presents papers by both physicists and mathematicians. Mirror symmetry 1 (the 1st volume) constitutes the proceedings of the Mathematical Sciences Research Institute Workshop of 1991.
Author: Kentaro Hori
Publisher: American Mathematical Soc.
ISBN: 0821829556
Category : Mathematics
Languages : en
Pages : 954
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Book Description
This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
Author: Michael Kapovich
Publisher: Springer Science & Business Media
ISBN: 0817649131
Category : Mathematics
Languages : en
Pages : 486
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Book Description
Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.
Author: Martin W. Liebeck
Publisher: Cambridge University Press
ISBN: 0521406854
Category : Mathematics
Languages : en
Pages : 505
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Book Description
This volume contains a collection of papers on the subject of the classification of finite simple groups.
Author: Shing-Tung Yau
Publisher: American Mathematical Soc.
ISBN: 082182743X
Category : Mathematics
Languages : en
Pages : 460
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Book Description
Vol. 1 represents a new ed. of papers which were originally published in Essays on mirror manifolds (1992); supplemented by the additional volume: Mirror symmetry 2 which presents papers by both physicists and mathematicians. Mirror symmetry 1 (the 1st volume) constitutes the proceedings of the Mathematical Sciences Research Institute Workshop of 1991.
Author: Thomas Nail
Publisher: Oxford University Press
ISBN: 0197526500
Category : Philosophy
Languages : en
Pages : 265
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Book Description
Karl Marx is the most historically foundational and systematic critic of capitalism to date, and the years since the 2008 financial crisis have witnessed a rebirth of his popular appeal. In a world of rising income inequality, right-wing nationalisms, and global climate change, people are again looking to the father of modern socialism for answers. As this book argues, every era since Marx's death has reinvented him to fit its needs. There is not one Marx forever and for all time. There are a thousand Marxes. As Thomas Nail contends, one of the most significant contributions of Marx's work is that it treats theory itself as a historical practice. Reading Marx is not just an interpretative activity but a creative one. As our historical conditions change, so do the kinds of questions we pose and the kinds of answers we find in Marx's writing. This book is a return to the writings of Karl Marx, including his under-appreciated dissertation, through the lens of the pressing philosophical and political problems of our time: ecological crisis, gender inequality, colonialism, and global mobility. However, the aim of this book is not to make Marxism relevant by "applying" it to contemporary issues. Instead, Marx in Motion, the first new materialist interpretation of Marx's work, treats Capital as if it were already a response to the present. Thomas Nail argues that Marx was a new materialist avant la lettre. He argues that Marx did not believe history was determined, or that matter was passive, or that humans were separate or superior to nature. Marx did not even have a labor theory of value. Marxists argue that new materialists lack a sufficient political and economic theory, and new materialists argue that Marx's materialism is human-centric and mechanistic. This book aims to solve both problems by proposing a new materialist Marxism.
Author: Mark Gross
Publisher: Springer Science & Business Media
ISBN: 3642190049
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS
Author: Claire Voisin
Publisher: American Mathematical Soc.
ISBN: 9780821819470
Category : Mathematics
Languages : en
Pages : 148
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Book Description
This is the English translation of Professor Voisin's book reflecting the discovery of the mirror symmetry phenomenon. The first chapter is devoted to the geometry of Calabi-Yau manifolds, and the second describes, as motivation, the ideas from quantum field theory that led to the discovery of mirror symmetry. The other chapters deal with more specialized aspects of the subject: the work of Candelas, de la Ossa, Greene, and Parkes, based on the fact that under the mirror symmetry hypothesis, the variation of Hodge structure of a Calabi-Yau threefold determines the Gromov-Witten invariants of its mirror; Batyrev's construction, which exhibits the mirror symmetry phenomenon between hypersurfaces of toric Fano varieties, after a combinatorial classification of the latter; the mathematical construction of the Gromov-Witten potential, and the proof of its crucial property (that it satisfies the WDVV equation), which makes it possible to construct a flat connection underlying a variation of Hodge structure in the Calabi-Yau case. The book concludes with the first "naive" Givental computation, which is a mysterious mathematical justification of the computation of Candelas, et al.
