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Analysis and Algebra on Differentiable Manifolds

2012-12-30 Mathematics
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Release : 2012-12-30
Genre : Mathematics
Kind : eBook
Book Rating : 525/5 ( reviews)

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Book Synopsis Analysis and Algebra on Differentiable Manifolds by : Pedro M. Gadea

Download or read book Analysis and Algebra on Differentiable Manifolds written by Pedro M. Gadea. This book was released on 2012-12-30. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers

2009-12-12 Mathematics
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Release : 2009-12-12
Genre : Mathematics
Kind : eBook
Book Rating : 648/5 ( reviews)

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Book Synopsis Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers by : P.M. Gadea

Download or read book Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers written by P.M. Gadea. This book was released on 2009-12-12. Available in PDF, EPUB and Kindle. Book excerpt: A famous Swiss professor gave a student’s course in Basel on Riemann surfaces. After a couple of lectures, a student asked him, “Professor, you have as yet not given an exact de nition of a Riemann surface.” The professor answered, “With Riemann surfaces, the main thing is to UNDERSTAND them, not to de ne them.” The student’s objection was reasonable. From a formal viewpoint, it is of course necessary to start as soon as possible with strict de nitions, but the professor’s - swer also has a substantial background. The pure de nition of a Riemann surface— as a complex 1-dimensional complex analytic manifold—contributes little to a true understanding. It takes a long time to really be familiar with what a Riemann s- face is. This example is typical for the objects of global analysis—manifolds with str- tures. There are complex concrete de nitions but these do not automatically explain what they really are, what we can do with them, which operations they really admit, how rigid they are. Hence, there arises the natural question—how to attain a deeper understanding? One well-known way to gain an understanding is through underpinning the d- nitions, theorems and constructions with hierarchies of examples, counterexamples and exercises. Their choice, construction and logical order is for any teacher in global analysis an interesting, important and fun creating task.

Analysis and Algebra on Differentiable Manifolds

2009-12-09 Mathematics
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Release : 2009-12-09
Genre : Mathematics
Kind : eBook
Book Rating : 639/5 ( reviews)

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Book Synopsis Analysis and Algebra on Differentiable Manifolds by : P.M. Gadea

Download or read book Analysis and Algebra on Differentiable Manifolds written by P.M. Gadea. This book was released on 2009-12-09. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 375 completely solved exercises on differentiable manifolds, Lie groups, fibre bundles, and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. It is the first book consisting of completely solved problems on differentiable manifolds, and therefore will be a complement to the books on theory. A 42-page formulary is included which will be useful as an aide-mémoire, especially for teachers and researchers on these topics. The book includes 50 figures. Audience: The book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics, and some branches of engineering.

Problems and Proofs in Numbers and Algebra

2015-02-09 Mathematics
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Release : 2015-02-09
Genre : Mathematics
Kind : eBook
Book Rating : 278/5 ( reviews)

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Book Synopsis Problems and Proofs in Numbers and Algebra by : Richard S. Millman

Download or read book Problems and Proofs in Numbers and Algebra written by Richard S. Millman. This book was released on 2015-02-09. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.

An Introduction to Manifolds

2010-10-05 Mathematics
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Release : 2010-10-05
Genre : Mathematics
Kind : eBook
Book Rating : 008/5 ( reviews)

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Book Synopsis An Introduction to Manifolds by : Loring W. Tu

Download or read book An Introduction to Manifolds written by Loring W. Tu. This book was released on 2010-10-05. Available in PDF, EPUB and Kindle. Book excerpt: 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'.

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