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Topology of Surfaces
" . . . that famous pedagogical method whereby one begins with the general and proceeds to the particular only after the student is too confused to understand even that anymore. " Michael Spivak This text was written as an antidote to topology courses such as Spivak It is meant to provide the student with an experience in geomet describes. ric topology. Traditionally, the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature, providing quick access to current research, but not developing any intuition o...
Why Knot?
Colin Adams, well-known for his advanced research in topology and knot theory, is the author of this exciting new book that brings his findings and his passion for the subject to a more general audience. This beautifully illustrated comic book is appropriate for many mathematics courses at the undergraduate level such as liberal arts math, and topology. Additionally, the book could easily challenge high school students in math clubs or honors math courses and is perfect for the lay math enthusiast. Each copy of Why Knot? is packaged with a plastic manipulative called the Tangle R. Adams uses the Tangle because "you can open it up, tie it in a knot and then close it up again." The Tangle is the ultimate tool for knot theory because knots are defined in mathematics as being closed on a loop. Readers use the Tangle to complete the experiments throughout the brief volume. Adams also presents a illustrative and engaging history of knot theory from its early role in chemistry to modern applications such as DNA research, dynamical systems, and fluid mechanics. Real math, unreal fun!
Foundations of Hyperbolic Manifolds
This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete refl...
R.S. Thomas
Published to mark the centenary of the sometime ‘ogre of Wales’, this volume (by the executor of his unpublished literary estate) deals with the idées fixes that serially possessed his fiercely intense imagination: Iago Prytherch, Wales, his family, and of course a vexingly elusive Deity. Here, these familiar obsessions are set in several unusual contexts that bring his poetry into startling new relief: his war poetry is considered alongside his early poetry’s relationship to English topographical tradition; comparisons with Borges and Levertov underline the international dimensions of his concerns; the intriguing ‘secret code’ of some of his Welsh-language references is cracked; and his painting-poems (including several hitherto unpublished) are moved centre stage from the peripheries to which they’ve been routinely relegated.
Lumen Naturae
Exploring common themes in modern art, mathematics, and science, including the concept of space, the notion of randomness, and the shape of the cosmos. This is a book about art—and a book about mathematics and physics. In Lumen Naturae (the title refers to a purely immanent, non-supernatural form of enlightenment), mathematical physicist Matilde Marcolli explores common themes in modern art and modern science—the concept of space, the notion of randomness, the shape of the cosmos, and other puzzles of the universe—while mapping convergences with the work of such artists as Paul Cezanne, Mark Rothko, Sol LeWitt, and Lee Krasner. Her account, focusing on questions she has investigated in...
Women, Identity and Religion in Wales
It is a study of the relationship between identity and religion in women’s lives in Wales today. It will help the reader have a better and more comprehensive understanding of the religious context in Wales to the present day. It will introduce the reader to theological and religious themes as well as reflections on identity in the work of several key female Welsh writers – Menna Elfyn, Jasmine Donahaye, Jam Morris, Charlotte Williams and Mererid Hopwood. It will help the reader to engage with issues of Welsh identity and religion and gain insight into challenges facing the churches today and engage with the lived experience of women in Wales.
Aesthetics of Interdisciplinarity: Art and Mathematics
This anthology fosters an interdisciplinary dialogue between the mathematical and artistic approaches in the field where mathematical and artistic thinking and practice merge. The articles included highlight the most significant current ideas and phenomena, providing a multifaceted and extensive snapshot of the field and indicating how interdisciplinary approaches are applied in the research of various cultural and artistic phenomena. The discussions are related, for example, to the fields of aesthetics, anthropology, art history, art theory, artistic practice, cultural studies, ethno-mathematics, geometry, mathematics, new physics, philosophy, physics, study of visual illusions, and symmetry studies. Further, the book introduces a new concept: the interdisciplinary aesthetics of mathematical art, which the editors use to explain the manifold nature of the aesthetic principles intertwined in these discussions.
Topology Now!
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
Geometry and Symmetry
This new book for mathematics and mathematics education majors helps students gain an appreciation of geometry and its importance in the history and development of mathematics. The material is presented in three parts. The first is devoted to a rigorous introduction of Euclidean geometry, the second covers various noneuclidean geometries, and the last part delves into symmetry and polyhedra. Historical contexts accompany each topic. Exercises and activities are interwoven with the text to enable the students to explore geometry. Some of the activities take advantage of geometric software so students - in particular, future teachers - gain a better understanding of its capabilities. Others explore the construction of simple models or use manipulatives allowing students to experience the hands-on, creative side of mathematics. While this text contains a rigorous mathematical presentation, key design features and activities allow it to be used successfully in mathematics for teachers courses as well.
Foundations of Hyperbolic Manifolds
This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.
