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Author: Loring W. Tu
Publisher: Springer Science & Business Media
ISBN: 1441974008
Category : Mathematics
Languages : en
Pages : 426
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Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author: Loring W. Tu
Publisher: Springer Science & Business Media
ISBN: 1441974008
Category : Mathematics
Languages : en
Pages : 426
Get Book Here
Book Description
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author: Chris Maynard
Publisher: Simon and Schuster
ISBN: 1416598170
Category : Cooking
Languages : en
Pages : 162
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Book Description
Giving new meaning to the term "fast food" Rest-stop grade F meat patty? Nah. Nuggets of reconstituted poultry bits? Pass. Deep-fried fish discus? No, really, thanks all the same. It's time to bid farewell to the roadside meal as you know it. Nearly twenty years ago, Chris Maynard and Bill Scheller opened the world's eyes to the beautym of car-engine gastronomy in the original Manifold Destiny. And now that another generation of both drivers and eaters has emerged, the cult classic is due for an overhaul. In this shiny, spanking-new edition, learn how to make s'mores in your Scion, poach fish in your Pontiac, even bust out a gourmet snack from under the hood of your Escalade. With step-by-step diagrams, crowd-pleasing recipes, and thorough instructions, now you can turn your car into a kitchen without ever crossing any golden arches. Hilarious, bizarre, and ultimately (seriously!) useful, Manifold Destiny is and always will be an unparalleled original. So, slap a ham steak under the hood of your car, hit the gas, and drive until you reach delicious -- which is in approximately fifty miles, depending on traffic.
Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 0387217525
Category : Mathematics
Languages : en
Pages : 646
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Book Description
Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Author: Stephen Baxter
Publisher: Del Rey
ISBN: 0345475585
Category : Fiction
Languages : en
Pages : 649
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Book Description
“As always, [Stephen] Baxter plays with space and time with consummate skill. . . . He continues to be one of the leading writers of hard science fiction, and one of the most thought-provoking as well.”—Science Fiction Chronicle The year is 2020. Fueled by an insatiable curiosity, Reid Malenfant ventures to the far edge of the solar system, where he discovers a strange artifact left behind by an alien civilization: A gateway that functions as a kind of quantum transporter, allowing virtually instantaneous travel over the vast distances of interstellar space. What lies on the other side of the gateway? Malenfant decides to find out. Yet he will soon be faced with an impossible choice that will push him beyond terror, beyond sanity, beyond humanity itself. Meanwhile on Earth the Japanese scientist Nemoto fears her worst nightmares are coming true. Startling discoveries reveal that the Moon, Venus, even Mars once thrived with life—life that was snuffed out not just once but many times, in cycles of birth and destruction. And the next chilling cycle is set to begin again . . . “When the travel bug bites and usual planets don’t excite, perhaps it’s time to burst the bounds of this old solar system and really see the sights. . . . Baxter’s expansive new novel is just the ticket.”—The Washington Times “Breathtaking in its originality and scope.”—The Washington Post
Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 038722727X
Category : Mathematics
Languages : en
Pages : 395
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Book Description
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Author: Vicente Cortés
Publisher: American Mathematical Soc.
ISBN: 0821821113
Category : Mathematics
Languages : en
Pages : 79
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Book Description
Let $V = {\mathbb R}^{p,q}$ be the pseudo-Euclidean vector space of signature $(p,q)$, $p\ge 3$ and $W$ a module over the even Clifford algebra $C\! \ell^0 (V)$. A homogeneous quaternionic manifold $(M,Q)$ is constructed for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \wedge^2 W \rightarrow V$. If the skew symmetric vector valued bilinear form $\Pi$ is nondegenerate then $(M,Q)$ is endowed with a canonical pseudo-Riemannian metric $g$ such that $(M,Q,g)$ is a homogeneous quaternionic pseudo-Kahler manifold. If the metric $g$ is positive definite, i.e. a Riemannian metric, then the quaternionic Kahler manifold $(M,Q,g)$ is shown to admit a simply transitive solvable group of automorphisms. In this special case ($p=3$) we recover all the known homogeneous quaternionic Kahler manifolds of negative scalar curvature (Alekseevsky spaces) in a unified and direct way. If $p>3$ then $M$ does not admit any transitive action of a solvable Lie group and we obtain new families of quaternionic pseudo-Kahler manifolds. Then it is shown that for $q = 0$ the noncompact quaternionic manifold $(M,Q)$ can be endowed with a Riemannian metric $h$ such that $(M,Q,h)$ is a homogeneous quaternionic Hermitian manifold, which does not admit any transitive solvable group of isometries if $p>3$. The twistor bundle $Z \rightarrow M$ and the canonical ${\mathrm SO}(3)$-principal bundle $S \rightarrow M$ associated to the quaternionic manifold $(M,Q)$ are shown to be homogeneous under the automorphism group of the base. More specifically, the twistor space is a homogeneous complex manifold carrying an invariant holomorphic distribution $\mathcal D$ of complex codimension one, which is a complex contact structure if and only if $\Pi$ is nondegenerate. Moreover, an equivariant open holomorphic immersion $Z \rightarrow \bar{Z}$ into a homogeneous complex manifold $\bar{Z}$ of complex algebraic group is constructed. Finally, the construction is shown to have a natural mirror in the category of supermanifolds. In fact, for any $\mathfrak{spin}(V)$-equivariant linear map $\Pi : \vee^2 W \rightarrow V$ a homogeneous quaternionic supermanifold $(M,Q)$ is constructed and, moreover, a homogeneous quaternionic pseudo-Kahler supermanifold $(M,Q,g)$ if the symmetric vector valued bilinear form $\Pi$ is nondegenerate.
Author: Stephen Baxter
Publisher: Del Rey
ISBN: 0345475577
Category : Fiction
Languages : en
Pages : 622
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Book Description
“Reading Manifold: Time is like sending your mind to the gym for a brisk workout. If you don’t feel both exhausted and exhilirated when you’re done, you haven’t been working hard enough.”—The New York Times Book Review The year is 2010. More than a century of ecological damage, industrial and technological expansion, and unchecked population growth has left the Earth on the brink of devastation. As the world’s governments turn inward, one man dares to envision a bolder, brighter future. That man, Reid Malenfant, has a very different solution to the problems plaguing the planet: the exploration and colonization of space. Now Malenfant gambles the very existence of time on a single desperate throw of the dice. Battling national sabotage and international outcry, as apocalyptic riots sweep the globe, he builds a spacecraft and launches it into deep space. The odds are a trillion to one against him. Or are they? “A staggering novel! If you ever thought you understood time, you’ll be quickly disillusioned when you read Manifold: Time.”—Sir Arthur C. Clarke
Author:
Publisher: Delene Kvasnicka
ISBN:
Category :
Languages : en
Pages : 686
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Book Description
Author: Robert Messer
Publisher: American Mathematical Soc.
ISBN: 1470447819
Category : Mathematics
Languages : en
Pages : 254
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Book Description
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.
Author: Stephen Baxter
Publisher: HarperCollins UK
ISBN: 0007401140
Category : Fiction
Languages : en
Pages : 409
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Book Description
2015: Astronaut Reid Malenfant is flying over the African continent, intent on examining a mysterious glowing construct in Earth’s orbit.
